Affect and Problem Solving Performance: Modelling Relationships

Abstract

This semilongitudinal study sought to investigate whether any relationship between secondary school student algebra problem solving ability and affective factors exists or not, and if so, to describe it. 195 boys and girls aged 13 to 15 years from two different academic levels belonging to gender specific or coeducation schools, formed the subject group. All the participants completed seven affective factor scales and an algebraic word problem-solving test with the data collected twice, in the first term and at the end of the academic year. Standardised questionnaires using a 5-point Likert response format were used to measure the student affective factor levels and an algebra test generated from the pilot study was used to measure student problem solving ability. Students were divided into two major groups and other subgroups based on the level of their initial and subsequent performance in the algebra tests. Changes in algebra performance noted in the second test were then viewed against simultaneous affective factor changes and student representatives of the groups and subgroups were interviewed. An analysis of the data from the tests and interviews was then used to explore the existence and description of any associations between the variables. Statistical analysis revealed resonance between lower or impeded problem solving ability and lower and/or decreasing affective factors; and between stable or increasing problem solving ability and higher and/or increasing affective factors. A robust model showing the relationships between affective factors, learning and problem solving has evolved from the students' interview data. At a macro-level, the model relates the internal (cognitive and affective) and external factors to the students' performance. External factors reportedly influencing student performance were the teacher and collaborative work while effort was identified as cementing cognitive and affective factors. At a micro-level the model shows the interrelationship between affective factors, effort, understanding, and learning and performance in mathematics. Both statistical analysis and student interview comments suggest a contributory role of student self-related beliefs in learning and problem solving. From the model it is hoped that teachers can be encouraged to use affect as a tool to promote student learning and performance. Educationalists framing mathematics curriculums should be inclined to emphasise this aspect as an essential ingredient for interactive teaching and learning.