Children moved from microscopes to medicinal plants, then on to seaweed science. The people running the stalls came from different scientific backgrounds, but nobody seemed particularly interested in protecting the boundaries of their subject.

One moment that stuck with me was when a child asked a question and the scientist responded with, “I know a little bit about that, but you should ask that person over there.”

That answer stayed with me. There was no embarrassment in admitting that his knowledge had limits. He simply recognised that somebody else was better placed to answer the next question. I began to wonder whether educational research could do more of the same.

An Academic Archipelago: Why One Lens Is Not Enough

Research into learning can feel like an archipelago. Like a group of islands, each with its own language, traditions and preferred methods.

Cognitive scientists, neuroscientists and behaviour scientists are often looking at the same students and worrying about similar problems. Yet they may describe those problems differently, collect different kinds of evidence and work at different levels of explanation.

Sometimes, they appear to be arguing about completely different things. Sometimes, they are describing related aspects of the same classroom problem. This distinction matters.

Here in Australia, the phrase “science of learning” is often associated with guidance that draws heavily on cognitive science. Documents from organisations and systems such as AERO, the NSW Department of Education, the Victorian Department of Education, Melbourne Archdiocese Catholic Schools and Catholic Education Archdiocese of Canberra and Goulburn have made important contributions to teacher understanding.

Their focus on memory, attention, prior knowledge and cognitive load is valuable. As John Sweller (2017) argues:

This article is not a criticism of those organisations or cognitive science, but that collectively we need to understand that knowing about cognitive architecture is not the whole story. It was nice to hear, Dr. acknowledge this at ResearchEd, Canberra.

If we rely on one disciplinary lens, we risk overlooking the biological conditions that affect learning and the environmental arrangements that influence what students actually do. Cognitive science can help us understand the demands a task places on the mind. Neuroscience describes the biological systems in which that processing occurs. Behavioural science can help us examine the conditions under which students practise, respond and improve.

The phrase “science of learning” should not become a label for one field. Teachers need explanations that can speak to one another, even when the researchers behind them do not always do so.

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My Own Journey Through The Disciplines

I came to research on learning through cognitive science and vividly remember reading that learning involves a change in long-term memory. It helped me understand why prior knowledge matters, why working memory places limits on instruction and why students cannot be expected to think critically about information they have not yet learned.

That framework changed the way I looked at how I teach. I became more attentive to what students already knew, how much new information I was presenting and whether a task contained too many unfamiliar elements.

Behavioural science gradually became just as important to me, although for a different reason. It gave me some observational “look-fors” when I am in action in front of a class.

When a lesson is not working, it encourages questions that are difficult to ignore. What exactly are students being asked to do? Have they been taught the component skills (subskills)? How many chances have they had to respond? Is the task too hard? What happens after a correct answer, an incorrect answer or no answer at all?

Neuroscience is the field I know least well. Even so, listening to and reading the work of people such as Jared Cooney Horvath, Daniel Ansari and Stanislas Dehaene has made it difficult to ignore the value the field can bring.

I am not suggesting that the three fields merge into one. They should not. Their differences are useful. The challenge is learning how to move between them without pretending that one can answer every question.

Cognitive Science: What Happens In The Mind?

In “Why Don’t Students Like School?”, talks about how, “Memory is the residue of thought.

A student can look as though they are paying attention and still fail to learn what we have taught. They might be listening, copying notes and watching the board, but if the information is not connected to what they already know, then learning hasn’t happened. Cognitive science gives us a language for thinking about this gap between being present in a lesson and actually learning from it.

Working memory is severely limited. Cowan (2001) proposed that people can hold around four chunks of information under some conditions, although the amount depends on factors such as familiarity, complexity and distraction.

This is one reason sequencing matters. It is also one reason prior knowledge matters. Knowledge in long-term memory does more than provide facts for a quiz. It helps students recognise patterns, interpret new information and hold ideas together while they are thinking.

A student who knows very little about a topic has to treat more of the lesson as new. An experienced student can draw on existing schemas and devote more attention to the unfamiliar part (Sweller, et al., 1998).

Long-term memory provides a vast store of facts, concepts and procedures. As students gain knowledge and practise important skills, information becomes more connected and easier to retrieve. What initially requires considerable effort can become more efficient and less demanding on our working memory (Willingham, 2006).

This is why knowledge matters. It does not merely provide content for recall. It changes what a student can notice, understand and think about.

Why Useful Learning Can Feel Difficult

The most effective learning strategies do not always feel easy at the time. Retrieval practice, spacing and interleaving can make initial performance less comfortable while improving long-term retention (Bjork & Bjork, 2020; Roediger & Butler, 2011; Carpenter et al., 2022).

A student who rereads a page may feel fluent because the material looks familiar. A student who closes the book and tries to explain the idea may feel less confident. Yet that effortful attempt to retrieve the information may produce more durable learning.

The difficulty, however, has to be manageable. Desirable difficulties is not the same as confusion. Students need enough prior knowledge and support to attempt the task successfully.

Worked examples can be particularly useful for novices. Showing a fully solved problem alongside a minimally different problem can help students focus on the structure of the solution rather than wasting limited working-memory capacity trying to guess what to do next (Atkinson et al., 2000).

The Limits Of Cognitive Science

Cognitive science can help us understand memory and mental processing, but it does not answer every classroom question. Even cognitive scientist, Dr. Hendrick has recognised the limitations of the cognitive science research in his article, Retconning the Curriculum. A strategy that works under controlled conditions does not mean it will instantly transfer when faced with the complexities of a classroom.

While it provides an excellent blueprint of how information is processed, cognitive psychology alone cannot tell us exactly how to engineer the physical environment, sequence a concept, or manage the complex behavioural dynamics when a room full of teenagers disengages. For that, we need other questions.

Neuroscience: What Conditions Make Learning Possible?

Cognitive science asks what a learner can hold, connect and retrieve. Neuroscience reminds us that these processes take place in a developing biological system.

Attention, stress, sleep and development all affect how ready a student is to learn. They also affect what happens after the lesson, when new knowledge needs to settle and connect with what is already known.

As Stanislas Dehaene, beautifully writes in How We Learn:

The brain isn’t a blank slate or a finished product. It changes through an ongoing interaction between biology and the social and cultural world (Ansari, 2012; Jolles & Jolles, 2021).

Conditions That Support Learning

Experience leaves a biological trace. Language, relationships, practice and instruction all influence what the brain becomes better at doing (Dehaene et al., 2015). However, teachers are not literally ‘brain sculptors’. That phrase gives classroom instruction more control than it has. A more useful claim is that teachers help create the conditions in which the brain can change (Bowers, 2016).

Dehaene (2020) describes four broad conditions that support learning:

• Attention: relevant information needs to be selected and prioritised.

• Active engagement: learners need to make predictions, attempt solutions and connect new information with what they already know.

• Error feedback: students need information that helps them compare their expectations with what actually happened.

• Consolidation: learning needs time to stabilise, with sleep playing an important role.

These ideas overlap with familiar classroom practices. A teacher might gain students’ attention before presenting an important explanation, ask them to predict an answer, provide feedback after an attempt and revisit the content later.

Neuroscience does not replace the teaching strategy. It helps explain why the strategy may be useful.

Development Matters

Brain maturation does not end in childhood. The systems involved in cognitive control, emotional regulation and social behaviour continue developing through adolescence and into emerging adulthood (Steinberg, 2019). This does not mean lowering expectations or treating adolescent behaviour as biologically inevitable. It means recognising that independence and self-regulation are developed rather than assumed.

A student who forgets equipment, loses focus or reacts emotionally may still need clear expectations and consistent consequences. They may also need explicit teaching, routines and scaffolding that support the skills we want them to develop.

The Limits Of Neuroscience

The distance from an fMRI scanner to the classroom is vast. Neuroscience can tell us that learning changes the brain, but it cannot by itself tell us how to teach.

As Daniel Willingham (2009) pointed out, neuroscientists and teachers are trying to solve entirely different problems. A neuroscientist might study a single, isolated cognitive function in a perfectly quiet, highly controlled laboratory. Teachers, on the other hand, have to manage the messy, interacting emotional and social realities of thirty students on a Friday afternoon.

There is also a fundamental logic problem when we try to force brain science into the classroom. Neuroscience describes what is happening biologically, but education is an artificial environment driven by what ought to happen instructionally. You cannot just take a biological fact and automatically turn it into a lesson plan.

Because of this massive gap in complexity, pointing to a brain scan to “prove” a teaching method works is a bit of a trap. As Jeffrey Bowers (2016) argues, all learning changes the brain. If a student learns something, their biology has undeniably changed, but just because a classroom activity lights up an imaging scan does not mean it is actually a good use of instructional time.

When we ignore this gap, complex science gets rushed into schools by commercial vendors and mutates into toxic “neuromyths” like learning styles theory or Brain Gym. For teachers, brain science only becomes meaningful when it helps us make better, practical decisions about what our students can actually understand, retain and do.

Behavioural Science: What Does Learning Look Like In Action?

Behavioural science asks the question: What does learning look like in the classroom?

Applied behaviour analysis (ABA) sits within the broader field of behavioural science. It examines how environmental conditions influence observable behaviour, then uses that information to make teaching more effective.

In a classroom, this might mean looking closely at what happens before and after a student responds. What instructions were given? Was the task clear? Did the student have the skills needed to begin? What happened when they attempted the work? Did they receive useful feedback, attention or an opportunity to try again?

These questions shift the focus away from describing a student as “unmotivated” or “disengaged” and towards identifying what may be maintaining the pattern. If a student regularly avoids writing, for example, the pattern may be associated with task difficulty, unclear expectations, limited fluency or the removal of demanding work after avoidance. These possibilities need to be tested rather than assumed.

ABA is therefore not a separate theory of learning competing with cognitive science or neuroscience. It provides a way of observing behaviour, measuring change and adjusting the conditions around instruction. Cognitive science may help explain why a task is overwhelming. Neuroscience may remind us that attention and self-regulation are affected by development, stress and fatigue. Behavioural science helps us examine what the student does next, and which features of the environment make a more successful response more likely.

Used carefully, this creates a practical feedback loop: observe, measure, adjust and observe again. The purpose is not to reduce students to their behaviour. It is to make classroom decisions more precise, while remembering that observable behaviour is only one part of a learner’s experience.

When Students Struggle

When a student struggles, ask what stage of learning are they at. Are they still trying to acquire the skill? Or are they accurate, but painfully slow?

A student who is still acquiring a skill may need modelling, prompts and immediate feedback. A student who is accurate, but slow may need less explanation and more carefully designed practice (Haring & Eaton, 1978).

Accuracy Is Not Always Enough

In many foundational skills, accuracy needs to be accompanied by sufficient fluency, the ability to respond accurately, efficiently and consistently under ordinary classroom conditions (Binder, 1996). Without sufficient fluency, a basic skill can consume so much attention that there is little left for the more complex task that follows.

The MESsAGe framework describes fluent performance as more likely to be:

• Maintained over time

• performed with Endurance

• Stable despite distractions

• available for Application

• used in Generative problem-solving (Johnson & Street, 2012).

The Limits of Behaviour Science

Behavioural science has a public-relations problem in education due to individuals either using the science unethically or a misunderstanding as to what it actually is. It is often reduced to a caricature of rewards, compliance and robotic instruction. That caricature misses the broader point. Behavioural science can help teachers design environments in which students acquire academic, social and problem-solving skills (Johnson & Layng, 1996). I’ve written about how we can, “Engineer the Aha Moment” here.

However, behavioural measures still require interpretation. A student’s performance is observable, but the reasons for that performance may not be. Behavioural data can tell us what happened. It does not always tell us why.

The strongest approach is therefore neither to dismiss behavioural science nor to treat it as a complete theory of learning. It is one part of a larger account.

What Each Discipline Helps Us See

In this next part, I describe what happens through the three different lenses for an Open-Ended Maths Problem for two different students.

Student A

• The Situation: The student has not yet developed fluency with the problem-solving tool or component skills.

• Result: The student tears up their worksheet as soon as they look at it.

Cognitive Science: The student is unable to make connections to relevant schema within their long-term memory. Without foundational knowledge readily available, the problem overwhelms their working memory placing too much demand on working memory, including unnecessary extraneous load.

Neuroscience: Due to a history of failed learning experiences in maths, a biological stress response may be triggered (such as a spike in cortisol). These emotional, respondent behaviours are involuntarily elicited by stimuli in the environment (in this case, the maths worksheet) based on painful past encounters.

Behavioural Science: A functional analysis examines the environmental events occurring immediately before the behaviour. Here, the antecedent was insufficient because the teacher did not provide explicit instructions on what to do. The tearing of the paper is an observable response to an environment that lacks the necessary instructional support.

Student 2

• The Situation: The student has already been taught the necessary component skills through explicit instruction, practice and feedback. They can read the problem fluently, retrieve essential maths facts, recognise familiar problem structures and use the problem-solving strategy independently.

• The Result: The student reads the problem, identifies the relevant information, represents it mathematically and selects an appropriate operation. They check their work and continue without needing a prompt.

