Research: quick summary

This page is intended to show all research, that we reference, in alphabetical order by first named researcher.

Each has either a summary by us (in regular text)

or a quote or quotes from the researchers (in this quote format)

and sometimes also

  • a link to where we talk about the reference within this, the Customer Knowledge Base

  • a link to a freely available copy of the article.

Agarwal et al 2016

The benefits from retrieval practice are greater for students with lower working memory capacity.

Agarwal, P.K., Finley, J.R., Rose, N.S., & Roediger H.R., Benefits from retrieval practice are greater for students with lower working memory capacity Memory 25(6):1-8 August 2016

See smaller working memory

Bjork 1992

  • Easy to recall? then practice won’t add much to storage strength in Long Term Memory

  • Hard to recall? then practice will significantly increase storage strength in Long Term Memory

They coined the phrase desirable difficulties.

Bjork, R. A., & Bjork, E. L. (1992). A new theory of disuse and an old theory of stimulus fluctuation. In A. Healey, S. Kosslyn & R. Shriffin (Eds) From Learning processes to Cognitive Processes: essays in Honor of Willaim K Estes (Vol 2 pp 35-67) Hillside NJ: Erlbaum

See retrieval practice

Black 2001

"What is needed is a culture of success, backed by a belief that all can achieve. Formative assessment can be a powerful weapon here if it is communicated in the right way.”

"The formative assessment experiments produce typical effect sizes of between 0.4 and 0.7 : such effect sizes are larger than most of those found for educational interventions.  

• A gain of effect size 0.4 would improve performances of pupils in GCSE by between one and two grades.

• A gain of effect size 0.7, if realised in the recent international comparative studies in mathematics (TIMSS—Beaton et al., 1996), would raise England from the middle of the 41 countries involved to being one of the top 5.

Inside the Black Box Raising Standards Through Classroom Assessment Paul Black and Dylan Wiliam (2001)

See assessment for learning

Cox 2008

The gap between high- and low-achieving students was extended following the transition to secondary school.

Cox, S. & Kennedy, S. (2008). Students’ achievement as they transition from primary to secondary schooling: Report no. 1 on the students’ transition from primary to secondary schooling study. Research and Evaluation Team, Research Division, Ministry of Education, New Zealand. 

Dunlosky et al 2013

Practice testing and distributed (over time) practice (a.k.a. retrieval practice) are the only 2 of the 10 techniques considered which are given their “high-utility” rating.

Dunlosky, D., Rawson, K.A., Marsh, E.J., Nathan, M.J., Willingham, D.T., Improving students’ learning with effective learning techniques: Promising directions from cognitive and educational psychology, Psychological Science in the Public Interest, January 2013

See arguing for change

Ebbinghaus 1885

Did experiments to find out how we forget. He called a graph showing this die Vergessenskurve or in English the forgetting curve. It shows that as time goes on, memory fades. 

See retrieval practice and increasing interval retrieval practice

Education and Training Inspectorate 2016

With respect to low attainment and poor attendance:

While the correlation is evident, causation is more complex.

Part 1 Attendance in schools, DfE

EEF 2014

"Since the spacing effect was first discovered by Ebbinghaus in 1885, research has consistently shown that learning performance improves if multiple study sessions are separated in time (or “spaced”) rather than massed together.” (page 29-30)


They summarise that the “strength of evidence for educational effectiveness” of retrieval practice is high. (Page 10)

A Review of Educational Interventions and Approaches Informed by Neuroscience

EEF 2018

The evidence indicates a large dip in mathematical attainment as children move from primary to secondary school in England, which is accompanied by a dip in learner attitudes. There is very little evidence concerning the effectiveness of particular interventions that specifically address these dips. However, research does indicate that initiatives focused on developing shared understandings of curriculum, teaching and learning are important. Both primary and secondary teachers are likely to be more effective if they are familiar with the mathematics curriculum and teaching methods outside of their age phase. Secondary teachers need to revisit key aspects of the primary mathematics curriculum, but in ways that are engaging and relevant and not simply repetitive. Teachers’ beliefs about their ability to teach appear to be particularly crucial for lower-attaining students in Key Stage 3 mathematics … Evidence indicates a significant dip in mathematical attainment at transition. For example, in a large national study of primary attainment in England, Brown et al. (2008) found that, at the end of Year 7, a full year after the transition to secondary school, learners’ performance on a test of primary numeracy was below their performance at the end of Year 6 (page 163)


“there is no research evidence concerning the effectiveness of specific interventions in this area … Although some of the studies were conducted some time ago, there is no reason to suppose that the current situation is any different”(page 164)

Hodgen, J., Foster, C., Marks, R., & Brown, M. (2018). Evidence for Review of Mathematics Teaching: Improving Mathematics in Key Stages Two and Three: Evidence Review. London: Education Endowment Foundation.

