It’s important to provide students with opportunities to discuss, reflect on and evaluate their problem-solving approaches.
When students explain their working, it provides them with an informal opportunity to articulate their thought process and justify that their answers are well-reasoned.
For the rest of the class listening, it cements their own understanding, exposes them to a more efficient strategy, or simply allows them to hear a peer voice explain how to solve the problem if they struggle to do so themselves.
Discussion can also reinforce that there may be more than one way to solve a problem. Sometimes, different strategies may be equally efficient; other times, the discussion can enable students to engage in meaningful dialogue about which strategies are more or less effective for a particular problem.
Here are three ways you can facilitate problem-solving discussions in your iMaths lessons:
A number of iMaths student book topics include a problem-solving task. When students complete one of these tasks independently, ask two or three students to explain how they arrived at the solution. First ask (or nominate) a student who had the correct answer to explain their working. Then ask the class who else got the correct answer but used a different approach to tackle the problem and nominate other students to explain their different ways of solving the problem.
In addition to conducting one-on-one conferences with each of your students to assess performance in an iMaths investigation, why not also ask students to present their investigation findings to the class?
Investigations provide the opportunity in a whole-class setting to explain thought processes using real-world contexts that make the purpose of the maths more relatable.
The pair and group work included in iMaths investigations also provide a great dynamic for students to collectively discuss their findings.
When you have your students share their investigations with the class, have the Communicating and reflecting questions from the Investigation Teaching Plan handy to use as prompts if students get stuck during their presentation to the class.
When it’s clear students may not have used the best strategy to solve a problem, steer the discussion back to a more efficient strategy by explicitly stepping out a worked solution to the problem. A simple segue is to point out ‘that’s one way to approach the problem and it’s good because you were able to arrive at the correct solution, but another way is to use the ‘Find a pattern or use a rule’ strategy. Let’s see how this strategy can be used to solve the problem.’
Before you demonstrate how the strategy can be applied to the problem, watch the relevant Problem-Solving Strategy video available at iMaths Online to remind students of the key components of that strategy. Then use the strategy steps to work through the solution.
Each iMaths investigation allows you to bring maths to life by incorporating other learning areas in a practical and engaging way. See how these investigations link to other learning areas:
Mathematics and storytelling aren’t often used in the same context. However, Professor Chris Matthews, chairman of ATSIMA (Aboriginal and Torres Strait Islander Mathematics Alliance), encourages teachers to explore how mathematic equations can be expressed and understood through storytelling.