Cognitive science: The student’s working memory is available for mathematical reasoning because the component skills have become fluent. Reading the problem, retrieving basic facts and applying the problem-solving routine require less conscious effort. Extraneous cognitive load has also been reduced. Rather than asking students to manage several unfamiliar demands at once, instruction introduced the relevant knowledge and skills one at a time, with each element practised before the next was added. This allows the student to concentrate on the structure of the problem rather than trying to work out how to read it, what the vocabulary means, which operation to use and how to organise the solution all at once.

Neuroscience: The student’s performance reflects biological changes that have developed gradually through repeated learning experiences. Networks involved in reading, language, attention and mathematical processing have been strengthened and coordinated through practice. With repetition and consolidation, the neural activity supporting these skills becomes more efficient, so previously effortful processes can be carried out with less conscious attention. The student is not displaying the result of a single “brain-based” teaching technique. Their response reflects the cumulative effects of instruction, practice, feedback, rest and time on a developing nervous system.

Behavioural science: The relevant antecedents are already in place:

• The student has been given a clear problem

• Has learned the component skills to fluency

• Has access to a problem-solving tool they can use independently.

A prompt is not needed because the tool and its component skills have already been taught to the point where the student can use them without additional assistance. The student’s reading, representation, strategy selection and persistence are the observable products of a well-established learning history. Previous practice and feedback have made these behaviours more likely. While the student’s success, feedback and experience of progress help maintain these behaviours.

Building Bridges

My hope is that these academic fields can build more bridges between one another. Bridging the gap between research and practice is hard enough without asking teachers to navigate isolated islands of information to find what they need.

That was the quiet lesson of Science in the Scrub. The scientists did not need to pretend their disciplines were the same. They understood that no one person could answer every question. They shared the patch of grass, compared what they could see and stayed within the limits of their expertise.

We do not need one discipline to win. Teachers need better explanations, better measures and better ways to decide what to do next. That requires cognitive science, neuroscience and behavioural science to connect without pretending they are interchangeable.

The goal is not to create a grand unified theory of learning. It is more practical than that. We need better explanations, better measures and better teaching. And we need the humility to recognise that each field sees only part of the landscape.

In practice, this means slowing down before labelling a student as lazy, anxious, disengaged or incapable. Ask a better question. What does the student know? What might be affecting their readiness to learn? What exactly are they doing, and what happens next? The answers will not always come from the same field. That is precisely why teachers need more than one lens.

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References

Ansari, D. (2012). Culture and education: new frontiers in brain plasticity. Trends in Cognitive Sciences, 16(2), 93–95.

Atkinson, R.K., Derry, S.J., Renkl, A. and Wortham, D., 2000. Learning from examples: Instructional principles from the worked examples research. Review of Educational Research, 70(2), pp. 181–214.

Binder, C., 1996. Behavioral fluency: Evolution of a new paradigm. The Behavior Analyst, 19(2), pp. 163–197. Available at: https://doi.org/10.1007/BF03393163

Bjork, R. A., & Bjork, E. L. (2020). Desirable difficulties in theory and practice. Journal of Applied research in Memory and Cognition, 9(4), 475.

Booth, J.L., Lange, K.E., Koedinger, K.R. and Newton, K.J., 2013. Using example problems to improve student learning in algebra: Differentiating between correct and incorrect examples. Learning and Instruction, 25, pp. 24–34

Cowan, N. (2001). The magical number 4 in short-term memory: A reconsideration of mental storage capacity. Behavioral and Brain Sciences, 24, pp. 87–114.

Dehaene, S. (2020). How We Learn: The New Science of Education and the Brain. Penguin Books.

Dehaene, S., Cohen, L., Morais, J. and Kolinsky, R., 2015. Illiterate to literate: Behavioural and cerebral changes induced by reading acquisition. Nature Reviews Neuroscience, 16(4), pp. 234–244

Haring, N. G., & Eaton, M. D. (1978). Systematic instructional procedures: An instructional hierarchy. In N. G. Haring, T. C. Lovitt, M. D. Eaton, & C. L. Hansen (Eds.), The fourth R: Research in the classroom (pp. 23–40). Charles E. Merrill Publishing Company.

Johnson, K. R., & Layng, T. J. (1996). On terms and procedures: Fluency. The Behavior Analyst, 19(2), 281-288.

Johnson, K., & Street, E. M. (2012). From the laboratory to the field and back again Morningside Academy’s 32 years of improving students’ academic performance. The Behavior Analyst Today, 13(1), 20

Jolles, J. and Jolles, D.D., 2021. On neuroeducation: Why and how to improve neuroscientific literacy in educational professionals. Frontiers in Psychology, 12, p. 752151.

Roediger, H. L., & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15, pp. 20–27.

Steinberg, L. (2019). Adolescent brain development and the law. Current Directions in Psychological Science, 28(5), 450–456.

Sweller, J. (2017). Cognitive load theory and instructional design. Cognitive Research: Principles and Implications, 4(1), 1–9.

Sweller, J., van Merriënboer, J. J. G., & Paas, F. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10(3), 251–296.

Willingham, D. T. (2006). How knowledge helps. American Educator, 30(1), pp. 30–37.

Willingham, D. T. (2009). Three problems in the marriage of neuroscience and education. Cortex, 45(4), pp. 544–545.

Listeners will discover why the rise of AI actually makes a teacher’s deep subject knowledge more critical than ever. Haili also breaks down the stark difference between awkward roleplay and highly effective instructional rehearsal. Finally, she explains why true teacher wellbeing is never about cake in the staffroom, but rather sensible systems and genuine professionalism. This is a must-listen for educators seeking practical and research-grounded strategies to drive real improvement.

Resources mentioned:

• Teaching WalkThrus

• Tant, Maddox & Phillipsi - The Science of Learning and Generative AI: A Guide for Secondary Teachers

• Jamie Clark’s one-pager on problems and principles

• Direct Instruction videos

• Rosenshine’s Principles of Instruction

• Coaching for Adaptive Expertise (Upcoming book)

• Doug Lemov - Teach Like a Champion

• Oak National shared resources

• Ochre Education shared resources

• EEF (Education Endowment Foundation) research on implementation and professional development

• AERO (Australian Education Research Organisation) classroom resources

• Resources from subject associations (such as the English Association, Historical Association, Royal Society of Physics and Royal Society of Chemistry)

You can connect with Haili:

Substack: @hailihughes

X / Twitter: @HughesHaili

Bluesky: @hugheshaili.bsky.social

LinkedIn: Haili Hughes

You can connect with Brendan:

Twitter: @learnwithmrlee

Facebook: @learningwithmrlee

Website: learnwithlee.net

About Haili

Dr Haili Hughes is an Associate Professor of Educational Change and Impact at La Trobe University. Her career is dedicated to strengthening the conditions in which educators develop, thrive and remain in the profession. Working at the intersection of research, policy and practice, she focuses on how evidence-informed educational change can be designed and implemented to improve outcomes for teachers and students alike.

Before moving into higher education and system leadership, Haili taught English in the UK state sector for 20 years. She has served as Director of Professional Development across 11 schools in a multi-academy trust and as Professor of Teacher Mentoring and Coaching at Academica University of Applied Sciences. In England, she advised the Department for Education as an ITT Quality Advisor, assessed National Professional Qualifications and served on The Teaching Commission to support national teacher recruitment and retention.

An expert in instructional coaching, teacher mentoring, adult learning and professional agency, Haili is the author of ten education books and a contributor to over 30 edited volumes. At La Trobe, she continues to champion strong, evidence-informed partnerships between schools, universities and systems to foster educational change that is ambitious, humane and sustainable.

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In this episode, you will learn why the MTSS pyramid is actually a map of school resources rather than a tool for sorting students. Stephanie reveals the dangers of the “screen to intervene” trap, explaining why we must evaluate core Tier 1 instruction before pulling kids into intervention groups. We also discuss why expecting teachers to overhaul their practice without structural support ignores the reality that adults go through an acquisition stage of learning too. Get ready to shift your focus from admiring the problem to taking definitive instructional action.

Resources mentioned:

• MTSS for Reading Improvement by Dr Sarah Brown and Dr Stephanie Stollar

• MTSS for Reading Improvement - Free Reproducibles

• Routines for Reading Results (upcoming second edition of Teaching Struggling and At-Risk Readers)

• Effective Universal Instruction book by Bradley C. Niebling, Kimberly Gibbons and Sarah Brown

• StephanieStollarConsulting.com

• System Impact Consulting

You can connect with Sarah:

Linkedin: @sarah-brown-ph-d-9177b516

Website: systemimpactconsulting.com

You can connect with Stephanie:

Twitter/X: @SStollar6

Facebook: @StephanieStollarConsulting

Linkedin: @stephanie-stollar

Website: stephaniestollarconsulting.com

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website:learnwithlee.net

Substack: knowledgeforteachers.substack.com/

About Sarah

Dr. Sarah Brown is a consultant and co-author of the books, Effective Universal Instruction, MTSS for Reading Improvement, and Routines for Reading Results. She empowers schools through her MTSS Data Academy. She’s served in a variety of educational roles, including Bureau Chief leading Special Education and MTSS implementation for Iowa, Special Education Director, Professional Learning Administrator, and School Psychologist. Dr. Brown is passionate about empowering systems to improve outcomes for every learner. She splits her time between the midwest and the southwest and her greatest accomplishment to date is toilet-training her cat, Oliver.

About Stephanie

Stephanie is passionate about using MTSS as the framework for helping all students become skilled readers. She is the co-author of the books MTSS for Reading Improvement, Promoting Effective MTSS Implementation, Reading Assessment Done Right and Routines for Reading Results.

Stephanie is creator of the Reading Science Academy, co-creator of MTSS CollecAve, and serves on the boards of the Evidence Advocacy Center and the International MTSS Association.

Her past roles include Assistant Professor, Vice President of Professional Learning at Acadience Learning, and School Psychologist. Stephanie believes that supporting all educators to have deep knowledge about reading is foundational to high achievement for every student.

Support the Knowledge for Teachers Podcast:

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Resources mentioned:

• Evidence-Based Education (EBE)

• The Great Teaching Toolkit

• The Great Teaching Toolkit: Evidence Review (2020)

• The Great Teacher Toolkit: School Environment and Leadership Evidence Review (2022)

• EEF Teaching and Learning Toolkit (Steve Higgins)

You can connect with Stuart:

Twitter: @profkime

Linkedin: @stuart-kime-ebe

Website: evidencebased.education

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

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About Professor Stuart Kime

For the last 15 years, Stuart Kime has been exploring the Science of Learning from a teacher’s perspective: what it is, what it’s not, and how we can use it to elevate learning. He’s worked as a teacher and school leader in England, a Visiting Professor in Germany, and a policy adviser in the UK government.

These days, he focuses solely on developing powerful, accessible ways to help teachers build their expertise in the things that matter most to students’ learning.

Listeners will discover surprising data from the frontlines of education, including why 81 per cent of children aged two to five are already using the internet. Karen unpacks how to transition from traditional, fear-based warnings to a strength-based curriculum that builds critical thinking. Crucially, you will learn how Life Ed carries the load for time-poor educators, with research revealing that 89 per cent of teachers report significantly improved confidence in embedding wellbeing strategies post-visit.

Tune in for a thoughtful discussion packed with practical, research-grounded insights to help your students truly thrive.

You can connect with Karen:

Linkedin: @karen-robertson-mtc

Website: lifeed.org.au

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website:learnwithlee.net

Substack: knowledgeforteachers.substack.com/

Support the Knowledge for Teachers Podcast:

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In my previous article - The Lost Blueprint of Learning, I walked through the taxonomy developed by Philip Tiemann and Susan Markle (1983). Their central insight is beautifully simple: not all learning tasks belong to the same class. Gaining a precise understanding of how different forms of knowledge are constructed fundamentally changed how I teach, how I co-plan and how I deliver professional learning for other teachers.

Recently, I was supporting a group of Kindergarten/Foundation teachers during a collaborative planning session. They were preparing a subtraction lesson.

The initial unit draft leaped straight into the procedure. The plan was to hand the five-year-olds a collection of counters, tell a brief story and show them how to physically take the blocks away to find how many were left.

I paused and asked the team a question: “Before we show them how to do the action of taking away, do they actually know what subtraction is?”

The initial planning was going to result in the students executing a mechanical routine, a counting algorithm. But to truly set them up for success, we had to start by teaching the concept of subtraction first. Subtraction isn’t just an action, it is a structural mathematical category where a part is separated from a whole. If we jump straight to the procedure of moving counters, students focus entirely on the physical steps of the task rather than learning to discriminate a subtraction scenario from any other mathematical relationship.

The Conceptual Understanding Debate

Dr. has reopened a conversation that matters deeply to how we spend our days in the classroom. In his recent posts on Filling the Pail (Conceptual understanding is a myth and The curse of conceptual understanding), he revisits the persistent question of what we truly mean by ‘conceptual understanding’.