EEF 2021a

Retrieval practice

The findings in this area are mostly positive, suggesting moderate effect sizes, but there were an appreciable number of neutral or negative results. (page 78)

“The overall evidence is therefore positive for retrieval practice. One area of concern in the main results was the low ecological validity of the studies in the review: many interventions were wholly scripted with a standardised procedure.” (page 92)

Cognitive Science in the classroom - Evidence and practice review

… but are the benefits of spacing and retrieval practice additive?

“For example, many teachers and practice review sources firmly linked retrieval practice and spaced practice. Both are forms of desirable difficulty for which the effects may not be entirely additive, as explained in a point by Putnam and Roediger:

‘Combining retrieval practice with spacing creates an interesting situation, however, because retrieval practice is more effective when it is successful, but increasing the gaps between retrieval practice opportunities makes retrieval more difficult (less successful). Thus, the positive effects of spacing and retrieval practice may be working against one another, at least when no feedback is provided on the test.’ (Putnam and Roediger, 2018, p. 177) page 84.

However if one can get the timing right, and timely practice usually can, one can increase the spacing between retrieval practices and ensure the learner is successful (because the timing is personalised, so one can gradually increase the durability of recall-ability) we should see the benefits of retrieval practice and spacing.

EEF 2021b

Research on teaching using worked examples

“suggests a small to moderate positive effect of using worked examples for secondary-age students in maths and science, compared to conventional problem-solving techniques” (page 104)

Cognitive Science in the classroom - Evidence and practice review

EEF 2021c

Teaching using scaffolding

Overall, evidence suggests that well-targeted scaffolds, guidance, or schema-based supports are an effective approach to support students to solve problems or learn from complex tasks in Key Stage 2 to Key Stage 4 (age 8 to 16) in a range of subjects. (page 111)

Cognitive Science in the classroom - Evidence and practice review


EEF 2021d

Managing cognitive load

Overall, the evidence is promising and indicates the value and importance of teachers seeking to optimise learners’ cognitive load. There are numerous studies showing appreciable positive effects for strategies to manage cognitive load within the evidence we have. There are also appreciable numbers of neutral and negative results, suggesting complexity in the principles and challenges of making it work in practice. (page 118)


Our confidence is in the value of optimising cognitive load rather than a specific strategy for doing so, or for specific learner needs.’ The main results also suggested great complexity and practical challenges for optimising cognitive load in practice. (page 134)

Cognitive Science in the classroom - Evidence and practice review

EEF 2021e

Within-class attainment grouping

Since Danielle Mason 2018 EEF Blog: Grouping pupils by attainment, what does the evidence say?

“Within-class attainment grouping’ shows a positive average attainment impact, equivalent to around +3 months of additional progress.”

The impact has been downgraded to + 2 months

El-Hage et al 2006

Learners living with trauma are likely to have a smaller working memory capacity than their peers.

El-Hage, W., Gaillard, P., isingrini, M., Belzung, C., Trauma-related deficits in working memory, February 2006, Cognitive Neuropsychiatry

Elliot 2010

When primary school teachers use strategies which reduce the working memory requirements of tasks, proved to be a predictor of the progress of learners with smaller working memory relative to their peers with a larger working memory capacity.

Elliott, J., Gathercole, S.E., Alloway, T.P., Holmes, J. & Kirkwood, H. An Evaluation of a Classroom-Based Intervention to Help Overcome Working Memory Difficulties and Improve Long-Term Academic Achievement. Journal of Cognitive Education and Psychology, 9, 227-250

See also smaller working memory

Farah et al 2006

Learners living with poverty are likely to have a smaller working memory capacity than their peers.

Farah M.J., Shera, D.M., Savage, J.H., Betancourt, L., Giannetta, J.M., Brodsky, N.L., Malmud, E.K., Hurt, H. Childhood poverty: Specific associations with neurocognitive development. Brain Res 1110 : 166 - 174

See also smaller working memory

Gathercole 2008

“The majority of children with poor working memory are slow to learn in the areas of reading, maths and science, across both primary and secondary school years”.

Learners with smaller working memories experience a double whammy of disadvantage -

  • they are more reliant on chunks in long term memory to learn and yet

  • are less likely to build these chunks in lessons.

