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Learning by Imitative and Creative Reasoning (LICR)

Research project The design research programme learning by imitative and creative reasoning (LICR) studies whether, how and why tasks and teaching that enhance creative reasoning lead to a more productive struggle and more efficient learning of mathematics than the common but inefficient task designs based on imitating given solution procedures.

Despite 20 years of comprehensive reform efforts mathematics still consists for many of facts and procedures to be memorized without understanding. This leads to both inefficient learning and that mathematics is perceived as dull and pointless. Recently, new opportunities have opened up by interdisciplinary research collaboration. The project considers four main learning models which provide different opportunities to understand mathematics, from a math educational perspective and from a neuro-scientific perspective. Data from interviews, behavioral studies and studies of brain activity are linked together via a third area of research, cognitive psychology.

Head of project

Project overview

Project period:

2009-01-01 2025-12-31


Finansår , 2009, 2010

huvudman: Johan Lithner, finansiär: Kempestiftelserna, y2009: 500, y2010: 500,

Participating departments and units at Umeå University

Department of Science and Mathematics Education, Faculty of Science and Technology, Umeå Mathematics Education Research Centre

Research area

Educational sciences, Mathematics

Project description

Mathematics is the world’s largest educational subject and a foundation for many activities within technology and science, but also within medicine, economy, etc. A central problem in Swedish and international mathematics education is that we want the students to understand mathematics and become good problem solvers, but even after 20 years of research and reform consists school mathematics for many students only of a large number of facts and procedures to memorise without understanding. This leads to inefficient learning and that mathematics is apprehended as boring and meaningless, which in turn leads to that students avoid mathematically intense programs and/or have difficulties to manage the courses.
A central question is which teaching methods work best? The question is difficult since learning is affected by many complex factors, and there is much more that we do not know than what we know. There are indications that some methods may work better than other, but there are essentially no scientific evidence under what conditions, in what ways and why this may be the case. Recently new methods are appearing through multi-disciplinary collaboration between educational sciences (in this study mathematics education), psychology and neuroscience.
The purpose of the research project is to study character and efficiency of four basic methods to learn mathematics:
I) To memorise facts, e.g. the multiplication table.
II) To memorise algorithmic procedures without understanding, for example a stepwise method to solve equations (e.g. 3x-4=2).
III) To learn algorithms with explanation, for example that the teacher describes how the equation algorithm works but also explains why.
IV) That the student herself constructs a solution method, for example by starting with simple equations and stepwise solve more difficult equations and simultaneously develop insights in the principles of equations.
Method I is rare since it is applicable only on a few types of mathematical tasks, for example asking for facts (how many centimetres is a metre?), definitions (what is a rectangle?) and mathematical proofs. Extensive national and international research show that method II is common and applicable on most practice and test tasks in primary, secondary and tertiary education. Method III seems to be the prevailing ideal among teachers, even though practice is largely focussed on II. Educational science has indicated that method IV has a large potential, but there is a lack of empirical evidence.
Latest update: 2019-10-01