Bill McCallum, writing at , takes a different tack, arguing the term can still guide us if we look closely enough. While they arrive at different conclusions, both are trying to solve the exact same high-stakes classroom puzzle from different angles. Ultimately, they are both chasing a way to ensure that what we teach sticks, transfers and empowers a child to think mathematically.

I share Ashman’s unease with the word “understanding.” As a cognitive label it is hard to observe and harder still to measure. When a student repeats our favourite diagram or explanation, we are often too quick to label that performance as understanding. It might be, but the evidence is thin.

I agree with both impulses regarding transfer, but the missing piece is clarity about the kind of transfer we want. True transfer is not about running a different procedure, rather it is about carrying a structural concept into unfamiliar examples and still recognising the category.

Most of us were never taught to think about instruction through the lens of Tiemann and Markle. I know I was never told about it. Their work sits quietly in the background of the principles of Direct Instruction (DI), behaviour analysis and instructional design. Yet when we adopt their categories, the fog around “understanding” begins to lift.

Introducing their categories here isn’t about using a theoretical weapon to prove anyone wrong or declare a winner in the maths wars. Instead, their work offers a practical bridge. Concepts become teachable. Assessments gain sharper edges. The framework repays the effort it takes to learn it.

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The Hidden Anatomy of a Problem

To see why this distinction matters so early on, we need to turn to the framework developed by Tiemann and Markle (1983). Their work provides the exact toolkit we need to rescue concepts from educational mysticism.

When we teach a student to add two-digit numbers on an empty number line or the order of operations or the standard vertical algorithm, we are teaching a sequence. Tiemann and Markle call this simple cognitive learning. It is choreography. It answers the “how.”

A concept is different. A concept is a mental category, a class of objects, symbols or events that share common, defining characteristics (Layng, 2019). Concept learning has occurred when a student can look at a completely novel, unseen instance and correctly identify whether it belongs in that category or not based on its attributes (Johnson & Bulla, 2021).

Learners demonstrate it when they meet a brand new instance and decide, with confidence, “In or out?” That is discrimination and generalisation working together. If we want conceptual understanding, we want students who can do this even when the surface features keep changing.

Unpacking Ashman’s Example: (3x = 18)

Ashman offers a familiar algebra question:

“If a student sees (3x = 18) and writes (x = 6) what kind of knowledge is that?”

Tiemann and Markle give us a structured answer. Solving (3x = 18) involves three kinds of learning:

1. Paired Associates (Basic Memory): Recognising “3” and “18” and recalling instantly that (18 ÷ 3 = 6) so working memory stays free. If this memory is not automated, their working memory stalls before they even begin.

2. Algorithms (Procedural Sequence): The student executes a step-by-step routine. They look at the expression, determine the operation connecting the number and the variable, apply the inverse operation to both sides and calculate the final value.

3. Concepts (Complex Cognitive Category): This is where true conceptual understanding lives. To solve this equation with actual insight, a student must master the concept of a variable (x) as a placeholder for an unknown value and the concept of the equals sign (=) as a structural state of balance, rather than a command that means ‘find the answer’.

Teach only the routine and students still succeed on (3x = 18). Present (18 = x∙3) or embed the relationship in a story problem and many hesitate. Students who hold the concept recognise the balance regardless of format. That is conceptual transfer.

Defining a Concept: Critical and Variable Attributes

To teach a concept explicitly so that students can navigate these variations, we cannot just recite a textbook definition and hope for the best (Layng, 2019). This is where the structural design of Direct Instruction intersects perfectly with content analysis. In DI, we focus on identifying the generative relations within a content domain to ensure learners can do more with less extensive instruction (Slocum & Rolf, 2021).

We bring this upfront analysis to life by breaking the concept down into its Critical Attributes (the features an instance must have to belong to the category, or ‘must-have’ features) and its Variable Attributes (the features that can change without altering the concept, or ‘can-have’ features) (Tiemann & Markle, 1983; Twyman & Hockman, 2021; Williams et al., 2025).

This plays out across subjects.

Prisms

• The “Must-Haves” (Critical): A 3D solid with two identical (congruent) faces opposite each other, connected by flat parallelograms.

• The “Can-Haves” (Variable): The shape of the base (triangle vs. hexagon), the size (scale), or whether it’s standing up or lying on its side.

• The Test: Show a cylinder. It has the identical opposite faces, but the surface is curved. It’s “out.”

  

Prime Numbers

• The “Must-Haves” (Critical): A whole number greater than 1 with exactly two distinct factors: 1 and itself.

• The “Can-Haves” (Variable): The number of digits, parity, whether it is near an even number, or how “dense” it is compared to other primes.

• The Test: Show the number 1. It has only one factor. It’s “out.” Show the number 9. It’s odd, but it has three factors (1, 3, 9). It’s “out.”

Mammals

• The “Must-Haves” (Critical): Warm-blooded vertebrates that possess hair/fur and mammary glands.

• The “Can-Haves” (Variable): Size, habitat (land vs. water), or means of movement (walking, swimming, or flying).

• The Test: Show a platypus. It lays eggs (a massive variable shift), but it has hair and mammary glands. It’s “in.”

Persuasive Writing

• The “Must-Haves” (Critical): A debatable claim, evidence tied directly to that claim, and language intended to influence an audience.

• The “Can-Haves” (Variable): The tone (angry vs. logical), the length, the format (an essay vs. a tweet), or the publication medium.

• The Test: Show an Instruction Manual. It uses professional language and has a clear goal, but it lacks a debatable claim. It’s “out.”

Students who internalise the concept protect those critical attributes. Remove one and they reject the example. Shift the variables and they stay steady.

The Danger of ‘Proceduralising’ Concepts

This is where good intentions can backfire. The common error in progressive pedagogy is trying to teach a concept by turning the explanation into a mandatory, step-by-step procedure. I call this the ‘proceduralisation’ of concepts. I know this because for much of my career, I’ve been there to!

If you force a student to draw a specific bar model, a rectangle or a fraction wall every single time they solve a problem, you have not taught the concept. You have simply taught a drawing algorithm. The student follows a new mechanical routine: Step 1: Draw a box. Step 2: Cut it into sections. Step 3: Shade the parts. The visual model, which was originally intended to illuminate the concept, shifts into just another mindless sequence to execute.

Direct Instruction avoids this confusion by aiming for faultless communication, structuring lessons so that they communicate one and only one, logical interpretation (Twyman, 2021). True conceptual instruction achieves this by presenting a ‘rational set’ of juxtaposed examples and close-in non-examples (Johnson & Bulla, 2021; Tiemann & Markle, 1983; Twyman & Hockman, 2021).

Following DI’s core sequencing rules, such as the Difference Principle and the Sameness Principle, we can systematically map out the exact boundaries of a concept for our students (Spencer, 2021; Twyman, 2021). We hold variable attributes steady while stripping away one critical attribute at a time to show students exactly where the boundary of the category lies.

Then we vary the variables. We rotate prisms. We shift persuasive writing from a speech to a social media post. We swap mammals from dolphins to bats to platypuses. Students who still see the concept are demonstrating the transfer Ashman and McCallum both want to find. We ensure their understanding is tied to the structural concept, not the specific visual tool we used during Tuesday morning’s lesson.

Locating Concepts in the Instructional Hierarchy

To understand why this matters for daily practice, we can place this structural analysis directly into the Instructional Hierarchy framework developed by Norris Haring and Marie Eaton (1978). This model reminds us that all learning progresses systematically through four distinct stages: Acquisition, Fluency, Generalisation, and Adaptation (Ardoin & Daly, 2007; Daly et al., 1996).

The current educational debate completely scrambles these stages. Progressive practices frequently demand Generalisation or Adaptation that forces students to solve complex word problems or write elaborate explanations before the student has achieved basic accuracy and Fluency with the underlying facts and algorithms. On the flip side, a purely mechanical approach traps students permanently in the Fluency stage of a single, highly specific procedure.

True concept learning bridges the vital gap between Acquisition and Generalisation. When we use a rational set of examples and non-examples, we are explicitly training the student how to generalise the concept to any valid scenario in the real world, while discriminating it from non-examples (Haring, 1988). Once a concept is fully generalised, and the procedural algorithms are fluent, the student naturally reaches the stage of Adaptation. They can apply their knowledge to solve novel, complex mathematical problems because their working memory is protected from collapse (Daly et al., 1996).

Assessing Conceptual Understanding

This brings us back to Greg’s core point: how do we measure this without the test turning into rote mimicry?

We do not test a concept by asking students to define the concept or to reproduce a familiar diagram they saw on the whiteboard. Those are simply verbal or motor algorithms that can be memorised and regurgitated on cue (Tiemann & Markle, 1983).

Ashman rightly questions assessments that value a student’s ability to act out an explanation over their actual mathematical capability. McCallum wants evidence that understanding exists. Both concerns are valid. We can respect them by designing tasks that require students responding to new instances.

If you want to know if a Year 6 student understands prime numbers, you do not ask them to list the primes up to 20. Instead, you hand them an unfamiliar number, such as 51, and ask them to determine if it belongs in the category, requiring them to justify their decision by testing for hidden factors.

Offer a Year 5 student a solid with matching triangular faces and curved sides. The response “Not a prism. The sides must be flat parallelograms” signals the concept is intact.

Ask a Year 8 science class whether a platypus remains a mammal despite laying eggs. Students who cite the critical attributes of warm blood, hair and mammary glands have transferred the concept. In English, hand students an unfamiliar article and ask if it fits the persuasive genre. Those who locate the claim, the evidence and the audience moves are applying the concept, not reciting a checklist.

Moving Beyond the Procedural vs. Conceptual Debate

Unpacking the exact architecture of a concept does more than just settle a debate about procedures. When we equip ourselves with a comprehensive taxonomy of learning, we gain utility that transforms how we plan everyday classroom interactions. The current debate gets stuck in a simplistic binary: procedural versus conceptual. Because of that, teachers frequently select the wrong instructional tools for the job.

Consider how often we try to force ‘conceptual understanding’ onto tasks where it doesn’t belong, such as basic maths facts. A maths fact is a basic memory task, what Tiemann and Markle (1983) call a Paired Associate. The instructional goal here is absolute automaticity, an instant stimulus-response relation (6 x 7 = 42). Yet, educators will often display a complex visual array or an area model at the exact same time they introduce the fact, hoping to anchor it conceptually.

This creates a massive split-attention effect. Instead of building a clean, automated memory association, the teacher inadvertently jams the student’s working memory with an analytical task. Visual arrays are fantastic tools for teaching the concept of multiplication during acquisition, but using them during a fluency drive on maths facts fundamentally misinterprets the category of learning required.

We see the exact opposite mistake when teachers introduce mental strategies. A mental strategy (e.g. choosing whether to round and compensate, jump along an empty number line, or use a double plus one) is supposed to be a Complex Cognitive Strategy (Tiemann & Markle 1983). It is a heuristic for navigating an ill structured problem.

Yet, because the system lacks a precise vocabulary, we routinely ‘proceduralise’ these strategies. We turn them into a rigid, robotic set of steps: Step 1: Look at the units. Step 2: Round to the nearest ten. Step 3: Subtract the difference. The moment we script the strategy into an invariant sequence, we transform it into a Simple Cognitive Algorithm. The student hasn’t learned a strategic problem-solving repertoire at all. They have just memorised a brand new, highly fragile procedure that falls apart the second a problem doesn’t fit the script perfectly.

Moving Forward Together

None of this diminishes the thoughtful critiques and defences that Ashman and McCallum bring to the table. Their writing highlights genuine problems we see every day. Empty rhetoric about understanding and the longing for something richer than rote routines. The Tiemann and Markle framework gives us tools to meet those problems head on. It clarifies what a concept is. It shows us how to teach it. It points to assessments that honour the goal without rewarding mimicry.

Procedural fluency and conceptual understanding are different cognitive architectures. Both matter. Both require instructional designs built for their specific demands. Algorithms flourish with explicit modelling, faded scaffolds and deliberate frequency building to minimise cognitive load (Johnson & Layng, 1992). Concepts flourish with sequences of examples and non-examples that etch the category boundaries in students’ minds (Twyman & Hockman, 2021).

Grounded in instructional design frameworks like Tiemann and Markle alongside the precise sequencing logic of Direct Instruction, we can confidently move past the old, cyclical ideological stalemates. We can define exactly what a concept is, teach it with laser precision and test it with complete objectivity.

If the term “understanding” continues to blur our thinking, we can set it aside and speak directly about concepts, procedures and the behaviours that demonstrate each. Once we do, the debate becomes far less mysterious and the path to better teaching becomes far easier to see.

Next time you introduce a new idea, ask yourself:

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References

• Ardoin, S.P. and Daly, III, E.J., 2007. ‘Close encounters of the instructional kind—How the instructional hierarchy is shaping instructional research 30 years later’, Journal of Behavioral Education, 16(1), pp. 1–6.

• Daly, III, E.J., Lentz, F.E. and Boyer, J., 1996. ‘The instructional hierarchy: A conceptual model for understanding the effective components of reading interventions’, School Psychology Quarterly, 11(4), pp. 369–386.

