Pupils using writing in the mathematics classroom

Barbara Adair, Wallace High School

Ken Houston, University of Ulster

Introduction

There are many activities that are promoted in the mathematics classroom to facilitate group work, investigative work and discussion. These help develop skills of reading, listening and talking. The skill of writing, particularly writing mathematics or writing about mathematics is conspicuous by its absence from this list. It is nevertheless a vital communication skill. This short paper describes some of the ways writing is being used in mathematics classrooms and our experience of experimenting with them.

There are two main categories of writing assignments — informal writing assignments dealing with students’ feelings and attitudes and formal writing assignments which deal with content and are often used to assess a student’s work. Research seems to suggest that not only do writing assignments enhance generic written communication skills but they also improve a students’ mathematical knowledge by causing them to reflect on their work. Writing assignments can also instil a greater rapport between student and teacher because quite often students can put things in writing more readily than in a conversation. Students enjoy the one-to-one communication with the teacher, thus avoiding the peer pressure that is all too apparent in a general class discussion. Furthermore writing assignments provide an opportunity for teachers to spot misunderstandings in their students at an early stage. The principal drawback of writing assignments is that time has to be found to implement them.

Selected writing assignments

The variety of writing assignments used is enormous, ranging from short sentences in kindergarten to final year dissertations in tertiary level education. All have a common aim — to enhance students’ mathematical understanding by allowing them to express themselves in writing in an interesting and motivational way. Writing assignments at Key Stages 1, 2 and 3 should all be of the informal variety. Primary school children should be encouraged to write in their own vocabulary about the mathematics they are doing. Then they would be in a better position to develop these skills to their full potential in secondary level. There are various different writing activities that can be explored.

Narrative writing activities include writing word problems based on a topic being studied, writing biographical sketches about the life of a notable mathematician or writing stories about geometrical shapes. Descriptive writing activities include writing descriptions of an algorithm (an idea often practiced orally), defining mathematical vocabulary, writing directions using measurements and summarising chapters of the text book using their own words. Expository writing contains activities such as interpreting a graph or correcting a problem which is presented incorrectly. The emphasis is not on producing the numerically correct answer but in the explanation of the processes used to arrive at that answer. It is suggested that

• students should be given the opportunity to write something every day, regardless of the length of the writing assignment,
• students should be encouraged to write in complete sentences,
• teachers should write with the students and share their work,
• teachers should praise their students’ work and display extracts in the classroom.

Writing can be incorporated into mathematics teaching through the use of learning log books. The purpose of these logs is for pupils to reflect on what they are learning and to learn from the reflection. This can be done through open-ended, guided or specific writing tasks. It is expected that pupils should write in their log books every day, with questions they want to ask or to describe any "A Ha" experiences they have had in class. Students could also be asked to explain fully any errors that have been identified in their work.

Impromptu Writing Prompts solicit from students a written response to a specific question or problem. Students are given a certain time to read the prompt and to formulate and write a response to it. A prompt can direct the learners towards specific content or can ask for an opinion about how a lesson is progressing. Such prompts can help students identify exactly what they are thinking. These prompts can also be used as an informed means of assessing understanding. Although pupils may be able to solve problems by working though the algorithms properly, on occasions it is evident through their writing that they did not understand the process clearly.

Writing word problems can be used as part of a writing-to-learn-mathematics approach. Students can be asked to write word problems involving, for example, only the process of addition, or subtraction, or multiplication or division. These word problems could be edited and collected into a look for the class to work at. Experience suggests that pupils are very careful when they know that their problems are going to be used by their peers, and a sense of pride and achievement is engendered. The problem could be "peer assessed" for complexity, originality and logical information and the "best" problem setter could be awarded a prize.

Journal writing or keeping a learning diary is another approach. This could be a students "mathematics autobiography". It encourages students to focus on their own learning and, by writing about it, they begin to take more responsibility for it. They can express feelings and fears, what they know and what they do not. It provides a record for referral, refution and remediation. Sometimes the journal can take the form of a dialogue with the teacher wherein students share their thoughts privately with their teacher.

Our experience

We experimented with a writing-to-learn approach with students in Years 8 to 11 at Dromore High School while Barbara Adair was teaching there. We used Journal Writing with a Year 9 class, Autobiographies with a Year 8 class, Impromptu Writing Prompts with classes in Years 8, 10 and 11, Poetry Writing in Year 9 and Word Problems with Year 9.

The majority of the pupils regarded it as a novel approach and, especially in the junior years, carried out their writing assignments without fuss. Only the more senior pupils began to raise objections.

We found that the open ended writing activities provided students with the opportunity:

• to express their feelings about the topic in their own language,
• to ask the teacher questions in private, thus avoiding peer pressure,
• to reflect on the work of the day or of the week, thus acting as a revision aid,
• to question themselves about their own thought processes,
• to take responsibility for their own learning.

This also provided a wealth of information for the teacher. By reading the students’ comments, a teacher can

• learn about the students’ previous mathematical experiences,
• discovers how individual students perceive mathematics,
• become aware of their own faults and qualities,
• indirectly evaluate their lessons,
• provide students with individual attention where necessary.

We recommend that you consider getting your pupils to use writing-to-learn-mathematics.

Acknowledgement

This paper is based on the MSc thesis "Pupils using writing in mathematics", by Barbara Adair (née Gallagher), University of Ulster, 1996.