Teach-Secondary-Issue-14.5

What’s the problem? Ama Dickson looks at why the process of getting students to applymathematical concepts to real-world scenarios doesn’t always run as smoothly as it should... P roblem solving continues to be an area of maths that many students struggle with, for a variety of reasons. Some of these difficulties stem from a lack of conceptual understanding. Students memorise procedures, which then results in difficulties when they try to apply those procedures in problem- solving scenarios. Rocky routines Withmaths being sequential, a shallow level of understanding canmake problem solving difficult at a higher level. Maths anxiety can further paralyse students’ thinking, resulting in them struggling to think creatively when approaching the problem at hand. Nor does it help that available classroom time for teaching problem solving techniques is typically quite limited, despite problem solving requiring a specific set of skills – such as working backwards, looking for patterns, making estimates and drawing diagrams. Many students will be unfamiliar with such strategies and ways of approaching a problem, instead relying on routine methods that they’re already familiar and comfortable with. But those familiar approaches won’t always work, causing students to become stuck when faced with non-standard problems. Roomfor improvement Empowering your students to approach problems in a number of different ways could well be essential to improving their long-term outcomes. Time constraints notwithstanding, working through problem solving activities in the classroom can play a pivotal part in helping students apply abstract mathematical concepts to real life situations. Take geometry, for example. When teaching students about area, perimeters and volume, you could perhaps ask them to design and furnish their own dream bedroom, taking account of carpet size, the room’s dimensions and the various items of furniture, fixtures and gadgets they’ll want to fill it with. This could be an effective means of introducing problem solving to them in a way that’s both familiar and engaging. We could then take this same problem and extend it further to stretch high ability learners. New considerations might include measuring the area of an L-shaped desk, the calculations needed to install built-in wardrobes or working out the angles of a loft conversion’s slanted walls and ceilings. Power fantasy The evenmore abstract concepts of algebra and substitution can be explained to students with reference to video games. We can start by applying formulae and variables to the statistics of imaginary video game avatars, to help students grasp what these are and what they do. By substituting our avatars’ statistics to determine their power level (where ‘power = 2*strength + 3*speed’, for example) students get to see how substitution can be used to evaluate an expression when the value of the variables have been given. Students can then be given different character cards with statistics that they need to substitute into a formula, before deciding which character has the highest power level. This introduces an interactive element, which will hopefully encourage students to engage more with their learning. We can then build in further complexity by adding multiple avatars with different, more complex formulae. The physical, game-like nature of this activity should help make the abstract nature of the problem less daunting, and can potentially increase students’ motivation and interest in an area that they might otherwise recoil from. “Maths anxiety can paralyse students’thinking, resulting in themstruggling to think creatively” 56 teachwire.net/secondary