Pupils' Written Mathematical Records (Speaking Mathematically)

David Pimm (1987)

Chpt5: Pupils’ written mathematical records

This chapter explores how written mathematics, one of the main themes in this book, is different from spoken mathematics and affects them. Firstly, the author clarifies the purposes of writing records in mathematics of both students and teachers. One of their reasons which was interesting to me is many teachers force their students to write their answers down the notebooks because their parents feel comfortable when seeing the outputs. Additionally, the author introduced threes styles of writing mathematics: verbal, mixed, and symbolic. Verbal style means that pupils do explanation in natural language without (or with little) mathematical symbols. The second one is a mix of verbal and symbolic style that they use both natural language and mathematics symbols together to explain something in mathematics. The last style is called symbolic and refers to that students utilize (only?) mathematical symbols, and the author points out this style is a goal for most mathematics teachers while it is too rapid to move the students in this stage. Lastly, the author argues that it is crucial to understand how pupils record mathematics spontaneously and recognize the purpose of the writing.

I have heard about many junior high students in my school are struggling to be accustom with letters in mathematics sentences. Because early mathematics (in elementary level) in Japan, they focus on real-life situations in mathematics and operations of numbers, so they are not familiar with abstract ideas at this stage. However, after they start to learn in middle schools, the mathematical contents slightly shift to abstract parts, and letters in mathematical sentences can be one of their difficulties. I believe most of them do not understand why they have to use letters and what their merits are. Use of letter, for example, can expand, replace or simulate numbers to solve given questions, and it is an important idea to study mathematics in high school and post-secondary. However, many teachers seem to insufficiently explain the usefulness of using letters in mathematics, rather they force the students to use it without rational reasons.