• Haring, N.G. ed., 1988. Generalization for students with severe handicaps: Strategies and solutions. Seattle: University of Washington Press.

• Haring, N.G. and Eaton, M.D., 1978. ‘Systematic procedures: An instructional hierarchy’, in N.G. Haring, T.C. Lovitt, M.D. Eaton and C.L. Hansen, eds. The fourth R: Research in the classroom. Columbus: Charles E. Merrill Publishing Company, pp. 23–40.

• Johnson, K. and Bulla, A.J., 2021. ‘Creating the components for teaching concepts’, Behavior Analysis in Practice, 14(3), pp. 785–792.

• Johnson, K.R. and Layng, T.V.J., 1992. ‘Breaking the structuralist barrier: Literacy and numeracy with fluency’, American Psychologist, 47(11), pp. 1475–1490.

• Layng, T.V.J., 2019. ‘Tutorial: Understanding concepts: Implications for behavior analysts and educators’, Perspectives on Behavior Science, 42(2), pp. 345–363.

• Markle, S.M., 1991. Designs for instructional designers. Seattle: Morningside Press.

• Slocum, T.A. and Rolf, K.R., 2021. ‘Features of direct instruction: Content analysis’, Behavior Analysis in Practice, 14(3), pp. 775–784.

• Spencer, T.D., 2021. ‘Ten instructional design efforts to help behavior analysts take up the torch of direct instruction’, Behavior Analysis in Practice, 14(3), pp. 816–830.

• Tiemann, P.W. and Markle, S.M., 1983. Analyzing instructional content: A guide to instruction and evaluation. Champaign: Stipes Publishing Company.

• Twyman, J.S., 2021. ‘Faultless communication: The heart and soul of DI’, Perspectives on Behavior Science, 44(2), pp. 225-241.

• Twyman, J.S. and Hockman, A., 2021. ‘You have the big idea, concept, and some examples... Now what?’, Behavior Analysis in Practice, 14(3), pp. 793–804.

• Williams, C.L., St. Peter, C.C., Perone, M., Aguilar, M., Cederberg, B.A., Gregersen, D.J. and Richardson, E.J., 2025. ‘Using must-have and can-have features to improve conceptual learning’, Journal of the Experimental Analysis of Behavior, 124(1), e7003.

Listeners will hear Karina and Russ break down how to spot the hidden “tool skills” that frequently block student progress in reading and mathematics. They challenge common misconceptions about explicit instruction, detailing why the “We Do” phase must be a dynamic, data-driven interaction to build accurate acquisition. Plus, they share how to transition students into fluency building by measuring the rate of correct responses rather than simple percentages.

If you’re keen to delve deeper into the key mechanisms behind the Morningside Model of Generative Instruction and more, then this conversation is essential listening.

Resources mentioned:

• MorningsideAcademy.org

• Ryan O’Donnell’s documentary about Morningside Academy: The Morningside Model of Generative Instruction

• Thomas Gilbert’s Mathetics

• S01E01 – Dr. Russ Fox on building relationships, routines and using reinforcers

• Trina Spencer: Learning How Learning Works Helps Teachers Teach

• Mastery Schools Australia

• Brendan Lee: “Engineering the Aha! When Discovery Learning Actually Works”

• Stocker, K. L., Fox, R. A., Swain, N. R., & Leif, E. S. (2024). Between the lines: Integrating the science of reading and the science of behavior to improve reading outcomes for Australian children. Behavior and Social Issues, 33(1), 504-531.

You can connect with Karina:

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You can connect with Russ:

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You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast:

https://www.patreon.com/KnowledgeforTeachersPodcast

In this episode, I’m joined by Dr. Kent Johnson and Andrew Kieta from Morningside Academy. What makes this conversation so special is that it’s not just theory. Morningside has spent over 40 years in their Seattle lab school proving that these challenges have answers. They have essentially “cracked the code” on the most persistent problems we face in schools.

We dive into their world-renowned model of Generative Instruction, exploring how they use “Precision Teaching” to build effortless fluency and why they group students by achievement rather than age. You’ll learn why a student who is 100% accurate can still be struggling and how a “Money Back Guarantee” on student growth is actually possible when you engineer instruction with this much precision. This is a deep look at how we can stop “praying and spraying” our teaching and start giving every student the success they deserve.

Resources mentioned:

• MorningsideAcademy.org

• Morningside Summer Institute

• John Dewey: How We Think

• Lev Vygotsky

• Michael Maloney

• Israel Goldiamond

• Tom Gilbert - Mathetics

• Ogden Lindsley

• Carl Binder

• Owen White

• Norris Haring

• B.F. Skinner

• Jerome Bruner

• Fred Keller

• Brendan Lee: “Engineering the Aha! When Discovery Learning Actually Works”

• Ryan O’Donnell’s documentary about Morningside Academy: The Morningside Model of Generative Instruction

You can connect with Kent:

Linkedin

You can connect with Andrew:

Linkedin

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast:

https://www.patreon.com/KnowledgeforTeachersPodcast

When a lesson fails to land, our instinct is usually to search for something new. A new activity. A new framework. A new idea that promises to engage students in ways our current approach did not.

Lately, I’ve been wondering if we are actually wasting our time trying to invent new solutions when we would be much better off dusting off the old ones. Perhaps we are suffering from collective amnesia.

Decades ago, some of the most careful thinkers in instructional design laid out remarkably precise blueprints for effective teaching. Brilliant minds like Robert Gagne, Madeline Hunter, Thomas Gilbert, Robert Mager and of course Sigried Engelmann wrote about effective teaching decades ago, yet their work is rarely discussed today.

As Trina Spencer (2021) pointed out, what makes these highly structured instructional models so powerful is that they do not just teach rote facts; they are specifically designed to establish generative repertoires efficiently. They build the exact foundations students need to tackle complex, novel problems.

In this article, I’m going to unpack one of those great lost treasures. It comes from a 1983 book called, Analyzing Instructional Content: A Guide to Instruction and Evaluation by Phillip W. Tiemann and Susan M. Markle, and it might just change the way you look at every lesson you teach.

Last year, Dr. Russ Fox nonchalantly popped an original copy of the book in front of me and I’ve been obsessed with it ever since. I’ve only been able to get access to an electronic copy of the book on Internet Archives (heads up, it’s not a simple read).

The Problem

For years, I went into lessons hoping that what I had planned would land. My lesson preparation would be based on the content that I was teaching, but lacked purpose behind how I was going to teach it. If a lesson failed, I would blame it on a lack of engagement, without having an understanding of the fact that it may have had more to do with my poorly engineered lesson structure.

In education, not many people think about how we might need to teach different types of learning differently. We just think if it's something new we need to use explicit instruction (well, that’s what I’ve always thought). We treat a spelling rule, a historical fact and a complex maths problem like they require the exact same instructional moves. They don’t.

The Emotional Underpinning

If you look at Tiemann and Markle’s original taxonomy (below), they don’t just divide learning into cognitive and physical tasks. They argue that there is a foundational layer sitting beneath every single lesson we teach: Emotional Learning.

Every time a student is in your classroom, emotional learning is taking place. They are not just learning how to solve a fraction or write a sentence, but they are learning whether to feel curious, confident, frustrated or fearful about the subject. Tiemann and Markle point out that this isn’t just a byproduct of learning, rather it is an active, learned response. A student who happily volunteers in music class might shake with nerves when called upon in history.

Why does this matter for instructional design? Because when we mismatch our teaching tactics to the type of learning required—when we ask a student to “discover” a complex strategy without first building their factual fluency, or drill them on a concept they should be analysing—we breed frustration (this is why moments of genuine insight must be engineered rather than hoped for). We inadvertently cause students to learn avoidance behaviours. But when we align the instructional vehicle perfectly with the cognitive architecture of the task, the friction disappears.

Types of Learning

Tiemann and Markle mapped out the different types of learning in the diagram below. It is incredibly comprehensive, but for the sake of making this as practical as possible for the classroom, I have distilled it down to what I feel are its core components (with apologies to Tiemann and Markle, hopefully they aren’t turning in their graves).

The Types of Learning that I will unpack in this article are:

1. Psychomotor

2. Simple Cognitive (Facts and Procedures)

3. Complex Cognitive (Concepts, Principles/Rules and Strategies)

*And no, we are not talking about “Learning Styles” (Visual, Auditory, Kinesthetic). Those are a myth. We are talking about the Types of Learning.

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1. Psychomotor (The Physical Execution)

“The attainment of complex cognitive learning can only be demonstrated through psychomotor responses which students must learn first.” Tiemann & Markle, 1983

This is all about the physical body, including the vocal tract. It’s not about deep understanding; it’s about knowing how to physically move your muscles, limbs or mouth to produce a desired result.

Why it is Necessary

Cognitive knowledge is useless if the physical execution fails. More importantly, a lack of psychomotor fluency can completely mask what a student actually knows (Binder, Haughton and Van Eyk, 1990). For example, we might think a student is struggling with their multiplication facts during a timed test, when in reality, the barrier is their lack of handwriting fluency. They simply cannot physically write the numbers fast enough. Or we might want them to partition a large number, but because they haven’t mastered the physical skill of aligning their numbers in straight columns, the entire maths problem falls apart. Psychomotor learning bridges the gap between knowing what to do and physically executing it effortlessly.

Examples

• Holding a pencil correctly with a tripod grip.

• Physically placing the tongue behind the top teeth to correctly articulate the ‘th’ sound.

• Performing a standard layup in basketball.

The Mistake

Talking too much or teaching “words about a concept” instead of the movement itself.

How to Teach it in Five Simple Steps

1. Model the complete chain at full speed: Show them the final product first so they know exactly what the fluent pperformance looks and/or sounds like.

2. Model the chain slowly, step-by-step: Break the movement down into its smallest teachable parts.

3. Highlight the critical physical cues: Direct their attention to specific body parts.

4. Maximise practice opportunities: Eliminate passive waiting or “standing in line”. Set up the room or the routine so that every student is getting high-rate physical or vocal practice simultaneously.

5. Provide feedback: Provide immediate physical or verbal correction. Do not let them practice mistakes; guide their movement until the execution becomes automatic.

2. Facts (The Factual Foundation)

“Memorising often is looked upon as a low and therefore unworthy kind of learning. But when people become experts - with all the facts at their fingertips, we take a different view of their ability." Tiemann & Markle, 1983

Some people might not like hearing this, but this is rote memorisation. The student needs to reproduce an exact fact fast. There is no room for creativity here. It is simply stimulus and response: when you see “b”, your verbal response needs to be “bee”.

Why it is Necessary

Facts are the raw materials of thought. Fluency in factual recall is necessary because it frees up working memory (Poncy et al., 2007). If a student is using all their cognitive capacity to remember what 6 x 7 is they have no brain power left to solve the actual multi-step word problem. When knowledge is not fluent, thinking becomes effortful in ways that are often invisible to teachers.

Examples

• Recalling that 6 x 7 = 42.

• Naming the capital cities of Australia.

• Identifying the chemical symbol for Potassium (K).

• Recalling the exact year World War II began.

The Mistake

Asking leading questions to correct a rote fact or using discovery methods for simple associations.

How to Teach it in Five Simple Steps

1. Ensure accuracy first: Do not test before you teach. Heavily prompt the correct answer on day one.

2. Complete timed practice: Use 1-minute timings to build high-rate, effortless responding.

3. Do it everyday: Consistency is required to move from accuracy to automaticity.

4. Track progress: Have students track their own correct and error rates.

5. Respond to data: Compete against yourself, not others, and adjust based on the numbers.

3. Procedures (The Rigid Sequence)

"Algorithms are sequential sets of rules or steps that generate correct solutions or products for all problems of a given type." Tiemann & Markle, 1983

If facts are a single stimulus and response, procedures are a chain of them. This is the realm of the algorithm. We aren’t asking students to invent a new way to solve a problem; we are asking them to follow a predetermined, step-by-step procedure flawlessly. Doing step three before step two means the whole thing falls apart.

Why it is Necessary

Procedures automate multi-step processes so students don’t have to reinvent the wheel every time they encounter a standard problem (Gagné, 1984). It builds reliable pathways for executing standard tasks accurately every single time.

Examples

• The standard algorithm for long division (Divide, Multiply, Subtract, Bring down, Repeat).

• Following a rigid proofreading checklist (Check for a capital letter, check for finger spaces, check for a full stop)

• Lighting a Bunsen burner

• Completing the steps to label the parts of a plant from a diagram

The Mistake

Showing the entire 15-step process once and expecting the student to replicate it flawlessly from memory.

How to Teach it in Five Simple Steps

1. Break it into discrete links: Do a task analysis. Write down every single micro-step of the procedure so you know exactly what the chain looks like.

2. Choose your direction: Decide if you are using forward chaining (teaching step one first) or backward chaining (doing everything for the student except the final step, so they get the immediate win).

