Junior Cycle - Higher Level
Ideas for Teachers
Socrates maintained that students need to reach a point of being perplexed (“aporeia”) before they learn. In teaching Maths, it’s good to introduce mystery and puzzlement before moving towards a method of solving problems. For example, when introducing simultaneous equations, ask students to guess the answers for x and y before introducing methods that work in solving them. It means that before methods are introduced, students understand that the task in hand is to find a value of x and a value of y which satisfy BOTH equations simultaneously.
Similarly, when introducing quadratic equations, I often ask, “Is it possible that there will be two solutions to the following problem: x² -3x - 10 = 0? Then I ask students to guess solutions and we see if they work. Students then understand that the task is to find TWO numbers which satisfy the equation.
I often use The Hungarian Method when introducing a new topic, such as Problems that lead to a simultaneous equation: instead of doing one or two examples and then letting them at it, I start with the questions in the exercise. I ask one student to read out the question, and we all set about solving it. Suggestions might come from the floor. We start by defining what x and y stand for. Then we suggest two equations from the text. Then we solve. Then we check to see if our solution works. Then on to the next question. Gradually, students take the helm and start working away on their own. This (I believe) is the way they teach Maths in Hungary: a country with a great record for the teaching of mathematics.
The Hungarian Method is good because it avoids loads of students getting stuck. It also makes students write down a few solutions – much better than just reading – before they get at them themselves.