## Key Ideas > [!abstract] Core Concepts > > - **Prioritises hands-on over learning**: Emphasises interactive tasks and engagement rather than systematic knowledge building > - **Cognitive overload risk**: Complex activities can overwhelm students with irrelevant details instead of mathematical thinking > - **Memory is residue of thought**: Students may think about cutting, arranging, or matching rather than actual mathematical concepts ## Definition An activity-based curriculum prioritises hands-on activities and interactive tasks over direct instruction and structured content delivery, often leading to gaps in foundational knowledge. ## Connected To [[Engagement]] | [[Motivation]] | [[Non-Explicit Teaching]] | [[Cognitive Load Theory]] | [[When Will I Ever Need This]] | [[Knowledge-Based Curriculum]] --- ## Memory and attention in activity-based learning An activity-based curriculum may get students thinking, but not necessarily about mathematics. Since memory is the residue of thought (Willingham, 2009), students generally do not learn effectively in this type of curriculum when their attention is diverted to activity mechanics rather than mathematical concepts. Engagement in cutting, arranging, or matching does not equal engagement in mathematical thinking. >[!Example] The case of $18 \times 5$ > > Jo Boaler and the DoE numeracy consultants I've met love to produce > and ask students (or conference attendees) to find as many ways as they can to find different ways of performing the calculation $18 \times 5$. > > |Doubling & Halving|Distributive Law|Factorisation| > |---|---|---| > |$18 \times 10 \div 2$| $5 \times 10 + 5 \times 8$| $2 \times 5\times 9$| > > This is an appropriate activity for students who are already experts; it helps them develop [[fluency]] in using different arithmetic methods. > > However, this exercise is accompanied by the argument that memorising [[multiplication facts]] is unnecessary if students can derive the facts from other methods. This is false. > > When selecting activities, it is crucial to ensure they are appropriate for the students' level of expertise. Novices require explicit teaching to build foundational knowledge, whereas relative experts can handle activities with more superficial contexts due to their greater cognitive capacity. ## Contextualisation and motivation When selecting challenging academic topics, asking "What are the most [[Motivation|motivating]] contexts for learning?" can be misconceived for several reasons. A classroom contains 30 students with different interests. An [[Engagement|engaging]] lesson combining probability and cricket might intrigue cricketers but lead to [[Cognitive Load Theory|cognitive overload]] for students unfamiliar with the sport (Sweller et al., 2019). Finding universally motivating contexts is impossible. Mathematics involves thinking and solving problems. These problems do not necessarily require [[When Will I Ever Need This|real-world applications]]. Crosswords and Rubik's cubes engage people through puzzle satisfaction and problem-solving challenge without real-world utility. Mathematical puzzles similarly build logical thinking through pure reasoning. Contrived "real-world" problems often create artificial and confusing contexts that add cognitive load without enhancing understanding. The notion that everything must be "relevant" to children represents a limited view of professional teaching. The idea that children can only learn through their own interests and that asking them to consider things outside of that somehow beats the love of learning out of them is demeaning to both teachers and students. It assumes children incapable of intellectual growth beyond immediate interests. Teachers contribute most by introducing students to worlds beyond the limited borders of their own experience, allowing them to see the previously unseen, and make new enriching connections that were unavailable to them. Education expands horizons; it does not merely validate existing preferences. ## Activity structures and efficiency Tarsia activities exemplify the tension between engagement and learning efficiency. These jigsaw puzzles require students to match questions to answers. They are popular because they are "hands-on" and keep students motivated and engaged. However, student attention focuses on cutting out pieces neatly, finding the answer pieces, and arranging pieces so edges match properly, with minimal time thinking about actual questions (Willingham, 2009). The same questions could be completed in a quarter of the time with a worksheet (Kirschner et al., 2006; Mayer, 2004). Given classroom time constraints, these activities often waste valuable learning opportunities. More efficient alternatives include direct question practice that focuses attention on mathematical thinking (Sweller, 1988), pure mathematical problems that avoid cognitive overload from elaborate contexts (Sweller et al., 2019), individual then pair work that provides clear accountability, and intrinsically interesting puzzles that generate natural engagement without forced real-world connections. ## Appropriate uses of activities Engaging activities can serve as rewards or consolidation in end-of-term contexts when core learning objectives have already been achieved, students need a break from intensive learning, relationship building is the primary goal, or time pressure is not a concern. In these situations, the opportunity cost of activity-based approaches is lower, and their motivational benefits can outweigh efficiency concerns. Effective activity selection requires focusing on mathematical thinking rather than activity engagement. Teachers should choose activities where the cognitive effort goes toward the learning objective, avoid superficial contexts that distract from mathematical reasoning, and recognise that intrinsic mathematical beauty can be more engaging than forced relevance. ## References Kirschner, P. A., Sweller, J., & Clark, R. E. (2006). Why minimal guidance during instruction does not work: An analysis of the failure of constructivist, discovery, problem-based, experiential, and inquiry-based teaching. *Educational Psychologist*, 41(2), 75-86. https://doi.org/10.1207/s15326985ep4102_1 Mayer, R. E. (2004). Should there be a three-strikes rule against pure discovery learning? *American Psychologist*, 59(1), 14-19. https://doi.org/10.1037/0003-066X.59.1.14 Sweller, J. (1988). Cognitive load during problem solving: Effects on learning. *Cognitive Science*, 12(2), 257-285. https://doi.org/10.1207/s15516709cog1202_4 Sweller, J., van Merriënboer, J. J. G., & Paas, F. (2019). Cognitive architecture and instructional design: 20 years later. *Educational Psychology Review*, 31(2), 261-292. https://doi.org/10.1007/s10648-019-09465-5 Willingham, D. T. (2009). *Why don't students like school? A cognitive scientist answers questions about how the mind works and what it means for the classroom*. Jossey-Bass. ---