Learning difficulties arise because they

“are unable to meet the memory demands of many structured learning activities” and “as a consequence, their working memory becomes overloaded ... information that is needed to guide the ongoing learning activity ... is lost”.

Gathercole, S. Working memory in the classroom, Presidents’ Award Lecture at the Annual Conference of The British Psychological Society

See smaller working memory

Gobet 2005

“Use an ‘improving spiral’, where you come back to the same concepts and ideas and add increasingly more complex new information”

Deliberate practice of similar but different problems assists the learner in building chunks in long term memory, which enables learning to be retained. Chunks also provide perceptual cues or triggers, so that the expert (or in our case the low attaining learner) can quickly and easily decide which chunk or chunks are likely to be useful to help solve a given problem.

Gobet, F. (2005). Chunking models of expertise: Implications for education. Applied Cognitive Psychology, 19, 183-204.

See chunk-based learning

Gobet 2012

A clear prediction of chunk-based theories is that individual differences play a large role in the early stages of learning

Chunk-based models actually warn us against any excess of optimism in the use of new technologies, as long as they do not help circumvent the key limiting constants of human cognition (i.e. attention, STM = working memory , and learning rates).

Gobet, F & Lane, P 2012, Chunking mechanisms and learning. in NM Seel (ed.), Encyclopedia of the Sciences of Learning. Springer, pp. 541-544.

See chunk-based learning

Goddard 2020a

Comparing 2 years maths teaching from the 4 lowest attaining sets, we find the timely practice class increases the median GCSE score from year 9 to year 11, more than the 3 business as usual classes (2 of which were previously more highly attaining).

Goddard 2020b

Guidance on the most worthwhile activities during lockdown:

Factoring in retrieval practice to remote education activities will help [the teacher] to maintain firm foundations for when learning hopefully continues back in school in September. This must be our priority: extending the durability of current learning, with the icing on the cake being new learning.

Much retrieval practice in schools is still inadvertent. End-of-unit and end-of-term tests are high-stakes, summative assessments. These can and should be missed out during school closure. Instead we should use well-timed retrieval practice to embed learning. For low, middle and high-attaining learners the suggested wait between teaching and first practice is 1 to 3 days, 7 to 10 days and 14 days respectively

Goddard 2022

Two types of scaffolding make learning easier for learners with smaller working memories.

  1. completion (either of a scaffold diagram or of a partial solution )

  2. gradually increasing complexity ( or )

Our evidence comes from proportion of retrieval practice questions which are given feedback and/or given assessment outcomes.

Hattie 2007

The most effective forms of feedback provide cues or reinforcement to learners; are in the form of video-, audio-, or computer-assisted instructional feedback; and/or relate to goals. 

The Power of Feedback REVIEW OF EDUCATIONAL RESEARCH 2007 77: 81 DOI: 10.3102/003465430298487 John Hattie and Helen Timperley is behind a pay wall here is a summary

See feedback

Hattie 2013

The Goldilocks principle of challenge, not too hard and not too easy. Let learners deliberately practice and coach them to help learners reduce the gap between where they are and where they want to be.

see 10:30 know deeply what the learners know already and share what success looks like

Hogan 1997

8 top tips on scaffolding

Hogan, K., & Pressley, M. (Eds.). (1997). Scaffolding learner learning: Instructional approaches and issues. Cambridge, MA: Brookline Books.

See scaffolding and fading scaffolding

Homes 2018

A small proportion of learners with smaller working memory capacities, don’t go on to become low attaining learners in maths, but most do.

Joni Holmes - Working memory and classroom learning, Cambridge University Press ELT 2018

Holmes 2010

Place holding problems, missing steps and giving up are clearly cited, as working memory overload symptoms. (However, muddling methods, my 3rd sign of working memory overload for maths teachers - a combination of place holding and missing steps isn’t given).

Joni Holmes, Susan E. Gathercole, and Darren L. Dunning, Poor Working Memory: Impact and Interventions. In Joni Holmes, editor: Advances in Child Development and Behavior, Vol. 39, Burlington: Academic Press, 2010, pp. 1-43. ISBN: 978-0-12-374748-8

Kang 2016

When learners do repeated retrieval practice attainment is raised.

Kang, S.H.K. (2016) Spaced Repetition Promotes Efficient and Effective Learning: Policy Implications for Instruction. Policy Insights from the Behavioral and Brain Sciences, 3 (1), 12-19

See retrieval practice and increasing interval retrieval practice

Kang 2014

Expanding interval, as opposed to fixed-interval, retrieval practice is more efficient.