3. Isolate the target step: Model and heavily prompt just the single step you are currently teaching. Do not overwhelm them with the whole sequence at once.

4. Demand mastery of the link: A student must be able to execute the current step flawlessly before you introduce the next one.

5. Link the chain: Once the single step is secure, attach it to the next step. Practice them together until the entire procedure is a single, unbroken routine.

4. Concepts (The Mental Filing System)

“A definition may be a good place to start, but it is a poor place to stop (when analysing a concept).” Tiemann & Markle, 1983

Now we are moving away from simple recall and just asking students to reproduce exactly what we showed them. A concept requires a student to classify completely new examples that they have never seen before.

Why it is Necessary

Concepts build the mental filing system. They allow students to organise a chaotic world into neat categories. Without concept mastery students are just memorising isolated instances rather than understanding underlying properties. As Twyman (2021) highlights, the goal of this careful sequencing is 'faultless communication'—designing and arranging the examples so perfectly that the learner is left with only one possible logical interpretation of the concept.

Examples

• Recognising mammals among unfamiliar animals

• Deciding whether an unfamiliar shape is a polygon

• Identifying whether a newly presented number is prime or composite.

• Spotting metaphors in a previously unseen poem.

The Mistake

Only showing standard, typical examples. If you only show Golden Retrievers, students will think a "dog" must be fluffy and golden.

How to Teach it in Five Simple Steps

These steps also lean heavily on the work of Engelmann and Carnine (1991) as they are the ones who perfected the architecture of “rational sets” and “faultless communication”.

1. Identify “Must Have” Features: Clearly define the critical attributes of the concept.

2. Identify “Can Have” Features: Identify the irrelevant noise that changes from example to example.

3. Juxtapose “Close In” Non-examples: Show a non-example that almost fits the rule to sharpen discrimination.

4. Juxtapose “Maximally Different” Examples: Show wildly varying examples that still fit the “Must Have” features.

5. Unpredictable Testing: Test with novel examples not used during teaching.

5. Principles (The Predictive Rule)

"More complex than concept learning is learning to apply principles. A principle is a statement that sets forth a relationship between two or more concepts... a student demonstrates mastery of a principle only when applying that principle in a new situation.” Tiemann & Markle, 1983

If concepts allow us to name the world, principles allow us to predict it. This is the realm of cause and effect. We aren’t just asking students to categorise isolated things anymore, but we are asking them to apply a reliable rule to see how those things interact in entirely new situations. It is the fundamental understanding that if a specific condition is met, then a specific, predictable action must follow.

Why it is Necessary

Principles move students from just categorising things to predicting how things interact. They provide the “cause and effect” rules of the universe allowing students to navigate new situations reliably.

Examples

• Applying the silent e (CVCE) spelling rule

• Applying the rule for subject–verb agreement in unfamiliar sentences

• Using the distributive property to solve new multiplication problems

• Applying the rule of buoyancy to predict if an object will float.

The Mistake

Stating the rule, providing two perfect examples and moving on.

How to Teach it in Five Simple Steps

1. Check the component concepts: A student cannot apply a rule to a concept they don't understand. Verify they can classify the concepts before you ask them to predict how they interact.

2. State the “If-Then” Rule Explicitly: Tell them the exact cause and effect relationship.

3. Demonstrate Across Varied Examples: Show the rule working in multiple contexts.

4. Throw the Curveball: Introduce situations where the “If” condition is NOT met.

5. Test with the Unknown: Assess application in entirely new contexts.

6. Strategies (The Uncharted Territory)

“Strategies are also ways of dealing with new situations - situations not faced before by the learner... That person is not behaving in a trial-and-error fashion, but has learned a rational strategy to be applied.” Tiemann & Markle, 1983

If principles give us reliable rules for predictable situations, strategies are what we use when those rules aren’t enough. This is the realm of ambiguity. We are no longer dealing with neat textbook examples that have a single correct answer. We are asking students to attack messy, completely novel problems where they have to monitor their own thinking, choose an attack path and pivot when their first attempt fails.

Why it is Necessary

The real world rarely hands us perfectly structured procedures. We need to equip students to handle ambiguity. Strategy instruction prepares students to monitor their own thinking, change course when a plan fails and tackle problems that don’t have a textbook answer (Gagne 1984).

However, we cannot expect students to successfully navigate this ambiguity if they are still struggling with the basics. Johnson and Layng (1992) demonstrated that true fluency in foundational tool skills is what actually allows completely novel problem solving strategies to emerge. If a student is using all their working memory just to recall a basic maths fact or decode a simple word, they have no cognitive space left to evaluate their own thinking or adapt to a curveball. Strategy instruction is vital but it relies entirely on the fluent foundations built in the earlier stages.

Examples

• Solving an unstructured multi-step maths word problem (UPSCheck: Understand, Plan, Solve, Check).

• Planning how to structure a narrative (CSPACE: Characters, Setting, Purpose, Action, Conclusion, Emotion)

• Summarising a dense informational text where the main idea isn’t explicitly stated (RAP: Read a paragraph, Ask yourself what it’s about, Put it in your own words).

The Mistake

Throwing students into the deep end with a complex task and saying "give it a go" or “just keep at it,” hoping a brilliant problem-solving strategy will magically emerge from the struggle.

How to Teach it in Five Simple Steps

1. Verify fluency in tool and component skills: Students cannot employ a strategy if they lack the foundational facts.

2. Introduce Ill Structured Problems: Give them messy problems without obvious solutions.

3. Equip with Problem-Solving Repertoires: Provide a reliable attack strategy to navigate the unknown.

4. Shift to Heuristic Questioning: Move from giving answers to asking questions that keep minds moving.

5. Demand Justification: Require students to explain their reasoning and strategy choice.

Links to the Instructional Hierarchy

When teaching any type of learning and it is new for students, they are right back in Acquisition. However, once acquired we can think about the different types like this:

• Psychomotor skills, Facts and Procedures are worth building fluency in

• Concepts and Principles enable us to generalise our knowledge to new contexts

• Strategies give us a way to adapt and appy what we know

Aligning teaching with learning

Perhaps the most powerful implication of Tiemann and Markle’s work is also the simplest.

When instructional tactics are chosen without regard for the type of learning required, lessons become inefficient and sometimes counterproductive. Students may appear disengaged or incapable when the real issue is a mismatch between task demands and instructional design.

Recognising different types of learning allows teachers to act with greater precision and confidence. It shifts lesson planning from hopeful experimentation towards deliberate engineering.

Key takeaways

• Learning can be categorised into distinct forms, each requiring different instructional approaches

• Emotional responses to learning are shaped by repeated experiences of instructional success or failure

• Factual and procedural fluency are essential foundations for conceptual and strategic thinking

• Effective teaching involves aligning methods with the cognitive architecture of the task

If we want teaching to feel less uncertain and more predictable, we do not necessarily need more innovations. We already have the blueprint! We do not need to constantly reinvent our teaching methods. The research and structures for highly effective instruction have existed for decades. A comprehensive half-century meta-analysis by Stockard et al. (2018) proved conclusively that these highly structured, direct instructional models produce vastly superior outcomes across almost every measure.

References

Binder, C. V., Haughton, E. and Van Eyk, D. (1990) ‘Increasing Endurance by Building Fluency: Precision Teaching Attention Span’, Teaching Exceptional Children, 22(3), pp. 24–27.

Engelmann, S. and Carnine, D., 1991. Theory of instruction: Principles and applications. Eugene, OR: ADI Press.

Gagné, R. M. (1984) ‘Learning Outcomes and Their Effects: Useful Categories of Human Performance’, American Psychologist, 39(4), pp. 377–385

Johnson, K.R. and Layng, T.V.J., 1992. ‘Breaking the structuralist barrier: Literacy and numeracy with fluency’, American Psychologist, 47(11), pp. 1475-1490.

Poncy, B. C., Skinner, C. H., & Jaspers, K. E. (2007). Evaluating and comparing interventions designed to enhance math fact accuracy and fluency: Cover, copy, and compare versus taped problems. Journal of Behavioral Education, 16(1), 27-37.

Spencer, T.D., 2021. ‘Ten instructional design efforts to help behavior analysts take up the torch of direct instruction’, Behavior Analysis in Practice, 14(3), pp. 816-830.

Stockard, J., Wood, T.W., Coughlin, C. and Rasplica Khoury, C., 2018. ‘The effectiveness of direct instruction curricula: A meta-analysis of a half century of research’, Review of Educational Research, 88(4), pp. 479-507.

Tiemann, P. W. and Markle, S. M. (1983) Analyzing Instructional Content: A Guide to Instruction and Evaluation. 3rd edn. Champaign, Illinois: Stipes Publishing Company.

Twyman, J.S., 2021. ‘Faultless communication: The heart and soul of DI’, Perspectives on Behavior Science, 44(2), pp. 1-13.

Kim also challenges some widely held assumptions, including the limits of discovery learning and the over-reliance on grades as meaningful measures of progress.

If you’re looking for practical, research-informed ways to sharpen your teaching and better support every learner, this episode offers a powerful new lens.

Resources mentioned:

https://fitlearning.com/

• Blindspots by Kimberly Berens

• The Technology of Teaching by B.F. Skinner

• Theory of Instruction by Sigfried Engelman and Doug Carnine

• The Standard Celeration Chart

• The Morningside Model of Generative Instruction (Johnson, Street, Kieta and Robbins)

• Program of International Student Assessment (PISA)

• National Assessment of Educational Progress (NAEP)

• FitLite (and the FitLite Literacy model)

• Scientist Educator Training Series

You can connect with Kimberly:

Twitter: @KimberlyBerens5

Instagram: @drkberens

Linkedin

Website:

https://www.drkimberlyberens.com/

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast:

https://www.patreon.com/KnowledgeforTeachersPodcast

About Kimberly

Kimberly Nix Berens, Ph.D., is the Founder of Fit Learning and CEO of Fit Learning Online. She co-created a powerful system of instruction based in behavior science and the Technology of Teaching, which has transformed the learning abilities of thousands of children worldwide. For more than 20 years, her system of instruction has produced at least one year’s worth of academic growth in only 40 hours of training. Her learning programs effectively target such essential areas as early learning skills, basic classroom readiness, phonemic awareness, reading fluency, comprehension, inferential language, basic and advanced mathematics, logical problem solving, grammar, and expressive writing. From her early beginnings in a broom closet at the University of Nevada – Reno, Dr. Berens has helped grow Fit Learning to an organization with centers located throughout the US, Canada, Europe, and Australia. In her current role as CEO of Fit Learning Online, she focuses on increasing access for learners living in regions without a Fit Learning center. Dr. Berens is a frequent invited speaker and a contributor to many popular press publications such as Thrive Global, 74 Million, and Medium. Her first book, Blind Spots: Why Students Fail and the Science That Can Save Them, was released in October of 2020.

Tune in as we explore:

• Why the idea that academic language develops naturally is a damaging myth.

• Why some students struggle despite strong phonics teaching

• How just 30 minutes of explicit spoken language instruction daily can close the achievement gap.

• Why expecting teachers to act as instructional designers is an unfair burden.

If you are looking for practical, evidence-based ways to boost your students’ language skills without adding impossible workloads, this conversation is a must-listen.

Resources mentioned:

• Story Champs

• trinaspencer.com/

• CUBED

• DYMOND

• MAP (Measuring Academic Progress)

• Spencer, T. D. (2021). Ten instructional design efforts to help behavior analysts take up the torch of direct instruction. Behavior Analysis in Practice, 14(3), 816-830.

• Pamela Snow, Why the Big Six should actually be the Big Five.

• Doug Peterson

You can connect with:

Twitter/X: @TrinaDSpencer2

Facebook

Instagram: @trinastoolbox/

Linkedin

Website:

https://trinaspencer.com/

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast:

https://www.patreon.com/KnowledgeforTeachersPodcast

About Trina

Dr. Spencer is a senior scientist and director of the Juniper Gardens Children’s Project and is a professor in the Department of Applied Behavioral Science at the University of Kansas. Drawing from learning sciences and multiple disciplines (e.g., behavior analysis, speech-language pathology, applied linguistics, and education), she concentrates her efforts on the oral academic language that serves as a foundation to the reading comprehension and writing composition of preK to 3rd grade students, with and without disabilities.

Dr. Spencer maintains a spirited research agenda that has yielded 76 peer review publications, 184 invited presentations, $16M in external funding, and several commercialized curricula, interventions, professional development systems, and assessment tools. Her innovations are used broadly in several countries, and she continues to develop culturized interventions with international collaborators for their contexts. Dr. Spencer values researcher-practitioner partnerships, community engagement, and inter-disciplinary collaborations to accomplish high impact and
innovative applied research. www.TrinaSpencer.com

Fluency is often treated as a small piece of mathematics learning, but in reality, it may be one of the most important and overlooked foundations for long term success.

In this episode of the Knowledge for Teachers podcast, Brendan Lee speaks with Dr. Brian Poncy, Professor at Oklahoma State University and the creator of Facts on Fire, a highly regarded program designed to build maths fact fluency through short, structured, and evidence informed daily practice.

