Categorization and analysis of explanatory writing in mathematics

Abstract

The aim of this article is to present a scheme for coding and categorizing students’ written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to mathematical problem-solving processes. The rationale for the study was the recognized importance of mathematical problem-solving, the widely acknowledged challenge of teaching problem-solving skills directly and the evidence in the literature that writing in mathematics provides a tool for learning. The study was carried out in a first-year mathematics course at the University of Cape Town, South Africa. Students’ written submissions were categorized and analysed through use of an adaptation of a journal entry classification scheme. The scheme successfully observed positive changes over the experimental period in students’ level of engagement with the mathematical material and with their stance towards knowledge.

Keywords:

• problem-solving
• writing
• coding schemes
• classification schemes

Notes

1. Since the writing initiative was explicitly intended not to interfere with the standard running of the course, the tutorial sheets were not manipulated by the author to contain strictly defined problems. Most weeks, there were no strict problems on the tutorial sheets, simply exercises, often of a challenging nature. The assigned ‘problems’ were, in general, exercises that were considered to best benefit from a look-before-you-leap approach.

2. The degree programmes of the students in the tutorial groups were varied. The cohort included students registered in the Commerce Faculty (three different degree programmes), the Engineering Faculty (five degree programmes), the Science Faculty (five degree programmes) and one degree programme in the Humanities Faculty.

3. Retaining Waywood's terminology, the word ‘summary’ is used in two contexts. Lowercase use represents conventional usage of the word, whereas uppercase use refers to the coding scheme's category.

4. In the interests of brevity, mathematical problems henceforth in this article will be included without the writing instructions seen by the experimental groups in the study.

5. Detailed evidence of the development of problem-solving processes in the student cohort is beyond the scope of this article. The reader should be aware, however, that the scheme described in this article successfully and unambiguously measured progress which was verified by concurrent and complementary forms of analysis 34.

6. In contrast to other research studies in writing to learn 30, no improvement was observed in metacognitive phenomena.

7. This analysis took the forms of structured analysis of problem-solving assessment tasks as well as Piagetian investigation of student interview data.