Retrieval practice over the long term: Should spacing be expanding or equal-interval? Kang, S.H.K., Lindsey, R.V., Mozer, M.C., and Pashler, H. Psychonomic Society, Inc. 2014

See retrieval practice and increasing interval retrieval practice

Kluger 1996

Feedback should be about how to improve the task and not ego involving

Kluger, A. N., & DeNisi, A. (1996). The effects of feedback interventions on performance: A historical review, a meta-analysis, and a preliminary feedback intervention theory. Psychological Bulletin, 119(2), 254-284. 

See feedback

Koh 2018

Bite-Sized lectures (3 x 20 minute lecture + practice sessions) show statistically significant improvements in assessed learning outcomes over the traditional one hour lecture.

Koh, N. S., Gottipati, S. and Shankararaman, V. Effectiveness of bite-sized lecture on student learning outcomes. (2018). 4th International Conference on Higher Education Advances (HEAd’18), Valencia, Spain, 2018 June 20-22: Proceedings. 515-523. Research Collection School Of Information Systems.

Kornell 2009

The title says it all: Unsuccessful Retrieval Attempts Enhance Subsequent Learning

Kornell et al 2009 Nate Kornell, Matthew Jensen Hays, and Robert A. Bjork Journal of Experimental Psychology Vol. 35, No. 4, 989–998

Kulik 1990

When teachers hold back from teaching new learning until the learners have mastered all the pre-requisite skills, attainment is raised.

Effectiveness of mastery learning programs: A meta-analysis Kulik, C.C., Kulik, J.A., & Bangert-Drowns, R.L.

See mastery learning

Larkin 2001

Through interviewing teachers experienced in scaffolding, she gives 5 top tips. I’ve found these more useful than Hogan' s 8 top tips.

Larkin, M. J. (2001). Providing support for student independence through scaffolded instruction. TEACHING Exceptional Children, 34(1), 30-34.

See scaffolding and fading scaffolding

Manning 2021

Medical residents were taught with 4 to 5 brief (8 minute) teaching micro-sessions instead of one 40 to 50 minute teaching session. 

The BST group scored significantly higher than the control group. However there was no significant difference in post test scores between BST and control groups in tests two and six weeks later. (page 8 )

Manning, K.D., Spicer, J.O., Golub, L. et al. The micro revolution: effect of Bite-Sized Teaching (BST) on learner engagement and learning in postgraduate medical education. BMC Med Educ 21, 69 (2021). 


Mayfield 2002

For what we consider higher order skills, such as generalising and problem solving, research suggests, Mayfield & Chase (2002), that when students are using two different pieces of knowledge/skills/methods to learn a third, the students are most successful if both the two existing pieces of knowledge/skills/methods are more strongly embedded before the third is learned. 

Mayfield & Chase (2002). The effects of cumulative practice on mathematics problem solving. Journal of applied behavioural analysis, 35, 105-123.  

See cumulative practice

Moran 2016

Anxiety effectively reduces working memory capacity.  

whether [anxiety is] self-reported or experimentally induced it is related to poorer performance across a wide variety of tasks.

Moran TP. Anxiety and working memory capacity: A meta-analysis and narrative review. Psychol Bull. 2016 Aug;142(8):831-864. doi: 10.1037/bul0000051. Epub 2016 Mar 10. PMID: 26963369

Oakley and Sejnowski

Week 1: big thinking and small thinking can’t be done at the same time, try the 4 minute video (with adverts) or sign up to the course for free (see link below)

Week 2: chunk based theory - see the 48 minutes of videos on building and using chunks.

Pan and Sana 2021

investigated the relative efficacy of pre testing (i.e., errorful generation) and post testing (i.e., retrieval practice).

Pre testing involves taking tests before to-be-learned information is studied,

whereas post testing involves taking tests after information is studied.

The key phrase used to describe this is test potentiated learning.

The experiments are all based on learning from reading a passage of text - so may not be as applicable to maths learning. If one only allows one test, then pretesting seems to be more effective than posttesting.

Of course if one wants to extend recall beyond the 48 hour delay and and one allows several retrieval practice questions, then retrieval practice with feedback can be expected to be more effective. Nonetheless pretesting, can be a valuable tool.

Pashler 2007

Giving feedback when the learner can’t retrieve (recall the learning) makes retrieval practice more effective. Feedback after a nights sleep is more effective than immediate feedback.

Pashler, Rohrer, Cepeda & Carpenter (2007). Enhancing learning and retarding forgetting: Choices and consequences. Pyschonomic Bulletin & Review 2007, 14 (2) 187-193

Overlearning, getting learners to practise more questions once the learners have “got the skill”, adds little durability to learning.