Brian challenges the common resistance to timed practice, arguing that fluency—defined strictly as accuracy plus speed—is the bridge that frees up working memory for higher-order problem solving.

Listeners will discover why timed practice only works when students are placed at the right starting point, how small sets and careful sequencing can dramatically improve motivation and success, and what schools can do to implement fluency routines effectively in just a few minutes a day.

The episode also explores the powerful concept of contingency adduction, where mastering component skills can lead students to solve complex problems they have never been explicitly taught.

A practical and thought provoking conversation for any educator serious about improving mathematics outcomes.

Catch Dr. Brian Poncy in Australia:

Tickets can be purchased here:

• Perth: https://www.trybooking.com/DHYZM

• Adelaide: https://www.trybooking.com/DHZSU

• Melbourne: https://www.trybooking.com/DIABM

• Sydney: https://www.trybooking.com/DHYZG

Resources mentioned:

• M.I.N.D. 2.0 - FACTS ON FIRE

• Chalk and Talk podcast (Anna Stokke)

• Morningside Academy

• PBIS (Positive Behavioral Intervention Supports)

• Rocket Math

• Times Tables Rock Stars

• Engineering the “Aha!”: When Discovery Learning Actually Works

You can connect with Brian:

Twitter/X: @brian_poncy

Website: M.I.N.D. 2.0 - FACTS ON FIRE

You can connect with Brendan:

Twitter: @learnwithmrlee

Facebook: @learningwithmrlee

Website:learnwithlee.net

About Brian

Dr. Brian Poncy is a Professor of School Psychology at Oklahoma State University. His research focuses on academic interventions and behavioral principles of learning, specifically in the area of mathematics. Dr. Poncy created the Measures & Interventions for Numeracy Development (M.I.N.D.), a set of free materials to support teachers in the assessment and implementation of empirically validated interventions to increase early numeracy and computation skills (www.factsonfire.com). He is a co-author of Effective Math Interventions: A Guide to Improving Whole-Number Knowledge. To access sample trainings, podcast appearances, and research go to https://experts.okstate.edu/brian.poncy

Support the Knowledge for Teachers Podcast:

https://www.patreon.com/KnowledgeforTeachersPodcast

Implementing Effective Primary Maths Instruction

For School Leaders

This is a two day online course for school and middle leaders and it is all about implementation. We look closely at curriculum and lesson design, assessment, coaching and the systems that help teachers change practice in a sustainable way.

In this episode of the Knowledge for Teachers podcast, Brendan Lee speaks with Dr. Brian Poncy, Professor at Oklahoma State University and the creator of Facts on Fire, a highly regarded program designed to build maths fact fluency through short, structured, and evidence informed daily practice.

Brian challenges the common resistance to timed practice, arguing that fluency—defined strictly as accuracy plus speed—is the bridge that frees up working memory for higher-order problem solving.

Listeners will discover why timed practice only works when students are placed at the right starting point, how small sets and careful sequencing can dramatically improve motivation and success, and what schools can do to implement fluency routines effectively in just a few minutes a day.

The episode also explores the powerful concept of contingency adduction, where mastering component skills can lead students to solve complex problems they have never been explicitly taught.

A practical and thought provoking conversation for any educator serious about improving mathematics outcomes.

Catch Dr. Brian Poncy in Australia:

Tickets can be purchased here: Perth: https://www.trybooking.com/DHYZM Adelaide: https://www.trybooking.com/DHZSU Melbourne: https://www.trybooking.com/DIABM Sydney: https://www.trybooking.com/DHYZG  

Resources mentioned:

• M.I.N.D. 2.0 - FACTS ON FIRE

• Chalk and Talk podcast (Anna Stokke)

• Morningside Academy

• PBIS (Positive Behavioral Intervention Supports)

• Rocket Math 

• Times Tables Rock Stars

• Engineering the “Aha!”: When Discovery Learning Actually Works

You can connect with Brian:

Twitter/X: @brian_poncy

Website: M.I.N.D. 2.0 - FACTS ON FIRE

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast: 

https://www.patreon.com/KnowledgeforTeachersPodcast

Implementing Effective Primary Maths Instruction For School Leaders

This is a two day online course for school and middle leaders and it is all about implementation. We look closely at curriculum and lesson design, assessment, coaching and the systems that help teachers change practice in a sustainable way.

Register here

We dig into five common teaching habits you need to stop immediately, including why "Sat Nav teaching" is creating dependency rather than independence and why the popular idea of "productive struggle" might actually be setting your students up to fail. David challenges deep-seated beliefs about practice, compliance, and memory, offering a provocative look at what it really takes to make learning stick.

Resources mentioned:

Books

• David Didau – What If Everything You Knew About Education Was Wrong? 

• David Didau – Intelligent Accountability 

Websites & Tools

• Carousel Learning 

People

• Robert Bjork 

• Adam Boxer 

• Carl Hendrick 

• Christina Milos

You can connect with David:

Twitter/X: @DavidDidau

Linkedin

Substack: https://daviddidau.substack.com/

Website: https://learningspy.co.uk/

David Didau Events: Canberra - Thursday 12th March - https://events.humanitix.com/david-didau-full-day-event Melbourne - Thursday 19th March - https://events.humanitix.com/coach-to-5k-writing-workshop-with-david-didau  About David Didau

David Didau is an educator, author, and professional learning leader known for his evidence-informed work on teaching, writing, and curriculum. He is the author of several highly regarded books including What If Everything You Knew About Education Was Wrong? and The Secret of Literacy. David writes in his blog The Learning Spy, a widely read platform supporting educators to translate research into classroom practice.

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast: 

https://www.patreon.com/KnowledgeforTeachersPodcast

The Primary Maths Instruction Framework For teachers

This is a three day online course for teachers where we focus on how learning happens and how to design maths lessons that support acquisition, build fluency and help students generalise what they know.

Register here

Implementing Effective Primary Maths Instruction For School Leaders

This is a two day online course for school and middle leaders and it is all about implementation. We look closely at curriculum and lesson design, assessment, coaching and the systems that help teachers change practice in a sustainable way.

Register here

I have not changed my position.

Minimal guidance still does not work when students are novices and learning new content. The problem is not that discovery learning never works, but that we often misunderstand when it works and why. Framing this as a choice between explicit instruction and discovery is unhelpful.

Explicit instruction works most of the time. It works because teachers are constantly moving students onto new content and because novice learners do not yet have the knowledge they need to learn effectively through exploration. Without that knowledge, discovery does not deepen understanding. It overwhelms working memory.

Most teachers have seen it happen. A student suddenly “gets it”. They solve a problem they have never been shown how to solve. They make a connection you did not explicitly teach. They have an “aha” moment. For the student, it feels like they’ve climbed a mountain and found the view themselves.

For you, the teacher, it should be the result of a meticulously designed map. The question is not whether discovery learning can work. The question is when it works and what makes it possible. Enter contingency adduction.

In this article, I unpack four ideas:

• What Contingency Adduction Explains About Learning

• When Discovery Learning Actually Works

• What Happens When the Conditions Are Right

• Designing for Discovery in the Classroom

What Contingency Adduction Explains About Learning

I’ve only learnt about this term in the last 12 months after conversations with colleagues Dr. Russ Fox and Karina Stocker and have since dived deep into the “weeds” of it. However, I know that most people haven’t heard of it, but feel it answers a lot of questions for educators.

Contingency adduction is the process where skills learned in one context are recruited by a new situation to solve a novel problem (Andronis, Layng and Goldiamond, 1997).

Think of it this way, first, behaviours are learned and reinforced under one set of conditions. Later, a different set of conditions recruits those behaviours from the learner’s history. When this happens, the behaviours are triggered by new signals and begin to serve a different function than they originally did (Andronis et al., 1997). In other words, discovery should not feel like wandering in the dark. It should feel like a light switching on.

The discovery is genuine, but it should not be accidental.

Nothing new has been added to the student's head. What has changed is that the environment has been arranged to "call up" existing skills in a brand-new order. The student provides the insight, but you provide the trigger.

It’s like a musician sight-reading a new piece. If they have to think about every note, the music collapses. When scales and chords are automatic, they can respond to the score in real time. The performance looks intuitive because the fundamentals no longer demand attention.

When Discovery Learning Actually Works

The conditions required for discovery learning to work are:

1. Load the Toolkit

2. Make it Automatic

3. Design for the “Aha!”, Not the “Huh?”

When these conditions are met, discovery feels effortless to students and predictable to teachers. If discovery feels confusing, one of these three things is missing.

1. Load the Toolkit

Tool skills are the smallest building blocks (Johnson & Layng, 1992). Things like recognising letter sounds, recalling number facts or reading a sentence accurately. They are not the goal of learning, but they make everything else possible.

Component skills “depend on one or more tool skills” (Johnson & Street, 2013). For example, retelling what was just read, interpreting a word problem, or setting up an equation. These are the pieces that later get recruited when students face something new.

A skill’s classification is relative to the learner; what is a component for a beginner becomes a tool once it is fluent (Johnson & Street, 2013). Tool skills are the non-negotiable basics. Component skills are the intermediate steps (Spencer, 2021). If the tools aren't fluent, the component fails. If the components aren't fluent, the discovery fails.

In a traditional discovery model, if a student struggles, we assume they "aren't ready" or "need more time." In the contingency adduction model, student error is a critique of your design (Twyman, 2021).

2. Make it Automatic

Having the right tools is only the first step. A common mistake is assuming that just because a student “knows” a skill, they are ready to use it in a discovery context. They don’t just need to be accurate; they need to be fluent (Kubina & Morrison, 2000). Those tools need to work automatically.

One way to think about this is through the Instructional Hierarchy (Haring & Eaton, 1978). Learners first acquire a skill, then build fluency, before they can reliably generalise and adapt it. What we often label as “discovery” sits at the top of this hierarchy. It only becomes available once the earlier stages have done their work. Contingency adduction explains how that upper part of the hierarchy works. Fluent skills are recruited and recombined when the task demands it.

Fluency reflects performance that is stable, automatic and available under pressure, not knowledge that only works when conditions are carefully controlled (Binder, 1996; Johnson & Layng, 1996). At Morningside Academy, this looks like 80-100 maths facts per minute and for passage fluency 180-220 words per minute (Johnson et al., 2021).

Automatic does not mean mindless. It means the skill runs without effort. It does not compete for attention. It does not slow thinking down.

When skills are not automatic, students are busy just trying to perform them. They pause to recall facts, check steps, or decode the task itself. Working memory is consumed by execution, leaving very little space for reasoning.

When skills are automatic, something important changes. Students can think about what the task is asking rather than how to carry out each step. Their attention shifts from procedure to structure.

This is why fluency matters so much. Fluency is what turns a skill from something students can do into something they can use. It is the difference between knowing and thinking.

A simple way to tell whether a skill is automatic is to ask this:
Can the student use it while thinking about something else?

If the answer is no, discovery will not help. The task will feel confusing rather than revealing.

Making skills automatic is not about rushing or drilling for speed. It is about removing friction. It is about ensuring the basics are reliable enough to disappear into the background.

3. Design for the “Aha!”, Not the “Huh?”

Discovery does not begin with the task. It begins long before students ever see it. By the time a student reaches an “aha” moment, the teacher has already done the heavy lifting. Fluency has been built deliberately. What looks like insight at the end of the sequence is the result of careful preparation at the start (Layng et al., 2004).

When this work has not been done, discovery feels very different. Students hesitate. They guess. They focus on surface features. The task produces confusion rather than clarity. That is the “huh”.

Designing for the “aha” means being ruthless about prerequisites. It means asking in advance what students will need to already know and be able to do automatically before a task can work as intended (Tiemann & Markle, 1990). If a task requires blending, calculating, interpreting, or comparing, those actions cannot still be fragile. They must already run smoothly in the background.

This is where tool and component skills matter. Tool skills need to be reliable enough that students do not notice themselves using them. Component skills need to be familiar enough that students recognise when they are relevant. Only then can a new task quietly pull those skills together.

When teachers skip this preparation and move straight to the task, they often misread what they see. Struggle is mistaken for thinking. Errors are treated as productive. In reality, the task is asking students to do too many things at once.

Designing for the “aha” is not about making tasks easier. It is about making thinking possible. The task should demand connection, not recall. It should require recombination, not improvisation.

When the design is right, the task does the recruiting. This is when we see “curriculum leaps” (Johnson & Layng, 1992). Students are not told what to do. They simply see what needs to be done. The moment feels like discovery, because it is. It just happens to be one the teacher planned for.

The Five Signatures of Insight

Instructional designers have identified at least five distinct ways you can engineer this recruitment. If you want to build a discovery lesson, you are likely looking to trigger one of these specific variations (Johnson et al, 2021):

• Adduction of a New Sequence: You teach Skill A and Skill B separately. You then present a problem that requires doing A then B. The student “discovers” the chain. This is the backbone of complex maths.

