The Role of Expository Writing in Mathematical Problem Solving

Abstract

Mathematical problem-solving is notoriously difficult to teach in a standard university mathematics classroom. The project on which this article reports aimed to investigate the effect of the writing of explanatory strategies in the context of mathematical problem solving on problem-solving behaviour. This article serves to describe the effectiveness of using writing as a tool for deeper engagement with mathematical problems. Students' claims about, and tutor observations of, problem-solving behaviour were analysed through the lens of Piaget's theory of cognitive development. Examples of enhanced problem-solving behaviour are presented as well as reports from student interviews that writing "forces" deeper engagement. The analysis of students' work and reflections indicated that writing about problem-solving processes potentially resulted in a cognitive perturbation when students were forced to confront their incomplete understanding (and hence their unstable knowledge structures) and therefore had to achieve a deeper level of understanding in order to adequately describe the solution process.

An Appropriate Prompts System Based on the Polya Method for Mathematical Problem-Solving

“…Moreover, the study results show that the majority of the students in the high achievement group already presented above-par performance in the pretest, which limited their scope for improvement and prevented any significant differences. The results of this study support the findings of existing studies proposing that employing Polya's methods can significantly improve the overall performance of students (Lai, 2010;Chang, 2012;Craig, 2016;Devi, 2016;Romiszowski, 2016).…”

“…The results of the four-class teaching activity with Polya's problem-solving methods and appropriate prompts indicate that it had significant influence on the effectiveness of learning mathematics, creating a significant difference between the students of the experiment group and the control group. Students have long been taught using a single method and often absorb information passively by using the previous strategies (Craig, 2016;Devi, 2016;Han & Kim, 2016). By making use of the appropriate prompt mechanism in this study, the students could effectively overcome obstacles in their learning process.…”

“…At present, the majority of existing research (Craig, 2016;Devi, 2016;Han & Kim, 2016;Romiszowski, 2016;Rosli, et al, 2015) concerning Polya's methods focus on the development and assessment of relevant strategies and teaching applications. Few studies have included the topic of prompts.…”

An empirical investigation into student's mathematical word‐based problem‐solving process: A computerized approach

“…The results of this study support the findings of existing studies proposing that employing Polya's methods can significantly improve the overall performance of students (Craig, ; Özsoy & Ataman, ; Romiszowski, ). The statistical results show that the students' problem‐solving performance as well as their problem‐solving ability was improved via the proposed learning approach.…”

Learners’ and Their Teacher’s Experiences of an Authentic Online Assessment Test in the Understanding of Basic Accounting Content Knowledge

“…Enabling learners to use their cognitive structures enables them to achieve a deeper level of understanding in the learning task (Craig, 2016) within an authentic online assessment task that is designed according to the six levels of cognitive processes of the revised Bloom's taxonomy, namely remembering, understanding, applying, analysing, evaluating and creating (Anderson & Krathwohl, 2001). In the context of this study, only the first three levels of the revised Bloom's taxonomy were used with their related action verbs in the design of the online assessment as follows:…”