See feedback

Ramirez 2017

"Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics ... this proof-of-concept study suggests that children may deal with threatening classroom experiences by forgetting important course relevant knowledge."

Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study Front Psychol. 2017; 8: 2087.

Published online 2017 Dec 4. doi: 10.3389/fpsyg.2017.02087

See maths anxiety

Rohrer 2006

Overlearning, the most popular method for embedding learning in learners in maths lessons - doesn’t despite its great name - work very well. Even just one retrieval practice attempt makes significant improvements to the retention of maths learning than overlearning does.

Rohrer, D. & Taylor, K. (2006) The effects of overlearning and distributed practice on the retention of mathematics knowledge. Applied Cognitive Psychology, 20, 1209-1224.

See overlearning

Rohrer 2009

When learners see a list of problems, all of the same kind, they know the strategy to use before they even read the problem [that's] like riding a bike with training wheels. [With mixed practice] each problem is different from the last one, which means kids must learn how to choose the appropriate procedure — just like they had to do on the test.

Rohrer, D. (2009). The effects of spacing and mixing practice problems. Journal for Research in Mathematics Education, 40, 4-17

See retrieval practice

Schiefele 1995

Although culturally we believe motivation is the driver i.e. that motivation increases success, in fact the driver is success, success increases motivation.

Schiefele, U., & Csikszentmihalyi, M. Motivation and Ability as Factors in Mathematics Experience and Achievement, Journal for Research in Mathematics Education, Vol. 26, No. 2, (March 1995), pp 163-181

Stewart 2018

Ordinarily between six weeks and 1.8 months of maths learning is lost during the summer holiday.

Stewart, Watson & Campbell: The cost of school holidays for children from low income families. Childhood, Vol 25, 2018.

Sweller 1998


“Schema construction has two functions: the storage and organization of information in long- term memory and a reduction of working memory load.”

People have very limited working memory capacities so attempting reasoning in working memory is inefficient and often error prone. Whereas prior problem solving, which helps us create schema (a.k.a. chunks) helps us to automate future problem solving. it is assumed this is because this gives us more working capacity for the unfamiliar parts of a problem. Even a very complex schema can be used by working memory as a single element. Building and using an increasing number of ever more complex schemas, by

“combining elements of lower level schemas in long term memory”

allows skilled performance to develop.

When teachers teach the “right grain size” attainment is raised (summary of van Merrienboer 1997)


Sweller, J., van Merrienboer, J.J.G., & Paas, F.G.W.C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251-296.

See chunk-based theory

Taylor 2010

When practice problems are blocked, however, learners can successfully solve a set of practice problems without learning how to pair a problem with the skill. Indeed, because all of the problems relate to the topic—typically the one presented in the immediately preceding lesson—learners can choose the appropriate procedure for each practice problem before they read the problem. While this reduces the difficulty of the practice problems, learners are effectively relying on a crutch.


Taylor, K. & Rohrer, D. The Effects of Interleaved Practice. Appl. Cogn. Psychol. 24, 837-848, doi:10.1002/acp.1598 (2010). See especially the graph at the top of page 843

See interleaving

van de Pohl 2010

Teachers should fade scaffolding after teaching. The duration over which the “fade” should occur is not quantified, but this writer thinks during the course of a single lesson is too fast for many low attaining learners.

van de Pohl, J., Volman, M. & Beishuizen, J. Educ Psychol Rev (2010) Scaffolding in Teacher- Student Interaction: A Decade of Research 22: 271

See scaffolding

van Merrienboer 1997

When teachers teach the “right grain size” attainment is raised.

Summary quote from Sweller 1998

target group analysis should be integrated with knowledge analysis (hierarchical analysis of the material to be learned) when designing instruction, so that the knowledge can be communicated to the learners at the right grain size (van Merrienboer, 1997)

Van Merrienboer, J. J. G. (1997). Training Complex Cognitive Skills: A Four-Component Instructional Design Model for Technical Training, Educational Technology Publications, Englewood Cliffs, NJ. 

Wiggins 2012

7 keys to effective feedback

See feedback

Wiliam 2009

When teachers find out what learners know before and during teaching and alter their teaching responsively to this information, attainment is raised.

Assessment for Learning: why, what and how, Dylan Wiliam, An Inaugural Professorial Lecture, 2009, Institute of Education, University of London

Wiliam 2013

Good assessment can help learners learn at about double the rate

Wiliam 2016

How not to fly a plane

See assessment for learning