Introduction

For many years, school curriculum resources have been designed without explicit reference to research evidence and without extensive trialling in classrooms (Burkhardt & Schoenfeld, 2003; Foster et al., 2021). There are now increasing calls for the design of school curriculum materials to be informed by the best-available research evidence. But what exactly does that mean and how can it be achieved?

Over the past few years, as a team of researchers at Loughborough University, we have been attempting to design such a curriculum. In partnership with schools, we have developed materials that take account of the education literature as well as research into educational design and cognitive science. Our curriculum comprises a complete set of free resources for teaching mathematics to ages 11–14 (the LUMEN Curriculum).

In this blog post, we draw on our recent article in the Curriculum Journal (Foster et al., 2024) to consider some of the tensions that emerged as we sought to apply principles from cognitive science to our curriculum design.

‘For many years, school curriculum resources have been designed without explicit reference to research evidence and without extensive trialling in classrooms.’

Redundancy versus clarity

The ‘coherence principle’ recommends avoiding redundant visuals or information which does not directly serve the learning goal (Mayer, 2020). We found that this was sometimes in tension with clarity, where improving clarity meant making explanations longer, presenting ideas in more than one way (such as multiple representations (Foster, 2022)), or including images that risked redundancy, especially for more ‘expert’ students.

Seductive details versus richness

The ‘seductive details principle’ recommends avoiding interesting information which is irrelevant to the instructional goal (Rey, 2012). We often experienced a tension with this principle, wanting to include rich material which we felt was valuable, but perhaps not essential. For example, we concluded that including aspects of the history of mathematics was important from a decolonising perspective (Foster et al., 2022) and to pique students’ interest.

Personalisation and emotional design versus abstraction

The ‘personalisation principle’ recommends using social cues to prime a social response from the student, and we applied this principle throughout through fictitious student characters. We particularly used characters to model ‘being wrong’ as a positive learning opportunity. Although we found this principle to be in tension with the ‘abstract’ nature of much mathematics, we used personalisation to help students relate to concrete, real-life scenarios.

Spatial contiguity and signalling versus parsimony

The ‘spatial contiguity principle’ (derived from the ‘split-attention effect’) recommends placing corresponding text and pictures as close together as possible, and the ‘signalling principle’ recommends using arrows or colour to guide students’ attention to important information (Mayer, 2020). These principles allowed us to improve clarity and readability, but they required a balance to avoid materials becoming overcrowded or overwhelming. For example, we often used colour to highlight different variables or mathematical structures, but we were mindful of colour becoming overwhelming or disadvantaging to students with colour-blindness.

Pre-training and worked examples versus exploration

The ‘pre-training principle’ recommends recapping essential concepts or terminology before an explanation, while the ‘worked example principle’ recommends using worked examples to teach new processes. We found these principles valuable but in tension with giving students the freedom to explore ideas before presenting a solution. We employed faded worked examples (removing later steps as students’ competence increases (see for example Renkl, 2021)) and questioning to encourage self-explanation or considering students’ own approaches before being shown a method.

Conclusion

The tensions that we have set out in our article and here represent some of the challenges of applying cognitive science research to curriculum design and highlight the importance of future research exploring how these principles interact when applied simultaneously. This research has been extremely useful in enhancing our curriculum design and highlights that these principles cannot be applied mechanically. We encourage other designers to consider similar tensions when applying these principles in their own contexts.

This blog post is based on the article ‘Challenges in applying principles from cognitive science to the design of a school mathematics curriculum’ by Colin Foster, Bethany Woollacott, Tom Francome, Chris Shore, Caroline Peters and Hannah Morley, published by the Curriculum Journal.

References

Burkhardt, H., & Schoenfeld, A. H. (2003). Improving educational research: Toward a more useful, more influential, and better-funded enterprise. Educational Researcher, 32(9), 3–14. https://doi.org/10.3102/0013189X032009003

Foster, C. (2022). Using coherent representations of number in the school mathematics curriculum. For the Learning of Mathematics, 42(3), 21–27. https://repository.lboro.ac.uk/articles/journal_contribution/Using_coherent_representations_of_number_in_the_school_mathematics_curriculum/20066657

Foster, C., Francome, T., Hewitt, D., & Shore, C. (2021). Principles for the design of a fully-resourced, coherent, research-informed school mathematics curriculum. Journal of Curriculum Studies, 53(5), 621–641. https://doi.org/10.1080/00220272.2021.1902569

Foster, C., Barichello, L., Bustang, B., Najjuma, R., & Saralar-Aras, İ (2022). Decolonizing educational design for school mathematics. For the Learning of Mathematics, 42(2), 9–14. https://repository.lboro.ac.uk/articles/journal_contribution/Decolonizing_educational_design_for_school_mathematics/19093382

Foster, C., Woollacott, B., Francome, T., Shore, C., Peters, C., & Morley, H. (2024). Challenges in applying principles from cognitive science to the design of a school mathematics curriculum. Curriculum Journal. Advance online publication. https://doi.org/10.1002/curj.249

Mayer, R. E. (2020). Multimedia Learning (3rd ed.). Cambridge University Press.

Renkl, A. (2021). The worked example principle in multimedia learning. In R. E. Mayer & L. Fiorella (Eds.), The Cambridge handbook of multimedia learning (3rd ed., pp. 231–240). Cambridge University Press. https://doi.org/10.1017/9781108894333.023

Rey, G. D. (2012). A review of research and a meta-analysis of the seductive detail effect. Educational Research Review, 7(3), 216–237. https://doi.org/10.1016/j.edurev.2012.05.003

Slavin, R. E. (2002). Evidence-based education policies: Transforming educational practice and research. Educational Researcher, 31(7), 15–21. https://doi.org/10.3102/0013189X031007015