Multiple-choice tests… Students looove multiple-choice tests. Until they take one and do not get the expected result. They think like “No writing! Yay!”, and then they realise that it is that ‘writing’ part that earns the marks.
That is one of the reasons I always insist on showing clear work that leads to the answer. It is the core of English Maths Curriculum. Hence, it is the core of assessment, namely, IGCSE and A/AS Level Maths Exams.
Certainly, this is the short-term gain of it; show your work to get more marks, hence succeed the exam. However, it has deeper benefits to student learning; particularly in thinking and problem solving skills.
Why do we write anyway? The main reason is, ‘to remember’. Imagine that you are solving a multi-step problem; it is quite hard, not impossible though, to carry on all the steps mentally, as it is hard to remember each result after performing a step.
Apart from that, when you write the steps of a solution and the result of each step, you also start to organise your thinking. Practice makes perfect; with the help of the examples, you work on question after question, not only to ‘memorise’ the formula or ‘learn’ the bit of information, but you also learn how to best present your work, which is proof to your organised thinking and problem solving skills. Hence, it is not about performing the same steps of the same solution while solving a particular type of question. Rather it is about training and sharpening these skills to flexibly build a clear presentation leading to the answer, regardless of the question type.
‘Teaching maths’, as a consequence, is not just delivering the content, but also explaining the thinking behind, showing misconceptions and role-modelling the problem solving skill. And that is why, it is not ‘teaching’ anymore; it is ‘helping students learn’. Teachers should design their lessons based on a student-centred approach with less ‘chalk-and-talk’ time and more peer or group activity time. They should monitor students’ working with follow-up of each student’s progress, instead of ‘teaching’ in front of the board.
This idea is important in private tuition, as well as in the class. A private tutor should focus on student’s needs. Does s/he have a hard time understanding the content? Is it his/her difficulty on expressing the way s/he solves the problems? Does s/he lack the previous knowledge, and therefore cannot perform well? Does s/he get distracted easily? The answers vary for each kid, hence the tuition should be tailor-made to his/her needs. With the right approach and appropriate amount of effort, every child is capable of doing maths.