How to be a great mathematics teacher - what the research says

Being a teacher is hard work. Being an effective teacher is even harder. It is surprisingly difficult to find clear advice on how to improve classroom performance - or rather, it is surprisingly difficult to find advice that is pedagogically sound or not advocating some form of educational bandwagon. To the rescue comes a series of pamphlets produced by the International Academy of Education - an organisation with the aim of producing “a syntheses of research on educational topics of international importance”.  Despite the somewhat weighty title of “Effective pedagogy in mathematics” they have produced a highly readable, highly relevant booklet containing some principles of effective mathematics instruction.

According to the authors of the booklet,  Glenda Anthony and Margaret Walshaw, both associate professors at Massey University and also directors of the Centre of Excellence for Research in Mathematics Education, the traits of effective mathematics pedagogy can distilled to;

1. An ethic of care
Caring classroom communities that are focused on mathematical goals help develop students’ mathematical identities and proficiencies. “Teachers who truly care about their students work hard at developing trusting classroom communities.”
2. Arranging for learning
Effective teachers provide students with opportunities to work both independently and collaboratively to make sense of ideas.
3. Building on students' thinking
Effective teachers plan mathematics learning experiences that enable students to build on their existing proficiencies, interests and experiences.
4. Worthwhile mathematical tasks
Effective teachers understand that the tasks and examples they select influence how students come to view, develop, use and make sense of mathematics.
5. Making connections
Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences.
6. Assessment for learning
Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.
7. Mathematical communication
Effective teachers are able to facilitate classroom dialogue that is focused on mathematical argumentation.
8. Mathematical language
Effective teachers shape mathematical language by modelling appropriate terms and communicating their meaning in ways that students understand.
9. Tools and representations
Effective teachers carefully select tools and representations to provide support for students’ thinking.
10. Teacher knowledge
Effective teachers develop and use sound knowledge as a basis for initiating learning and responding to the mathematical needs of all their students.

The booklet is well worth reading and expands upon the extracts presented above.

There is little contained in the publication that will shock educators with an interest in mathematics teaching who have ventured beyond the use of standardised worksheets or textbooks.  However, there are some really reassuring aspects to this booklet. What pleases me most is that an ethic of care is mentioned first - caring for both the student as a learner of mathematics but also as a person.  This reflects the adage I first heard decades ago when I was training; “Students  don’t care how much you know until they know how much you care.”  Mathematics tends to have a dry and dusty “skills based” reputation so it is reassuring to see such a significant body placing emphasis on the teacher-student relationship as being of fundamental importance to effective teaching.

When we care about our students as much as the subject good things tend to result.

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Those with an interest in improving mathematical pedagogy might like to read a related post dealing with the work of Alistair McIntosh - Improving numeracy with the 7Cs.

Those with a general interest in mathematics might enjoy the maths page on this site which collects a range of posts dealing with mathematics.

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