Based on results from the TIMSS studies documenting weak performances in algebra among Norwegian students, this thesis investigates the question “Why is algebra so difficult?” by studying cognitive processes involved in solving algebra problems. Conceptual understanding, procedural fluency, adaptive reasoning, and strategic competence comprise what in this thesis is called proficiency, and serve as a theoretical framework for the empirical data presented and analysed. Written test responses from 412 8th-graders and 417 10th-graders constitute the empirical data, in addition to follow-up interviews with selected students. Diagnostic information, where strategy choices, errors, explanations, and justifications are central elements, is emphasised in the analysis.
The findings suggest a cognitive gap between informal and formal reasoning in grade 8 and pinpoint differences and similarities in formal proficiency in both grades. Formal procedures seem to be used in a highly algorithmic manner, not guided by a deeper understanding of linked core concepts (e.g. equivalence). Many of the same problems were seen in both grades, such as misconceptions due to limited arithmetic knowledge and over-generalizations in the transition from arithmetic to algebra. In addition, an inability to explain and justify their reasoning was evident among the majority of students. An overall message is that algebra teaching could benefit from an increased focus on different aspects constituting algebraic proficiency beyond the “skill versus concept” outlook, and that these aspects are closely intertwined in the development of proficiency.
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