As I’ve progressed through my teaching career I’ve become acutely aware of the complete lack of insight many students have concerning their learning. They simply don’t know what they are doing wrong or right. They don’t understand at what point their learning breaks down. They have few ideas about what they are successful at, and where they need to work harder.
Mathematics is highly conceptual and can become entirely overwhelming if students are missing particular pieces of the ‘mathematical jigsaw.’ It is not uncommon for students to develop the mindset that they can’t “do” mathematics, and develop mathematics anxiety and avoidance behaviour. The avoidance element of mathematics anxiety can influence whether students choose to study mathematics if it is not compulsory (such as in year 11, 12 and at university). Decreased participation in advanced mathematics can be attributed to mathematics anxiety.
Learned helplessness may be describe as a student giving up after a series of failures. Learned helplessness is often compounded by a fixed (entity) view of intelligence (i.e. that you have a certain level of ‘smartness’ that can’t change no matter how hard you work) and lower self-esteem. Learned helplessness results in decreased persistence, lower levels of academic achievement and lower self-efficacy.
When students get stuck (sucked) into that big black hole of mathematics, it can be extremely difficult to get out. It’s not feasible to go back and learn everything again, but many students cannot identify which parts they do and don’t understand.
My year 11 and 12 mathematics often likened mathematics to a toolbox. As we learn mathematics we’re learning how to use a whole bunch of different tools. We then have to select which of these tools are most appropriate to help us solve problems. If students don’t understand how to use all the tools in their toolbox they are going to be considerably disadvantaged when it comes to tackling progressively more difficult problems. The issue many students face is that they don’t know what tools they do and don’t have.
It’s no secret I’m a big proponent of the benefits of metacognition and reflection in the classroom. I have a particularly self-reflective, analytical personality. At times this contributes massively to my tendancy to be highly-self critical. However, I believe it also made me a better student. I understood intuitively what I was doing well, where I was going wrong, and what was stopping me from achieving success. My capacity for self-reflection and self-analysis has similarly benefited any of my very modest cultural and athletic pursuits, allowing me to work more efficiently and improve more quickly.
Self-reflection falls under a greater banner of skills for learning known as “metacognition.” Essentially, metacognition means ‘thinking about thinking’ or ‘knowledge about knowledge.’ It is the way in which we monitor and regulate our thought processes. Metacognition is particularly important for students as it incorporates knowledge of one’s own limitations with respect to learning, memory capabilities, and time frames; an understanding of what strategies are effective and ineffective; capacity to plan and execute tasks; effectively employing strategies to acquire and remember new material; understanding when knowledge was obtained successfully; and monitoring comprehension.
Emphasis on self-reflection has been found to decrease mathematics anxiety. By developing greater insight into their own learning process students are better equipped to make positive changes to improve their learning.
Self-reflection assists students in integrating new knowledge with their existing knowledge base, thus contributing to greater retention of information.
Towards the end of last year I started integrating reflective questions into my daily classroom practice. At the end of term four I asked my students to complete an online survey to provide me with feedback as to how useful they found the experience.
I was pleasantly surprised.
The students unanimously found a greater emphasis in reflection to be useful for their learning. They expressed that it helped them identify areas of strength and weakness, increased their capacity to plan their learning and study so they could work more efficiently. Interestingly, students found questions about what they needed work on to be the most useful. One particular student responded that reflective questions
“Help me reflect on WHY I’ve learnt it. With all the other things going on at shcool I don’t take much time to think about these kinds of questions, so it’s good to be reminded of them. These types of questions – the ones I don’t normally think about – are usually the most helpful.”
Too often in classrooms, students are taught material, without being given tools on how to make sense of this information. If students are unsuccessful in mastering concepts their chances of succeeding will not improve the next time they encounter the material, unless they understand why they have failed. In not assisting students to understand their learning we’re failing them. It’s not enough to simply transmit information, or even help students understand information. We need to help them to understand their own learning too, if we want them to develop into flexible, creative, thinking, problem-solvers.