Maths is More Than Meets the Eye

Since starting the Discovering Mathematics module I have been completely shocked and amazed at how interesting and relevant to real life the subject actually is!

For one of our tutor directed tasks we were asked to take a look at Liping Ma’s Knowing and Teaching Elementary Mathematics chapter 5. This chapter really made it clear to me what it takes to be able to teach Maths successfully in the primary school. Ma, L(2010) frequently uses the term “Profound Understanding in Mathematics” or “PUFM” and in chapter 5 she explains what it means to have PUFM and how to promote it through teaching.

A teacher’s knowledge of mathematics should go beyond the set topic areas, it should be extremely wide and thorough Ma, L.(2010, p.133). There should be clear connections between topics that also link directly to everyday life. I strongly agree with this as I believe that children find it harder to stay engaged with a lesson if they can’t see themselves using it in the future. Whereas if it is linked to real life situations or even just to an area of interest such as football or any other hobbies that the various pupils may have then they are far more likely to tune in and gain more from the lesson.

Ma, L.(2010, p.134) presents four key elements to teaching in this way.

1. Firstly she uses the term connectedness, a teacher should be able to create and display links between various concepts within mathematics, the subject should not be learned as isolated topics but as a combined chunk of knowledge.

2. Secondly, we should provide pupils with multiple perspectives, encouraging them to find various approaches to reaching a solution, however it is important to put emphasis on the importance of justifying their methods, this will then lead to a more flexible understanding of mathematics.

During one of our Discovering Mathematics inputs we were lucky enough to be visited by someone from the Dundee Science Centre. This was extremely interesting a greatly backed up Liping Ma’s idea of multiple perspectives. As humans on Earth we have a pretty big influence upon our environment. However if we look at ourselves as humans on a planet in our solar system within space, we are tiny. Even compared to the Sun the Earth seems pretty insignificant! This displays that at first when we reach a solution in maths it is important to explore a little more so that we can gain a wider understanding of the concept and not just start celebrating because we got the number that’s in the answers at the back of the book.


3. The third aspect Ma, L.(2010, p.134) highlighted was that teachers should reinforce basic ideas within mathematics, this will then encourage pupils to carry out real mathematical activity instead of just finishing a topic, moving on and forgetting everything that has been learned.

4. Finally, she talks about longitudinal coherence which to me, seems to be one of the most important. We should drop the attitude that certain topics are taught at certain stages in a child’s primary school life. We should always be referring back to previous learning and seizing opportunities to lay the foundations for the future. This one particularly stood out to me as many teachers may just teach the class what they need to know until they are no longer their responsibility.

I feel as though Liping Ma has really encouraged me to look at Mathematics in an entirely different way, in the future when I am about to teach a Maths lesson I will think more about what concepts are behind the topic that I am teaching, what parts of the children’s previous knowledge can I pull from to make it clearer for them and how can I link it to everyday life to make it more relevant?


Ma, L.(2010) Knowing and Teaching Elementary Mathematics. New York: Taylor and Francis.

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