“When will I ever use this?” - Powerful Problem-Solving and the interconnectedness of mathematics

Mathematics often gets a bad rap among students, with educators often asked, “When will I ever use this?” This question highlights the lack of understanding of the pervasiveness of mathematics and its inherent interconnectedness within our daily lives. Students need to understand that mathematics is not just about passing tests, it’s about developing a toolkit for navigating and making sense of the world. 

Young mathematicians need to understand that mathematics is woven into the fabric of our daily lives. We use mathematical thinking when we complete simple tasks like dividing snacks amongst friends or when shopping and comparing the value of two different purchase choices. Even playing at lunchtime requires number knowledge for team management and keeping score. Beyond these obvious examples, maths develops problem-solving and critical thinking skills that are essential in both their personal and eventual professional lives. 

As the tasks we complete become more complex, we require algorithmic thinking, a way of getting to a solution through a clear set of defined steps. Not only does the process need to arrive at the right answer, but consideration of the efficiency of the steps is needed as well. This is where Scitech’s Lighthouse Maths Powerful Problem–Solving (PPS) approach comes in. The class is presented with a challenging problem, often linked to a recent concept covered in class. Students are then given time in small groups to tackle the problem while the teacher circles round the room. Once the groups have been given time to unpack the problem, a class discussion follows, with the teacher highlighting the various strategies used and celebrating efficient solutions.      

It’s amazing how many seemingly unrelated mathematical concepts reveal themselves during these lessons. Carefully orchestrated discussions help the students grasp the links between mathematical concepts, seeing them not as isolated topics but part of a larger, interconnected web. This approach encourages students to recognise how concepts interlink and build on each other. Students are able to link new mathematical concepts to their existing understandings. This approach not only aids in better retention of mathematical concepts but also enhances problem-solving abilities by allowing students to draw on a broader base of knowledge. 

Another challenge in education today is the crowded curriculum. Teachers often struggle to cover all required topics within limited time. The Lighthouse Maths Problem Solving lesson can alleviate time pressures by addressing several mathematical concepts and processes simultaneously. By focusing on problem-solving, students are encouraged to think mathematically about a topic and draw on many skills, including data organisation and representation. Students work collaboratively to solve authentic problems, drawing on a range of skills and experiences, leading to a more comprehensive grasp of the concepts. This not only makes learning more efficient but also more engaging, as students see the practical connections between different areas of mathematics. 

The Lighthouse Maths Problem Solving lesson structure provides opportunities for students with various mathematical abilities to find success and showcase their understanding. By presenting problems that can be approached in multiple ways and at different levels of complexity, students with diverse skills can contribute meaningfully. Group work ensures that students of all abilities feel accomplishment in their contribution to a successful solution. This inclusivity fosters a supportive learning environment where students view learning as a collective effort, further enhancing individual confidence and interest in mathematics. Additionally, this process provides students multiple exposures to topics and concepts, which in turn increases their ability to commit to long term memory. 

Maths is far more than a subject confined to the classroom. It’s a critical part of our everyday lives and an interconnected discipline that builds valuable skills. By embracing the connectionist approach through Powerful Problem Solving, students see the immediate real-world value of mathematics and how it equips them to tackle a wide range of future problems. So, next time a student asks, “When will I ever use this?”, remind them that maths is everywhere, and the answer is “Constantly, and in ways you don’t even realise!”

Ryan Shaw – Lighthouse Maths Coach 2024

Lighthouse Maths is a year-long professional learning program delivered in partnership with Chevron Australia, which aims to build teachers’ skills and confidence by using a problem-solving approach to teaching maths.