Key ideas
Core concepts
- Direct application of specific knowledge, such as factorising quadratics, may rarely be needed outside school. Knowledge is better valued for the satisfaction of knowing and for intellectual enrichment than for mundane applications.
- Contrived real-world contexts can distract from mathematical thinking and fail to convince sceptical students.
Connected to
Motivation | Activity-Based Curriculum | Non-Explicit Teaching | Surface and Deep Structure
“When will I ever need this?” is one of teaching’s persistent challenges. It often prompts teachers to devise elaborate justifications connecting quadratic factorisation to career prospects or Shakespeare to social media success, or to relate everything students are learning to “the real world” through STEM, Project-Based Learning, or superficial contexts. This response accepts a flawed premise: that learning requires immediate, obvious practical application to justify the effort.
The reality is more complex. Mathematical procedures like factorising quadratics, or even basic algebra, may never appear in most students’ adult lives (Lave, 1988). The necessity of learning arithmetic is questioned when calculators are readily available. Convincing students to study subjects like Shakespeare can be challenging when they see examples of success that seem unrelated to formal education, such as YouTubers, sports stars, or tradespeople who did not complete high school.
This framing misses education’s deeper purpose. Learning for the satisfaction of knowing (Dewey, 1916; Hirsch, 1996) and for the intellectual enrichment that comes from understanding how ideas connect (Ryan & Deci, 2000) matters more than mundane application to shopping or DIY projects. Requiring a mundane practical use for every great idea misses the point.
Contrived real-world contexts through project-based learning or superficial scenarios often distract from mathematical thinking (Sweller et al., 2019; Willingham, 2009) whilst failing to convince sceptical students (Boaler, 2002). Transfer of learning from school contexts to real-world situations is complex and often does not occur as teachers expect (Perkins & Salomon, 1989).
The question deserves honesty rather than justification: we study ideas because understanding them has intrinsic value, not because they enable routine tasks.
References
Dewey, J. (1916). Democracy and education: An introduction to the philosophy of education. Macmillan.
Hirsch, E. D. (1996). The schools we need: And why we don’t have them. Doubleday.
Ryan, R. M., & Deci, E. L. (2000). Intrinsic and extrinsic motivations: Classic definitions and new directions. Contemporary Educational Psychology, 25(1), 54-67. https://doi.org/10.1006/ceps.1999.1020
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.
Boaler, J. (2002). Experiencing school mathematics: Traditional and reform approaches to teaching and their impact on student learning (Revised and expanded edition). Lawrence Erlbaum Associates.
Perkins, D. N., & Salomon, G. (1989). Are cognitive skills context-bound? Educational Researcher, 18(1), 16-25. https://doi.org/10.3102/0013189X018001016
Lave, J. (1988). Cognition in practice: Mind, mathematics and culture in everyday life. Cambridge University Press.