"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.
Practice testing and distributed 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
"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)
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
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 smaller 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
“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”.
“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.
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.
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.
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) 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
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
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.
"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.
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.
Rohrer, D. & Taylor, K. (2006) The effects of overlearning and distributed practice on the retention of mathematics knowledge. Applied Cognitive Psychology, 20, 1209-1224.
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
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
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
When teachers teach the “right grain size” attainment is raised.
“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, in turn helps us to automate future problem solving - giving 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.
Sweller, J., van Merrienboer, J.J.G., & Paas, F.G.W.C. (1998). Cognitive architecture and instructional design. Educational Psychology Review, 10, 251-296.
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