While researching for my Discovering mathematics essay I have massively broadened my own understanding of Ma (2010) key elements of profound understanding of fundamental mathematics (Basic ideas, connectedness, multiple perspectives and longitudinal coherence).  In particular, in this blog post, I am going to speak about Longitudinal Coherence which I honestly had no idea what it meant before starting this module in discovering mathematics. In Liping Mas’ Knowing and Teaching elementary mathematics book she describes it as:

“Longitudinal Coherence – Teachers with PUFM are not limited to the knowledge that should be taught in a certain grade; rather, they have achieved a fundamental understanding of the whole elementary mathematics curriculum. With PUFM, teachers are ready at any time to exploit an opportunity to review crucial concepts that students have studied previously. They also know what students are going to learn later, and take opportunities to lay the proper foundations for it.” (pg 122)

This is a direct quote from her book which I have read a few times and do understand but thought I should research further to find further meaning to longitudinal coherence. An excellent quote from a paper written by Wu (2002) has opened my mind even further:

“We endeavor to make students see the individual trees but, in the process, we shortchange them by not calling their attention to the forest.” (pg.16)

This quote followed by the explanation of fractions which I have inserted below has opened my mind to the importance of a teacher not only knowing what they are teaching but also being able to refer to other topics which will relate to the current one.  With this knowledge, the reinforcement of the basic ideas which is another key element of PUFM will broaden the knowledge of not only the pupil but also the teacher or student teacher.

Having researched this I feel for my own development in my student teaching leading onto my teaching career I need to build this PUFM throughout my time at university so I have a sound knowledge of what I will be teaching throughout the primary school.  I have enjoyed researching this and with the help of excellent scholars in this field, it has broadened my understanding of the importance of mathematics and the profound understanding of fundamental mathematics in schools.

Reference:

Ma, Liping (2010) Knowing and Teaching Elementary Mathematics: Teachers’ Understanding of Fundamental Mathematics in China and the United States. New York: Routledge.

Wu, H. (2002) “Longitudinal coherence of the curriculum” in What is so difficult about the preparation of mathematics teachers?. University of California: Berkley. Available at: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.15.9760&rep=rep1&type=pdf  Accessed 9 November 2017