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Analytical (relational) and non-analytical (associative) thought processes during mathematics learning – a functional brain imaging study.

Research project The aim of the research project is to examine brain activity during learning with and without understanding. In a model situation during fMRI, the participants either learn the meaning of symbols or associations between figure types.

Many students do not understand the mathematics and thereby do not develop problem-solving ability. Theories have pointed to the importance of Analytical-Relational knowledge and argued that it is fundamental for higher thought processes and critical for the understanding of mathematical concepts. Little is known about what distinguishes mathematics learning with and without understanding in terms of brain activity and brain structures involved. This study uses functional magnetic resonance imaging to examine brain activity during learning of relations or associations, which can be linked to understanding or lack of understanding in a learning situation.

Project overview

Project period:

2014-01-01 2015-12-31

Funding

The Kempe Foundations

Participating departments and units at Umeå University

Department of Science and Mathematics Education, Faculty of Science and Technology

Research subject

Educational sciences, Mathematics

Project description

This project is part of the overall project "Learning mathematics by imitative and creative reasoning".

One of the major problems in mathematics education nationally and internationally is that many students do not understand mathematics and thereby do not develop adequate problem-solving ability. The concepts "meaning" and "understanding" often occur in mathematics education contexts - usually as names for desirable aspects of learning, and in contrast to more superficial or simple aspects that appear to dominate. Theories and empirical studies in cognitive psychology has stressed "Analytical-Relational" knowledge and argued that it is fundamental for higher thought processes and critical for the understanding of mathematical concepts. Analytical-Relational knowledge differs from "Non-analytical-Associative" knowledge in a variety of ways, primarily through the use of symbols. Very little is known about what distinguishes mathematics learning with and without understanding in terms of brain activity and brain structures involved. Analytical-relational cognitive processes have been associated with activity in the dorso-and rostrolateral prefrontal cortex. The hippocampus is probably also involved when the analytical-relational processes are part of memory encoding or learning. Non-analytical associative cognitive processes have been linked mainly to the hippocampus in humans, and can depending on the degree of unconscious (implicit) learning involve the basal ganglia. fMRI studies focusing on analytic-relational processes involved in memory encoding and learning are, however, rare. The purpose of this study is to examine differences in brain activity during mathematics learning with and without understanding. For this purpose, a model situation has been designed so that a group of participants are expected to spontaneously learn the meaning of new symbols during practice, while another group is expected to spontaneously learn associations between shapes, without understanding the meaning of the symbols. The experimental set-up is identical for all participants. Participants' responses during practice, and at post-test and transfer-test is recorded. Group membership is determined from response patterns at the post test. Brain activity is compared between groups during practice and test. The main outcome variables are brain activation (fMRI) during practice and test, as well as response patterns and performance during practice, post-test and transfer test. Performance at the transfer test, carried out after fMRI, is the behavioral variable that is the strongest indication of understanding, and the acquisition of analytical-relational knowledge. Lack of understanding of mathematics is perhaps the most important problem in the field of research on mathematics teaching. This project is expected to contribute with neuroscientific knowledge of brain structures and processes involved.