• Adduction of a New Blend: You teach two distinct actions (like a student saying /c/ and /l/). When presented with a combined signal, the learner “blends” them into a novel composite (/cl/) (Layng, Twyman and Stikeleather, 2004).

• Adduction by Context: The learner knows a complex skill. You present a new context that requires only part of that skill. The learner “discovers” how to break their own behaviour down to fit the new constraint.

• Adduction by Elimination: You teach a student to select a specific shape. You then present a screen with that shape and a new, unknown shape, but ask them to select the new one. Through the process of elimination (rejecting the known), they “discover” the new category without being told what it is (Layng et al., 2003).

• Adduction of Equivalence: You teach that A = B and B = C. You never teach A = C, yet the student “discovers” this relationship on their own. This is how deep conceptual networks are formed (Sidman, 1994; Shapiro, 2024).

When these signatures appear, it is a sign the design is working. When they do not, it is a sign to revisit the preparation, not the task.

What Happens When the Conditions Are Right

Consider early reading instruction. In a landmark study by Layng, Twyman and Stikeleather (2004), learners were taught individual letter-sound correspondences to fluency. They were then presented with unfamiliar letter combinations and asked to respond. Crucially, the blended sounds had never been taught.

The result? Between 80 and 95 percent of learners correctly identified the new sound combinations on their very first attempt. The blending behaviour appeared immediately. This was not inference or trial and error. It was the recombination of fluent component skills under new stimulus conditions. The discovery was real and it was engineered.

We see the same “curriculum leap” in mathematics. At Morningside Academy, students struggled with complex fraction word problems. Rather than teaching the problems directly, educators focused on the components:

1. Fraction computation (the maths)

2. Whole number word problem schemas (the logic)

Once these two skills were built to high fluency, students were tested on fraction word problems they had never seen. Performance improved dramatically (Johnson & Layng, 1992). The students automatically recruited their calculation fluency and applied it to the word problems. This focus on fluency allowed students to make ‘curriculum leaps,’ averaging over two years of academic growth for every year of instruction (Johnson & Street, 2012).

The “aha” occurred only because the underlying skills were so well established that they could be recruited and combined. This is the opposite of discovery as trial and error. It is discovery as recombination.

Why this matters

These findings are important because they show that discovery is not a mysterious cognitive leap. It is a predictable outcome when instruction has done its work. When component skills are fluent, the learner finally has the cognitive space to think.

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Designing for Discovery in the Classroom

Planning for contingency adduction looks different from traditional lesson planning. It starts with the outcome you want learners to reach and works backwards to make that outcome likely.

1. Start with the complex behaviour

Be clear about the kind of thinking or problem solving you want learners to demonstrate independently. This is the behaviour that should eventually feel like discovery to the learner.

2. Identify the tools and components

Break the complex behaviour into tool skills and component skills.

Tool skills are the smallest building blocks. Component skills are combinations of those tools that still need to be taught explicitly. These are the skills that will later be recruited when learners face something new.

If the tools or components are missing, discovery cannot happen.

3. Sequence for strength, not exposure

Ensure that each prerequisite is firmly in place before it is required.

This is not about covering content. It is about building a broad enough repertoire that skills are available when a task demands them. The stronger the foundation, the more likely recombination becomes.

4. Make fluency non-negotiable

Skills need to work without effort if they are going to be used in thinking. Prioritise repeated opportunities for high quality responding, so that core skills become automatic (Johnson & Layng, 1996).

If a skill still demands attention, it will block discovery rather than enable it.

5. Design the task to do the recruiting

Only once the prerequisites are fluent should you introduce a novel task.

Do not cue the solution. Do not break the task down again. Let the task quietly pull together what learners already know. When the design is right, success is reinforcing in its own right.

Discovery is not something you add at the end. It is what happens when the design has done its job. If you find yourself explaining the solution, the task was introduced too early.

In a nutshell

Contingency adduction provides a clear explanation for why discovery learning sometimes works and often fails. It works when learners have earned the right to discover through carefully sequenced instruction and sufficient fluency.

We do not need to choose between rigour and discovery. Explicit instruction is not the opposite of discovery. It is what makes discovery possible. When instruction is designed well, discovery is not a gamble. It is the outcome.

None of this is abstract theory. It has very real implications for how we design maths instruction day to day.

In my upcoming course, The Primary Maths Instruction Framework, we work through these ideas in detail using mathematics as the anchor: identifying prerequisite skills, building fluency intentionally and designing tasks that reliably produce insight rather than confusion.

If you’re interested in how all of this goes together, you can find the details here:
https://events.humanitix.com/the-primary-maths-instruction-framework

References

Andronis, P. T., Layng, T. J., & Goldiamond, I. (1997). Contingency adduction of “symbolic aggression” by pigeons. The Analysis of Verbal Behavior, 14(1), 5-17.

Binder, C. (1996). Behavioral fluency: Evolution of a new paradigm. The Behavior Analyst, 19(2), 163–197.

Haring, N. G. & Eaton, M. D. (1978). Systematic Instructional Procedures: An Instructional Hierarchy.

Johnson, K. R., & Layng, T.V.J. (1992). Breaking the structuralist barrier: Literacy and numeracy with fluency. American psychologist, 47(11), 1475.

Johnson, K. R., & Layng, T.V.J. (1996). On terms and procedures: Fluency. The Behavior Analyst, 19(2), 281-288.

Johnson, K. R., & Street, E. M. (2012a). From the laboratory to the field and back again Morningside Academy’s 32 years of improving students’ academic performance. The Behavior Analyst Today, 13(1), 20.

Johnson, K. R., & Street, E. M. (2013). Response to intervention and precision teaching: Creating synergy in the classroom. Guilford Press.

Johnson, K.R., Street, E.M., Kieta, A.R. & Robbins, J.K. (2021). The Morningside Model of Generative Instruction: Building a Bridge Between Skills and Inquiry Teaching. Cornwell-on-Hudson, NY: Sloan Publishing.

Kubina, R. M., Jr., & Morrison R. S. (2000). Fluency in Education. Behavior and Social Issues, 10, 83-99

Layng, T.V.J., Twyman, J. S., & Stikeleather, G. (2004). Engineering discovery learning: The contingency adduction of some precursors of textual responding in a beginning reading program. The Analysis of Verbal Behavior, 20(1), 99-109.

Leon, M., Layng, T.V.J., & Sota, M. (2011). Thinking through text comprehension III: The programing of verbal and investigative repertoires. The Behavior Analyst Today, 12(1), 22.

Spencer, T. D. (2021). Ten instructional design efforts to help behavior analysts take up the torch of direct instruction. Behavior Analysis in Practice, 14(3), 816-830

Tiemann, P.W. and Markle, S.M. (1990) Analyzing instructional content: A guide to instruction and evaluation. 4th edn. Champaign, IL: Stipes Publishing Company.

Twyman, J. S. (2021). The evidence is in the design. Perspectives on Behavior Science, 44(2), 195-223

But before we dive headfirst into the curriculum, we need to talk about the invisible architecture that holds our classrooms together. We need to talk about routines.

In the rush to get to the “good stuff”, it is tempting to gloss over the mundane mechanics of the classroom. We assume students know how to enter a room, how to transition between tasks or how to use equipment without turning it into a weapon of mass distraction.

But as Tom Bennett (2020) reminds us, “Routines are the building blocks of the classroom culture.”

They are not merely administrative tasks; they are instructional infrastructure. Without them, our best-laid lesson plans crumble under the weight of cognitive overload and low-level disruption.

The Cognitive Cost of Chaos

When you are in the acquisition stage of learning (which is most of the time for our students), thinking places heavy demands on working memory. Cognitive Load Theory teaches us that attention is a finite resource. Every micro-decision a student has to make—Where do I get a pen? How do I ask for help? What do I do when I’m finished?—steals precious cognitive bandwidth away from the learning at hand.

When we fail to automate these behaviours, we are effectively asking students to multitask and without focus, memory’s hocus-pocus.

If we want students to grapple with the complexities of algebra or the nuances of writing a compound sentence, we must reduce the unnecessary load generated by the environment. We need to make the process of learning invisible so that the content of learning can shine.

Taught, Not Told

A common mistake we make is assuming that students share our mental model of a “good student.” We tell them to “behave,” but we rarely define what that actually looks like in granular detail.

As I’ve written about previously, this is where a Behaviour Curriculum becomes essential. Just as we wouldn’t expect a student to intuitively know how to solve a quadratic equation without explicit instruction, we cannot expect them to read our minds about what the routines of a high-functioning classroom are.

Behaviour must be taught, not told. This means applying the same instructional rigour to routines as we do to content.

Running Routines in Five Simple Steps

1. Plan the Routine: Know exactly what you want students to do. Perform a task analysis to break it down step-by-step.

2. Teach the Routine: Provide examples and non-examples. Do they know what success looks like?

3. Practice the Routine: Start slowly with a small group and then gradually invite more students to have a go. This allows you to really hone in on providing targeted feedback (the next step). If we allow all of them to do it once, if things go wrong, it can be almost impossible to pinpoint where or who it started with.

4. Follow through with Feedback: Close the loop with specific praise or correction. Behaviour specific praise allows you to reinforce the behaviours that you want to see more of. If a correction is needed, closing the loop refers to getting them to do it again and then closing the loop by praising the behaviour.

5. Revise the routine: We can’t expect them to perfect it in one go.

Case Study: The Mini-Whiteboard Routine

Let’s look at a specific, high-leverage routine: the humble Mini-Whiteboard (MWB).

We love MWBs because they allow us to “check for understanding” across the entire class simultaneously. They are low-risk, high-frequency and provide immediate feedback. But without a tight routine, they quickly descend into a distraction—doodling, pen-flicking and slow transitions.

To make MWBs effective, we need to standardise the logistics.

The Distribution: How do they get the boards? Do you have station setups? Are they in seat pockets? Or do you pass them down the rows? Pick one method and stick to it.

• The Cues: Precise language cuts through the noise.

  • “Hover Boards”: Students hold boards face down (preventing early revealing or fiddling).

  • “Chin It”: A clear signal to show answers simultaneously under the chin (standardising visibility).

  • “Park It”: Equipment goes on the floor/desk, hands are free.

Teaching the routine

For the past two years, my colleague Karina Stocker and I have run a course for Think Forward Educators on this exact topic and I’ve really enjoyed seeing how participants have used the example script that we provided build their own routines. Here is an example of what you can say to set up a routine (credit goes to Karina for putting most of this together).

For passing equipment along a line:

1. Pre-cue

“In a moment, when I say go…”

Pause and wait for students to attend, scan the room making eye contact with students.

2. Direction with Positive Framing

Describe precisely the behaviours you want your students to do.

“...Line leaders, I would like you to 1… [hold up 1 finger as a visual prompt]…count how many people are in your row”

“... 2...” [hold up 2 fingers as a visual prompt]...pass the equipment out, starting with the whiteboards, then the markers and cloths”

“... and 3...” [hold up 3 fingers as a visual prompt]...do this quickly and quietly”

Repeat if necessary.

3. Check for understanding (CFU)

Cold Call 2-3 students to repeat the steps.

“What’s the first step you need to do… Sam?” [Hold up a finger for each step as a visual prompt]...”That’s it! Thanks”

“What do I want you to do next… Chelsea?” [Hold up a finger for each step as a visual prompt]...”Thanks, Chelsea!”

If required, provide an extra verbal prompt by repeating each individual step with the student.

By drilling these specific cues like using a “1, 2, 3” finger prompt system, we compress the time spent on logistics. We essentially “turn back time,” reclaiming minutes every lesson that would otherwise be lost to transition.

Check out Caiti Wade’s article on how we can teach students to actually use their boards effectively for learning here.

Codifying Your Playbook

If you are a school leader or a head of department, your role is to support staff in establishing these norms so that students don’t have to code-switch between different teachers’ expectations.

This is where creating an Instructional Playbook pays dividends. By agreeing on the “how” of these core routines—whether it’s entering the room, independent practice, or using MWBs—we create a predictable, safe environment where students can flourish.

The payoff

It might feel laborious to spend these first few weeks obsessing over how pens are handed out or how boards are wiped. It might feel like you aren’t “teaching.”

But you are. You are teaching students how to be successful in a classroom. You are building the infrastructure that will support their learning for the rest of the year.

Invest in the routine now, and you’ll reap the compound interest of focused attention all year long.

Want a practical framework for getting all of this right in maths?

If this article has resonated, then this is exactly what my upcoming course The Primary Maths Instruction Framework is designed to support.

This is a live-online, evidence informed course for primary teachers and leaders who want a clear, coherent and usable model for teaching mathematics well.

We go deep into:

• How learning actually happens in maths

• How to design lessons for acquisition, fluency and generalisation

• How to use routines, representations and worked examples properly

It is not about trends, gimmicks or surface level strategies. It is about building the instructional infrastructure that makes great teaching easier and more reliable.

If you are serious about lifting the quality and consistency of maths instruction in your classroom or school, I would love you to join us.

