The role of algebraic knowledge, higher-order thinking and affective factors on students' performance on novel algebraic word-problem solving

This thesis focuses on solving algebraic novel word-problems. The study aimed to investigate the role of algebraic knowledge, higher-order thinking and affective factors in problem solving. Sixteen Year 11 students were selected and requested to solve fifteen novel algebraic word-problems. Ginsburg's (1992) mixed methods involving the talk-aloud and clinical methods were used to interview the students as they solved the various word-problems. The interview sessions were videoed and the data transcribed. Protocol analysis was then used to examine in depth the performance of the students in terms of the factors studied. The results of this study showed that algebraic knowledge, higher-order thinking and affective factors were associated with success in novel algebraic word-problem solving. However, higher-order thinking was found to the most important factor in successful performance. The students who exhibited critical thinking by analysing the problems in sufficient detail, identifying/developing relationships between variables, identifying assumptions and engaging in high levels of metacognitive thinking performed better overall than the students who demonstrated low levels of critical and metacognitive thinking. Likewise, students who used algebraic methods were more likely to succeed than those who did not. Although algebraic knowledge was not as strongly associated with success as higher-order thinking the importance of domain knowledge was nevertheless noted in this study. Although affective factors were found to be less important than domain knowledge and higher-order thinking the results showed that students' belief, attitude, persistence and confidence were associated with performance. The students who demonstrated positive attitude and/or appropriate belief regarding algebraic methods used algebraic methods more often than others who demonstrated inappropriate attitudes and/or beliefs about knowledge generally. Further, the students who demonstrated high levels of persistence and confidence performed better overall in terms of number of correct solutions than the students who demonstrated low levels of persistence and confidence