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This episode of the Mr Barton Maths Podcast is kindly supported by Arc Maths.

You can find more information about their app for helping students remember those crucial maths skills – and register for a free trial – at arceducation.co.uk/for-schools/

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Hello, and welcome to another episode of the Mr Barton Maths Podcast, with me Craig Barton.

This time around I spoke to Paul Rowlandson

This marks Paul’s second appearance on the show, following his debut way back in February 2017. Paul is a maths teacher with a strong interest in research – so much so that he is now embarking upon a doctorate. He also holds the prestigious title of being Jo Morgan’s favourite maths blogger. His “Thinking about” series of posts are my particular favourite, where Paul explains in great detail how he thinks about putting together a sequence of lessons on a given topic, reflecting on his past mistakes and sharing the logic behind his new question choices, activities and so on. For teachers on any experience, they are gold dust.

Today we certainly touch upon the importance of such choices as we take a deep dive into interleaving. As I tell Paul, I because obsessed with interleaving when I first came across it in the work of Robert Bjork as part of my research for How I Wish I’d Taught Maths. But – on reflection, and especially having seen Paul’s researchEd talk – I am not sure I fully understood the nuances, the explanatory mechanisms, or the power of it. Fortunately, Paul is here to help, and after this conversation I feel much better informed, and have some practical strategies to apply to my sequencing, worksheet design, choice of examples, low-stakes quizzes and more. And I hope you will too!

You can download an mp3 of the episode here, use the player at the bottom of the page, or subscribe on all major podcast platforms so you never miss an episode.

Research we discussed:

• Birnbaum, M. S., Kornell, N., Bjork, E. L., & Bjork, R. A. (2013). Why interleaving enhances inductive learning: The roles of discrimination and retrieval. Memory & Cognition, 41(3), 392–402. https://doi.org/10.3758/s13421-012-0272-7
• Carvalho, P. F., & Goldstone, R. L. (2014). Putting category learning in order: Category structure and temporal arrangement affect the benefit of interleaved over blocked study. Memory & Cognition, 42(3), 481–495. https://doi.org/10.3758/s13421-013-0371-0
• Eglington, L. G., & Kang, S. H. K. (2017). Interleaved Presentation Benefits Science Category Learning. Journal of Applied Research in Memory and Cognition, 6(4), 475–485. https://doi.org/10.1016/j.jarmac.2017.07.005
• Foster, N. L., Mueller, M. L., Was, C., Rawson, K. A., & Dunlosky, J. (2019). Why does interleaving improve math learning? The contributions of discriminative contrast and distributed practice. Memory & Cognition, 47(6), 1088–1101. https://doi.org/10.3758/s13421-019-00918-4
• Kang, S. H. K., & Pashler, H. (2012). Learning Painting Styles: Spacing is Advantageous when it Promotes Discriminative Contrast. Applied Cognitive Psychology, 26(1), 97–103. https://doi.org/10.1002/acp.1801
• Kornell, N., & Bjork, R. A. (2008). Learning Concepts and Categories: Is Spacing the “Enemy of Induction”? Psychological Science, 19(6), 585–592. https://doi.org/10.1111/j.1467-9280.2008.02127.x
• Kornell, N., Castel, A. D., Eich, T. S., & Bjork, R. A. (2010). Spacing as the Friend of Both Memory and Induction in Young and Older Adults. Psychology and Aging, 25(2), 498–503. https://doi.org/10.1037/a0017807
• Rohrer, D., Dedrick, R. F., & Burgess, K. (2014). The benefit of interleaved mathematics practice is not limited to superficially similar kinds of problems. Psychonomic Bulletin & Review, 21(5), 1323–1330. https://doi.org/10.3758/s13423-014-0588-3
• Rohrer, D., Dedrick, R. F., Hartwig, M. K., & Cheung, C.-N. (2019). A randomized controlled trial of interleaved mathematics practice. Journal of Educational Psychology. https://doi.org/10.1037/edu0000367
• Rohrer, D., Dedrick, R. F., & Stershic, S. (2015). Interleaved Practice Improves Mathematics Learning. Journal of Educational Psychology, 107(3), 900–908. https://doi.org/10.1037/edu0000001
• Sana, F., Yan, V. X., & Kim, J. A. (2017). Study sequence matters for the inductive learning of cognitive concepts. Journal of Educational Psychology, 109(1), 84–98. https://doi.org/10.1037/edu0000119
• Taylor, K., & Rohrer, D. (2010). The effects of interleaved practice. Applied Cognitive Psychology, 24(6), 837–848. https://doi.org/10.1002/acp.1598
• Wahlheim, C. N., Dunlosky, J., & Jacoby, L. L. (2011). Spacing enhances the learning of natural concepts: An investigation of mechanisms, metacognition, and aging. Memory & Cognition, 39(5), 750–763. https://doi.org/10.3758/s13421-010-0063-y
• Zulkiply, N. (2013). Effect of Interleaving Exemplars Presented as Auditory Text on Long- term Retention in Inductive Learning. Procedia – Social and Behavioral Sciences, 97, 238–245. https://doi.org/10.1016/j.sbspro.2013.10.228
• Zulkiply, N., & Burt, J. S. (2013). INDUCTIVE LEARNING: DOES INTERLEAVING EXEMPLARS AFFECT LONG-TERM RETENTION? 10, 23.

On Twitter Paul is: @Mr_Rowlandson
Paul’s blog is: ponderingplanning.wordpress.com

My free course all about the Ultimate Scheme of Work 2.0 is here
My new course, Supercharging worked examples using variation and self-explanation, is here

Paul Rowlandson’s Big 3
1. What Does It Mean to be Evidence Informed – Tom Sherrington https://teacherhead.com/2021/07/19/what-does-it-mean-to-be-evidence-informed-in-teaching/…
2. Deconstructing Teacher-Centeredness and Student-Centeredness Dichotomy: A Case Study of Shanghai Mathematics Practice – Huang & Leung https://files.eric.ed.gov/fulltext/EJ845852.pdf…
3. Solving Algebra and Other Story Problems with Simple Diagrams: A Method Demonstrated in Grade 4-6 Texts Used in Singapore – Sybilla Beckman https://pennance.us/home/downloads/3041/beckmann.pdf

My usual plugs:

• You can help support the podcast (and get an interactive transcript of all new episodes) via my Patreon page at patreon.com/mrbartonmaths
• If you are interested in sponsoring an episode of the show, then please visit this page
• You can sign up for my free Tips for Teachers newsletter and my free Eedi newsletter
• My online courses are here: craigbarton.podia.com
• My books are “Tips for Teachers“, “Reflect, Expect, Check, Explain” and “How I wish I’d taught maths”