Key Ideas in Mathematics Education

International research in teaching mathematics and shows how students learn, why they sometimes get things wrong, and the strengths and pitfalls of different teaching approaches.

Background

This project, funded by the Nuffield Foundation, and the Oxford University Press set out to review the mathematics education research with a view to making it accessible to practitioners and educators.

Challenge

The range of research available in mathematics education can be bewildering and contradictory. In response this review covered areas such as theoretical explanations for how students learn mathematics, key ideas within mathematics education, conceptual growth in specific knowledge sub-domains, misconceptions and confusions, and the advantages and disadvantages of particular teaching approaches. 

Solution

The resultant publication is an authoritative account of the state of the art of mathematics education research pertaining to the teaching and learning of 9 to 19 year old students. 

Key findings:

• some ideas permeate the mathematics curriculum: ‘relations between quantities and properties is all pervasive’; ‘powerful implicit ideas characterise what makes mathematics mathematical’; ‘formalization moves from a focus on what is explicit in the everyday to what is hard to see in everyday situations’;
• some issues around conceptual growth recur in all knowledge sub-domains: ‘sources of confusion’; ‘a range of experiences designed to be purposeful facilitate powerful mathematical thinking’; ‘representations are key tools for mathematical learning’; ‘proportional reasoning is central';
• and in teaching approaches, the recurrent themes are: ‘concept definitions need to be introduced alongside non-examples and boundary cases’; ‘by exercising control over carefully designed software, students can ask new questions and engage more fully’; ‘graphical representation is a tool for learning and connecting representations in almost all knowledge sub-domains’.

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