# Reflection as part of learning

Our maths faculty head teacher set a ‘soft’ challenge a while ago to have some subjective assessments.

I took this on board and have devised an assessment task that incorporated self-reflection which was another skill I’d like my students to practice; 2 birds in one stone. Reflection is essential in developing sound mathematical thinking, apart from the fact that it is a good life skill itself. At its core, it necessitates looking at something from a different perspective such as looking back, looking deeper, looking from a different angle. From a Jesuit perspective, it also involves Action. Solving mathematical problems often involve all these.

Here’s what I’ve learned so far:

1. Reflections (or learning journals) are just as good for assessing understanding.

What a number is and what it stands for can be dramatically changed just by putting a tiny, little decimal point in front of it. For example, the numeral ‘1’ is a whole number and stands on its own. But as soon as you make it ‘0.1’ it now stands for 1 over 10.

This shows an understanding of the decimal point as the anchor that defines place values.

2. Aim for conceptual understanding; maths is more than just mechanics and shortcuts

I did not really understand the purpose of it and therefore was confused as to why we were doing it. It made me realize that just because you can do something and get the answers right, it does not mean that you don’t struggle with it.

Do I stop to check for conceptual understanding when the students have demonstrated they can do the mechanics?

3. Passion rubs off – case in point, Algebra

Many of my students expressed struggling with Algebra and yet have found it interesting, even fun. Algebra is my favourite maths strand and know that many are put off by it – often from what they’ve heard adults or older students say. With extra effort as well as creativity – and surely joy – many of my students have admitted to struggling with, but finding Algebra interesting; some even said useful and fun! No amount of objective testing will ever show this.

4. Students can be Teachers

I see myself in the reflections of my students. I can see where they’ve struggled and what they’ve enjoyed. I am learning new ways of perceiving topics in a way that is impossible to capture in ordinary class discussions – it is just impossible to hear everyone out every lesson. I can see that some students do appreciate the variety in delivery – modelling, direct instruction, investigation, problem-solving, questioning.

5. There can be some objectivity in the subjective

This sounds more like a philosophical discourse and, a lifetime ago, it was indeed (Philosophy of Man at uni). For now, all I mean is that there can be guidelines to help in marking subjective answers. I used Depth, Breadth and Details.

While I initially dreaded the prospect of marking these assessments, I was surprised to find myself enjoying reading my students’ comments especially the like the ones quoted above. These are just year 7 students. I look forward to Parts B and C of this assessment task.