Grammar Gazette - Issue 1, 2024

DR PETER JENKINS HEAD OF DEPARTMENT—MATHEMATICS CURRICULUM DEVELOPMENT

Reflections— ST A FF ESS A YS THE COMPLEX UNFAMILIAR PROBLEM

in the worst-case scenario where little to no progress is made in these questions. This can dramatically reduce student anxiety and support them to think more clearly in the face of the challenge. So, how does a student improve their ability to solve these problems (and all the other complex unfamiliar problems the world may throw at them)? First, students must have thoroughly mastered key concepts and techniques. Imagine a player attempting a challenging level in a video game without having completed the previous levels. It’s easy to underestimate the amount of practice needed; students must allocate some time each week to reviewing topics studied weeks or even months earlier. It’s also important for students to take advantage of every opportunity to practice complex unfamiliar problems. Consider the video game analogy again—this time imagine that our player completed all previous levels by following instructions found on the internet. This is not all bad; but they will neither be proficient in choosing the right move without instruction, nor be accustomed to the feeling of not knowing exactly what to do and being forced to try something new (and possibly failing). It also takes much of the joy out of playing video games in the first place! Mathematics learning is not exactly like a video game. The ‘moves’ you make when solving a mathematics problem often took the greatest minds in history years to develop. They require skilful explanation and teacher demonstration. That said, there are still many situations in which students should not be shown the way forward, and instead should practice making leaps on their own, so they can ultimately learn the joy and richness of the complex unfamiliar experience.

means that even the best mathematics students find them challenging— particularly in an examination, when panic can sometimes compromise the ability to think clearly and calmly. The ability to face and solve unfamiliar problems is one of the most important skills we need our future generation of professionals to possess, regardless of field. It is also the essence of mathematical thinking: it’s about developing a deep understanding of abstract patterns and structures so that we can create new, or adapt existing, rules and procedures to solve problems we haven’t yet encountered. At the same time, it would be a mistake to think that competence with the complex unfamiliar problem is all that matters. These problems comprise only 20 per cent of the marks in any exam, which means that students can still perform quite well in mathematics, even

T he bane of many secondary school mathematics students is the complex unfamiliar problem. As the name suggests, these problems are both complex (requiring knowledge of multiple concepts to complete several steps) and unfamiliar (different to problems already practiced). To complete such problems, students need a conceptual understanding of, and flexibility with, mathematical techniques. Although they are based on concepts and techniques that students have been studying, their unpredictable nature

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ABOVE DR PETER JENKINS TEACHING IN THE CLASSROOM

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GAZETTE • ISSUE 1, 2024 ISSUE 1, 2024

BRISBANE GIRLS GRAMMAR SCHOOL