# Developing a conceptual understanding in mathematics

The purpose of the project is to develop a better understanding of what a conceptual understanding entails, and to use this understanding to develop principles for teaching and for students’ opportunities to learn. A specific focus is on mathematical tasks and problem solving.

The aim of the project is to develop a theory as a base for understanding students’ development of a conceptual understanding, and to develop principles for the selection and design of mathematical tasks/mathematical problems.

The project is based on two doctoral thesis (Jäder, 2019; Wedman, 2020) and the notion of conceptually challenging tasks. The foundation for the building of the theory comes from the field of cognition science combined with other existing educational science theories. The theory will be used in a context where a conceptual understanding is to be developed through mathematical problem solving.

## Four steps can be used to describe the intended implementation of the project:

- Using the theoretical outset, mathematical problems which focus on properties and definitions of mathematical concepts, are selected and constructed through consultation with teachers.
- Data is gathered through students’ task solving and interviews with students, focusing on their understanding of the task solutions and on their conceptual understanding in a more general sense.
- Participating teachers and researchers discuss the significance of different occurrences during the task solving and interview sessions.
- Principles for task selection and design is developed through analysis of the data and based on a developed theoretical base.

These steps can be iterated for further development.

The project initially runs from October 2020 until June 2022, possibly extending beyond this. At the start of the project one school and one teacher is part of the project. Early fall 2021 the quest for interested schools and teachers continues, to carry on with the project.

**References**

Jäder, J. (2019). The challenges of mathematical problem solving – The conceptual and the creative challenge (manuscript). In Jäder (Ed.) *Med uppgift att lära - Om matematikuppgifter som en resurs för lärande* (Doctoral dissertation, Umeå University).

Wedman, L. (2020). The concept *concept* in mathematics education: A concept analysis (Doctoral dissertation, University of Gothenburg).