Throughout the ‘Discovering Mathematics’ course this semester there has been a focus on a key text – Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States (1999 and 2010 edition) written by Liping Ma. Ma outlined what a teacher should know regarding maths in order to teach it successfully to young learners.
Ma describes the understanding that teachers in China have regarding Mathematics as a ‘Profound Understanding of Fundamental Mathematics’ or PUFM for short. She explains that while PUFM has been achieved in China, it is something that should be obtained by teachers worldwide to ensure that both they and their students can understand maths. It is important for teachers to be able to be confident in their own maths ability as this will be projected through how they teach in the classroom. As student teachers, it is easy to fall into the trap of dreading maths lessons or feeling out of practice in the subject. At the beginning of this module, we were asked to raise our hands is the idea of teaching maths is worrying to us. The majority of the class raised their hands with anxious looks on their faces. However, we were told not to fear as this module would help us become more confident and aware of mathematics, something I feel has in fact been achieved.
In order to understand and gain a PUFM, we have to strip mathematics down to it’s most basic properties. She wrote of four main factors that make up mathematics – Connectedness, Multiple Perspectives, Basic Principles and Longitudinal Coherence. When we understand these four factors and can use them to teach maths confidently then a PUFM has been achieved.
Connectedness
Connectedness refers to how mathematics has links with several other topics. This module has proved this several times through inputs such as ‘Maths and Art’, ‘Maths and Music’, ‘Maths and Sports’ and many more. Through these inputs, it has become evident to me that maths has links and connections with several areas of education. This means that it can be taught in relation with a multitude of topics which well help make them easier to understand for children in class.
Multiple Perspectives
Ma also emphasizes the importance of having multiple perspectives when understanding mathematics. In order to achieve a PUFM we must look at maths topics from several perspectives so it can be understood in different ways. When it comes to teaching, children may need to have topics explained to them in different ways as each has a different method of learning and understanding. This means that by having multiple perspectives regarding mathematics, we can actually aid all children in their understanding of it no matter what stye they prefer.
Basic Principles
In order to have a PUFM it is important to understand what lies at the core of mathematics, Mathematics is not solely complex equations and calculus that terrified us in school, it has simple principles at it’s core and when these are understood, so can all mathematics in time. Therefore, Ma highlights the importance of stripping maths back to these basic principles and using them as building blocks for a complete mathematical understanding.
Longitudinal Coherence
Maths is a subject that needs to continually move forward. It is not something that we study for a time in school and then push immediately out of our minds as soon as we leave (even though sometimes that is what it feels like!). The knowledge and skills we gain in mathematics are essential for our future. We need to be able to use these fundamental principles in a range of situations as highlighted to me through this module. Therefore, the final principle of fundamental mathematics is probably the most important in my opinion as it ensures that maths keeps expanding and growing both in society and our minds.
Overall, I feel that the ‘Discovering Mathematics’ module has vastly improved my understanding of fundamental mathematics. The module has helped me experience all four of Ma’s important factors of it. I feel now that my knowledge on the topic has expanded and I can now carry this with me into the classroom to future classes. I know now that maths has to be broken down, explained in different ways and linked with other subjects in order to ensure it remains prominent in both my own mind and the minds of my pupils.
References-
Ma, L. (1999). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New Jersey: Lawrence Erlbaum Associates.
Ma, L. (2010). Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. 2nd ed. New York: Routledge
