Teach-Secondary-Issue-14.5

Angles and inequalities Trigonometry is another topic that can regularly present students with difficulties in problem- solving scenarios. Here, we could task students with applying SOH/CAH/TOA to the process of designing a water slide with an incline that will be enjoyable to use, whilst still being safe. In this instance, basic trigonometry can help students to better visualise the problem they’re being presented with. Allowing them to use cardboard, string and rulers to build a slide in the shape of a triangle, before physically measuring its angles and sides removes the abstractions of those missing lengths and angles. Interleaving this topic with numeracy can increase the level of complexity and encourage deeper thinking by making the cost of materials a factor in students’ final designs. We could also turn our attention to inequalities, which can similarly seem overly abstract to students. With the common misconception of writing inequality statements as equations, it’s evident that students often don’t understand inequality at a conceptual level. We can address this by providing students with examples of inequalities being used in decision making, thus embedding concepts of inequalities that they can use when solving problems. We could revisit video games, by showing how a minimum score needed to unlock the next level is an example of an inequality in action. Presenting problems that involve forming and solving inequalities to determine that minimum score can help to reduce the mistakes around inequality – particularly that of equal symbols being used interchangeably. This way, students can come to understand that the score doesn’t have to be an exact amount for the level to become unlocked, but that it does have to reach a minimum amount. Going viral Unlikely as it seems, we could even turn to social media to help illustrate problems involving powers and roots. Let’s say a video starts off with one view, but then starts to go viral, so that every day the number of views triples. Students can attempt to find out how many days it will take for the video to get a given number of views, or how many views the video will have after a set period of days. Again, there’s scope to turn this into a semi- practical activity by having students ‘tag’ one another in the classroom to represent the ‘views’ of the video increasing each day, with each person representing one additional ‘view’. In this way, we’re helping students to make inferences, draw on the prior knowledge they’ll need to solve the problem and use strategies – such as working backwards, or finding patterns – to ultimately solve the problem. Concrete activities of this kind can help students apply the concepts of a topic more effectively, while allowing them to explore the possibilities of how to solve a problem, trial various methods and create their own procedures in effort to find a solution. Creative confidence Through this process of discovery, the methods students end up using are more likely to stay with them than if they were simply passed on via direct instruction. Asking students to share sweets in a ratio as part of an activity, for instance – rather than asking themmemorise what the process of sharing in a ratio involves – will do more to help them solve further problems within the topic and hone their skills through added challenge. Increasing the quantity of sweets, or requiring students to share them in, say, the exact same 3:2 ratio will encourage them to devise their own methods and approaches to solving the problem presented to them. This adaptation could be vital in helping students access the processes of problem-solving and apply their knowledge to questions where previously, they might not have understood what was being asked of them. New concepts always take time to learn and store in long-termmemory. Concrete activities and real-life applications can help to reduce students’ cognitive overload, boost their motivation, increase their confidence to think more creatively, and in time, help them become better problem solvers. ABOUT THE AUTHOR Ama Dickson is a maths teacher and contributor to Collins’ series of maths revision guides; she also regularly posts maths instruction videos to TikTok as @mathscrunch 57 teachwire.net/secondary M AT H S