The development of students’ algebraic proficiency

Students’ algebraic proficiency is debated worldwide. To investigate the development of algebraic proficiency in Dutch secondary education, we set up a study, in which 1020 students in grades 8 – 12 took four algebra tests over a period of one year. Rasch analysis of the results shows that the students do make progress throughout the assessment, but that this progress is small. A qualitative analysis of test items that invite structure sense reveals that students’ lack of structure sense may explain the results: the majority of the students were not able to deal flexibly with the mathematical structure of expressions and equations. More attention to structure sense in algebra education is recommended

Promoting insight into algebraic formulas through graphing by hand

Teaching and Teacher Learning (ICLON

Tool use and the development of the function concept : from repeated calculations to functional thinking

The concept of function is a central but difficult topic in secondary school mathematics curricula, which encompasses a transition from an operational to a structural view. The question in this paper is how the use of computer tools may foster this transition. With domain-specific pedagogical knowledge on the learning of function as a point of departure and the notions of emergent modeling and instrumentation as design heuristics, a potentially rich technology-intensive learning arrangement for grade 8 students was designed and field-tested. The results suggest that the relationship between tool use and conceptual development benefits from preliminary activities, from tools offering representations that allow for progressively increasing levels of reasoning, and from intertwinement with paper-and-pencil work