You can find all the details and register here:
https://events.humanitix.com/the-primary-maths-instruction-framework

The conversation centres on burnout in education and what sustainable teaching and leadership actually look like beyond surface level wellbeing advice. Drawing on Brad’s lived experience and research informed work, this episode explores why burnout is more than just feeling tired, how hidden emotional labour shapes the work of teachers and leaders, and why framing burnout as a resilience issue can miss the real problem.

Listeners will hear a practical framework for resetting habits and expectations, learn why boundaries are essential rather than optional, and gain insight into how clarity, systems, and culture can reduce cognitive and emotional load.

This is a thoughtful and practical conversation for educators who want to keep doing this work well, without burning themselves out in the process.

You can connect with Brad:

Twitter/X: @brad_coaching

Linkedin 

Website: bradgaynor.com.au

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

The Primary Maths Instruction Framework For teachers

This is a three day online course for teachers where we focus on how learning happens and how to design maths lessons that support acquisition, build fluency and help students generalise what they know.

Register here

Implementing Effective Primary Maths Instruction For School Leaders

This is a two day online course for school and middle leaders and it is all about implementation. We look closely at curriculum and lesson design, assessment, coaching and the systems that help teachers change practice in a sustainable way.

Register here

Model clearly.
Guide practice.
Release students when they are ready.

Where explicit instruction breaks down

In theory, explicit instruction is often presented as a clean sequence.

1. I do

2. We do

3. You do

In practice, lessons are messier.

• Students hesitate.

• Errors appear.

• Accuracy fluctuates.

• Confidence comes and goes.

And in those moments, teachers are forced to make decisions in real time.

• Do I keep going?

• Do I go back?

• Do I add support?

• Do I remove it?

This is where explicit instruction either becomes powerful or mechanical.

Why resources are not the problem

Many schools respond to this complexity by providing teachers with detailed resources.

• Slide decks.

• Lesson sequences.

• Fully scripted programs.

• Textbooks with every step laid out.

This is often a sensible move.

It reduces teacher workload. It recognises that curriculum design requires a different level of expertise. It supports consistency across classrooms.

Fidelity without understanding leads to rigidity

Schools want teachers to deliver programs with fidelity. Teachers want to do the right thing. So when uncertainty creeps in, a very predictable pattern emerges.

• Teachers click through every slide.

• They follow every page of the textbook.

• They hesitate to skip, adapt or return to earlier content.

Not because they are unwilling to think, but because they are unsure what is essential and what is flexible.

Without a clear mental model of how learning progresses, fidelity becomes compliance.

Explicit instruction turns into a procedure.

The missing link is decision making

This is the part of explicit instruction that is most often left implicit.

The phases matter, but the real work sits between them. If this happens, then do this.

Without that understanding, teachers cannot make principled decisions about what to keep, what to change and what to skip. They either over adapt and break the design, or under adapt and move on when students are not ready. In The Essential Guide to Explicit Instruction in Mathematics I describe the three key phases of explicit instruction as:

1. Show

2. Support

3. Step Back

This is the language that I use in this post. To learn more about it, make sure that you check out the full guide.

When students hesitate

If students show uncertainty, hesitation, or confusion, the issue is rarely motivation.

It is clarity.

At that point, moving on is not productive struggle. It is abandonment.

The correct response is to model again with a worked example and a clear think-aloud. This is not ignoring the resource. It is using it intelligently.

When students can only perform with support

If students can complete steps only with prompts, the message is clear.

They are still in the Support Phase.

No amount of clicking forward will fix that. Guided practice needs to continue, prompts need to be adjusted and opportunities to respond need to increase.

The resource does not decide when to move on. The evidence does.

When errors become consistent

Consistent errors point to a flaw in understanding, not effort.

At this point, adding more practice only entrenches the error. The correct move is to return to modelling and address the source directly.

Again, this may mean revisiting earlier slides or skipping ahead less quickly than planned. That is not a lack of fidelity. It is fidelity to learning.

When accuracy improves but relies on prompts

This is progress, but not readiness.

Here, prompts should fade deliberately. Support changes shape rather than disappearing altogether. This is a judgement call that no resource can make on its own. I wrote more about this here.

When students are ready

When students are consistently accurate, confident, and no longer reliant on prompts, independent practice becomes productive.

If errors reappear, the response is not frustration. It is information.

Return to Support. Correct. Adjust. Try again.

What this means for schools

Resources are necessary. Understanding is essential.

Schools that want both consistency and responsiveness need to make the decision rules explicit. Teachers need clarity about the mechanisms that matter, not just the materials to use.

Without that clarity, even the best designed resources can lead to rigid teaching.

With it, teachers can adapt with confidence and purpose.

Responsiveness requires content knowledge

What we are really talking about here is responsive teaching. However, having the ability to be responsive is not just a teaching skill. It also relies on content knowledge.

To respond well in the moment, teachers need to recognise what an error signals, which example to show next and how to adjust instruction without introducing confusion. That requires secure understanding of the content being taught.

This is particularly important in primary classrooms, where many teachers are non-specialists in mathematics. Asking teachers to be more responsive without supporting their subject knowledge places them in an impossible position. They are expected to make precise instructional decisions without the tools to do so.

Resources can help, but they cannot replace understanding. Slides and textbooks model one pathway, but they cannot anticipate every student response. When learning deviates from the expected route, teachers need to understand the content well enough to diagnose the issue and adjust.

If we want instruction to be responsive rather than robotic, we must also support teachers to enact responsiveness within specific curriculum areas, not just tell them to be more flexible.

A final thought

If explicit instruction ever feels robotic, it is usually because decision making has been replaced with compliance.

The real work of explicit instruction lives in the moments where teachers interpret evidence and choose what happens next.

That is what turns resources into instruction.

More info

If you would like to explore this thinking further, you can download the full guide that unpacks explicit instruction in mathematics, including modelling, practice, and decision making here.

And if you are looking for more structured support in understanding how these ideas connect at the lesson, curriculum, and school wide level, you can learn more about the Primary Maths Instruction Framework course here.

The focus is not on adding more resources, but on helping teachers and leaders understand what to keep, what to change, and why.

Most conversations about improving maths instruction begin with assumptions. We assume certain routines are in place, that modelling is clear or that students are getting enough practice. In reality, improvement starts when we stop guessing and describe what is actually happening in classrooms. Without a shared way to measure instruction, planning quickly becomes opinion driven rather than evidence-informed.

For leaders, this distinction matters. Strategic improvement depends less on ambition and more on diagnostic clarity.

Why description matters before decision-making

One of the most persistent problems in school improvement is that decisions are often made before the problem is properly described. Professional learning is selected, programs are adopted and new practices are introduced without a clear understanding of what is actually happening in classrooms.

This pattern is not new. Decades of research into teacher effectiveness and professional learning show that traditional professional development often starts at the wrong point. It begins with the delivery of new knowledge or strategies identified by someone external to the classroom, rather than with an analysis of what students and teachers actually need to improve learning (Muijs et al., 2014).

When the need is externally defined, goals belong to others. Teachers are asked to engage with ideas without first understanding why they matter or how they connect to their own practice. Engagement becomes optional, resistance becomes understandable and change remains shallow.

A second issue is lack of specificity. Much professional learning is too general to be useful. It is often divorced from the realities of teaching particular students in particular contexts (Muijs et al., 2014). Research consistently shows that professional learning has the greatest impact when it is tightly focused on specific challenges, grounded in classroom evidence and linked directly to student outcomes rather than abstract principles (Antoniou et al., 2015; Timperley et al., 2008).

There is also a deeper inconsistency at play. We know a great deal about how people learn, yet we often ignore these principles when designing learning for teachers. Effective instruction for students relies on clarity, modelling, feedback and deliberate practice, but professional learning frequently fails to mirror these same conditions. As a result, teachers are expected to adopt practices they have never experienced as learners themselves.

Finally, schools are regularly encouraged to adopt new approaches or innovations without robust evidence of impact. Whether driven by policy, technology, or trends, this cycle of adoption without evaluation leads to wasted time, wasted resources and initiative fatigue. What is missing is disciplined diagnosis and ongoing evaluation, rather than enthusiasm for the next solution.

All of this points to the same conclusion. Improvement does not start with choosing what to do next. It starts with accurately describing what is happening now. Without that clarity, even well intentioned decisions are unlikely to lead to meaningful change.

The purpose of the Effective Maths Instruction Scorecard

The Effective Maths Instruction Scorecard was designed to give leaders a clear and shared language for discussing maths instruction.

In less than fifteen minutes, leadership teams can rate nine core elements of instruction, including retrieval practice, modelling, guided practice, independent practice, opportunities to respond, lesson structure, and alignment to the stage of learning. Each element is described across four levels, from emerging through to highly effective.

What matters is not the total score itself.
What matters is what the score makes visible.

The descriptors provide a common reference point. Instead of debating whether modelling is “good enough”, leaders can point to specific indicators that describe what modelling actually looks like at different levels of quality.

This moves conversations away from opinion and toward evidence.

Linking the scorecard to explicit instruction

I recently released The Essential Guide to Explicit Instruction in Mathematics and if you’ve read that, the scorecard will feel immediately familiar.

Clear modelling.
Purposeful guided practice.
Delayed release to independent work.

The guide focuses on building understanding. It explains why explicit instruction matters, how it reduces cognitive load and what it looks like during the acquisition stage of learning.

The scorecard serves a complementary leadership function.

It answers a different question.
Are these practices visible, consistent and reliable across classrooms?

For leaders, this distinction is important. Knowing what good instruction looks like does not guarantee that it is happening consistently. Measurement bridges that gap.

Why the end of the year is the ideal time to use it

The end of the year is rarely the right moment to introduce new initiatives.
It is, however, the ideal time to take stock.

Completing the scorecard now allows leadership teams to step back from day to day pressures and look for patterns. Where are expectations clear. Where does practice vary. Which routines are secure and which are fragile.

Most schools find that their results cluster in predictable ways. Modelling may be relatively strong, while guided practice varies. Retrieval might be present, but inconsistent. Students may be released for independent practice too early in some classrooms and too late in others.

These patterns are far more useful than a long list of unrelated improvement goals.

Turning measurement into focused action

The final section of the scorecard provides suggested next steps based on whether a school sits in the emerging, developing, proficient or exemplary range.

Importantly, these recommendations do not call for new programs. They focus on tightening routines, clarifying expectations and aligning teaching more closely with the stage of learning.

For leaders, this creates a clear bridge between diagnosis and action.

The scorecard can be used to

• guide walkthrough focus

• prioritise coaching conversations

• shape professional learning plans

• monitor growth across terms

Rather than asking “What should we work on next year?”, leaders can ask a more productive question.

“What does the scorecard tell us matters most right now?”

When reflection needs support

For some leadership teams, diagnosing the problem is the easy part. The harder work is supporting teachers to change practice in a sustainable way.

That is where Implementing Effective Primary Maths Instruction sits.

This two day online course is designed for school leaders and middle leaders who are responsible for turning reflection into consistent classroom practice. It focuses on curriculum and lesson design, assessment aligned to the stage of learning and the leadership moves that support teacher growth without overload.

Leaders learn how to use tools like the scorecard not as accountability instruments, but as guides for coaching, modelling and shared improvement.

Register NOW

A disciplined place to start

If you are planning for next year, start with restraint.

Measure before you modify.
Describe before you decide.
Choose one priority that genuinely matters.

Improvement does not begin with new initiatives. It begins with clarity.

Download the Scorecard HERE

References

Antoniou, P., Kyriakides, L., & Creemers, B. P. (2015). The dynamic integrated approach to teacher professional development: Rationale and main characteristics. Teacher Development, 19(4), 535–552.

Muijs, D., Kyriakides, L., Van der Werf, G., Creemers, B., Timperley, H., & Earl, L. (2014). State of the art–teacher effectiveness and professional learning. School effectiveness and school improvement, 25(2), 231-256.

Timperley, H., Wilson, A., Barrar, H., & Fung, I. (2008). Teacher professional learning and development (Vol. 18). International Adacemy of Education.

Resources mentioned:

• The Knowledge Gap by Natalie Wexler

• The Writing Revolution by Judith Hochman and Natalie Wexler

• Beyond the Science of Reading by Natalie Wexler

• Why Don’t Students Like School by Daniel Willingham

You can connect with Natalie:

Twitter/X: @natwexler

Linkedin

Website: nataliewexler.com

Substack: http://nataliewexler.substack.com

You can connect with Brendan:

Twitter/X: @learnwithmrlee

Facebook: @learningwithmrlee

Linkedin: @brendan-lee-kft

Website: learnwithlee.net

Support the Knowledge for Teachers Podcast: 

https://www.patreon.com/KnowledgeforTeachersPodcast

The Primary Maths Instruction Framework For teachers

This is a three day online course for teachers where we focus on how learning happens and how to design maths lessons that support acquisition, build fluency and help students generalise what they know.

Register here

Implementing Effective Primary Maths Instruction For School Leaders

This is a two day online course for school and middle leaders and it is all about implementation. We look closely at curriculum and lesson design, assessment, coaching and the systems that help teachers change practice in a sustainable way.

Register here