Abstract
Using a predetermined framework on students' productive struggles, the purpose of this study is to explore high school students' productive struggles during the simplification of rational algebraic expressions in a high school mathematics classroom. This study is foregrounded in the anthropological theory of the didactic, and its central notion of a - a praxeology refers to the study of human action, based on the notion that humans engage in purposeful behavior of which the simplification of rational algebraic expressions is an example. The research methodology comprised a lesson study involving a sample of 28 students, and the productive struggle framework was used for data analysis. Findings show that the productive struggle framework is a useful tool that can be used to analyze students' thinking processes during the simplification of rational algebraic expressions. Further research is required on the roles that noticing and questioning can play for mathematics teachers to respond to and effectively support the students' struggles during teaching and learning.
Highlights
The purpose of this study is to explore high school mathematics students’ productive struggles during the simplification of rational algebraic expressions
Exposing students to complex problem-solving tasks which are beyond their cognitive levels, skills and abilities can result in productive failures on the part of students [7]
When students engage in complex problem-solving tasks, they are likely to experience productive failure unless support structures are put in place
Summary
The purpose of this study is to explore high school mathematics students’ productive struggles during the simplification of rational algebraic expressions. Teachers of mathematics often view students’ struggles in mathematics as something that should be avoided and/or as a learning problem that needs to be diagnosed and remediated or eradicated [4, 5]. Exposing students to complex problem-solving tasks which are beyond their cognitive levels, skills and abilities can result in productive failures on the part of students [7]. When students engage in complex problem-solving tasks, they are likely to experience productive failure unless support structures are put in place. Research has shown that exposing students to complex problem-solving without putting in place efficient support structures can result in an unproductive cognitive process [9, 10]. To avoid unproductive failure learning situations, students must be provided with guidance during problem-solving. We are referring to: scaffolding of problems; feedback through questioning, among others
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