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Rohrer, D. (2009). The effects of spacing and mixing practice problems. Journal for Research in Mathematics Education, 40, 4-17
Rohrer 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
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
Sweller 1998
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.
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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
Sweller 1998
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.
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.
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