Research project It has been known for at least 30 years that the key to deepening students’ mathematical knowledge is to engage them in constructing their own mathematical reasoning. However, such practices remain uncommon and challenging to implement. This project investigates: How the combination of tasks and teacher support should be designed to foster students’ own mathematical reasoning. How characteristics of tasks and teacher support influence students’ reasoning and their mathematical knowledge.
The aim of the project is to specify how construction and imitation affect students’ learning processes and outcomes, and to develop guidelines for designing combinations of tasks and teacher support that promote learning of specific mathematical content. Using a design-based research approach, we will, through iterative cycles of design, analysis, and revision, examine how tasks and teacher support vary between classes and among students within the same class, and how this variation influences students’ reasoning and outcomes—an issue not previously investigated.
The project comprises three phases:
Phase 1: Teachers and researchers collaborate to develop a constructive instructional design. This phase is repeated for different mathematical content areas and results in 4–8 interventions. It also includes describing what an imitative instructional design looks like for the corresponding mathematical content.
Phase 2: The designed instruction is tested in comparative experiments. One group of students encounters the imitative design, which represents a controlled version of commonly occurring instruction: each task has a predefined solution method, and if a student gets stuck, the teacher explains the method again. The other group encounters the constructive design developed in Phase 1 and works on tasks without a given solution method. If students need support, the teacher uses formative assessment to facilitate students’ own construction of mathematical reasoning.
Phase 3: Data from all trials and experiments are analyzed, resulting in general principles for the design of tasks and teacher support that develop students’ mathematical knowledge. These principles can be used to revise and develop tasks and teacher support in other areas of mathematics as well.
The development of a constructive instructional design is based on close collaboration between teachers and researchers, and on teachers having the opportunity to test the ideas that are developed. Through iterative cycles in which ideas are tested by teachers in Grades 4–6, the specific expertise of both teachers and researchers will complement one another and contribute to the development of the instructional design. Since the teachers work with students in heterogeneous classrooms, the instructional design will be adapted to multiple levels of prior knowledge. The project’s findings and insights will be reported not only in scientific journals but also in publications directed at teachers. Because the project’s results are generated through iterative testing of instructional designs in regular classroom settings, they will be more readily applicable for teachers.
