**Chris Kyriacou** draws on recent research to identify the key features underpinning effective strategies for building students’ mathematics skills

**THE DEVELOPMENT OF STUDENTS’ SKILLS **in mathematics during their school years has been subject to a wealth of research. Moreover, the political importance for governments in fostering high achievement in mathematics is evident in most countries around the world. As such, taking stock of what research can tell us about effective practices for building students’ mathematics skills is a key area of both political and educational interest. In 2003, a Mathematics Education Review Group was established at the University of York by Maria Goulding and myself, funded by the UK Department for Education and Skills (now: Department for Children, Schools and Families). The group comprises researchers and teacher educators from eight universities, together with some representative teachers, local authority advisers, and policy makers. The group has carried out four systematic reviews of relevant literature focusing on key aspects of the teaching and learning of mathematics in primary and secondary schools in England (the equivalent of elementary and middle/high schools in the U.S.). The full report of these reviews can be found on the Evidence for Policy and Practice Information and Co-ordinating (EPPI) Centre website: www.eppi.ioe.ac.uk.

What we know |
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● Students need confidence in their ability and self-identity as learners of math. ● Strategies that promote inclusiveness, deep thinking, and ownership have a powerful effect. ● High-quality professional learning activities are needed to support teachers. |

The first of our reviews looked at the effectiveness of the teaching strategies underpinning the UK’s National Numeracy Strategy, which was introduced into primary schools in England in 1999. In particular, we focused on the use of whole class teaching in the context of the “daily mathematics lesson” for students aged 5–7 years. The second review focused on the effectiveness of strategies for enhancing the motivation of “lower-achieving” students aged 14–16 years. The third review looked at the use of computer-assisted instruction (CAI) to teach algebra in primary and secondary schools. Finally, our fourth review looked at the use of teacher–student dialogue in mathematics lessons to enhance mathematical understanding for students aged 7–14 years. Taken as a whole, there are a number of evidence-based practices that can be advocated, and these are highlighted here in terms of three key themes.

**Inclusiveness **

Perhaps the most powerful theme that has emerged from these reviews is the importance of classroom practices that promote a sense of inclusiveness. One of the main barriers to success in developing mathematics skills lies in a student’s belief that “math is not for them – it’s for the clever ones.” It is thus extremely important for teachers to ensure that all students are able to experience a sense of progress and success in the mathematics they are doing. An important aspect of this is the use of differentiated tasks, so that students can engage with mathematics in a way that is appropriate for their ability and level of prior understanding, and that they receive support and encouragement when needed. Inclusiveness also requires teachers to make use of strategies where the share of contribution each student in a class makes to discussion is equal and equally-valued by the teacher. Small group work tasks can enhance students’ engagement in mathematical activities by providing a safer (less exposed) learning context within which to share ideas and also by fostering a greater awareness of metacognitive strategies (how students think about, direct and evaluate their thinking while engaged in a problem-solving task) through observing and discussing with peers how to approach a problem. Such strategies can have a powerful effect on enhancing students’ self-identity as someone who can do mathematics.

**Deep thinking **

An important aspect of coming to see oneself as a student who can succeed in mathematics, is to be able to undertake tasks that are challenging but “achievable with effort.” A danger with mathematics teaching is that sometimes, in order to avoid students experiencing failure, a teacher will adopt a comfort zone around their work, so that students may not feel sufficiently challenged or stretched by the work they do. Our reviews, however, indicate that a powerful influence on how students develop a positive self-identity as learners of mathematics comes from experiences in which they are challenged to think harder and deeper about the mathematics they are doing. The insight they then develop in the context of this effort enables them to feel they can succeed, and to also get a sense of the enjoyment that comes from problem solving, which generates a deeper understanding of the mathematics they are doing. One particular aspect of this involves the use of CAI. At one level, the use of CAI by the teacher and students can act as a powerful motivator, but there is a danger that too much teaching and learning involving CAI can be superficial in terms of the depth of mathematical understanding being fostered. It is only when CAI is linked to the promotion of deeper learning that the real benefits of using CAI as a vehicle through which mathematics skills can be fostered are genuinely realized.

**Ownership **

In many classes, the teacher is viewed as the expert, and learning is seen by students as a matter of paying close attention to what the teacher says and does before trying some exercises for oneself. Ownership refers to the ways in which teachers make use of strategies where students can take greater control over the direction of the lesson. One example of this concerns how teachers can create a learning environment in which teacher–student and student–student dialogue is used to convey that students’ views are taken seriously, and are allowed to influence which approaches to problem-solving are explored and the interpretation of mathematical understandings that result. An effective strategy here is to go beyond the use of a teacher–student dialogue comprising a simple sequence of initiation– response–feedback (i.e. the teacher asks a question, the student gives an answer, the teacher comments on the answer) to enrich the dialogue by asking more challenging questions, asking students to explain their answers, and involving other students in a more extended sequence. The term co-construction has become more frequently used to describe how teachers can adopt a more equal role with students in how they generate and consider different approaches to solving mathematical problems and evaluate these together.

**Conclusion **

In order to become capable and strategic learners in mathematics, students need to have confidence in their own ability and self-identity as learners of mathematics. Strategies that promote inclusiveness, deep thinking, and ownership, can have a powerful effect on building students’ mathematics skills. This can be contrasted with those strategies which can be characterized as viewing learning in mathematics as elitist (only for clever students), superficial (the application of well-rehearsed procedures), and teacher-centered (follow what the teacher says and does). All four of our reviews have also pointed to the need for high quality professional learning activities to enable teachers of mathematics to make use of evidence-based strategies.

**About the author **

**Chris Kyriacou** is Reader in Educational Psychology at the University of York Department of Educational Studies, and co-director of the UK DCSF-funded Mathematics Education Review Group. He is also the author of two very popular textbooks on teaching: *Effective Teaching in Schools *and *Essential Teaching Skills*.

**Further reading **

Goulding M and Kyriacou C (2008), A Systematic Review of the Use of ICTs in Developing Pupils’ Understanding of Algebraic Ideas. In: *Research Evidence in Education Library. *London: EPPI-Centre, Social Science Research Unit, Institute of Education.

Kyriacou C (2008) Inclusive Teaching in Mathematics. *Mathematics in School*, 37(5), 17–19.

Kyriacou C and Goulding M (2004) A Systematic Review of the Impact of the Daily Mathematics Lesson in Enhancing Pupil Confidence and Competence in Early Mathematics. In: *Research Evidence in Education Library. *London: EPPI-Centre, Social Science Research Unit, Institute of Education.

Kyriacou C and Goulding M (2006) A Systematic Review of Strategies to Raise Pupils’ Motivational Effort in Key Stage 4 Mathematics. In: *Research Evidence in Education Library. *London: EPPI-Centre, Social Science Research Unit, Institute of Education.

Kyriacou C and Issitt J (2008) What Characterises Effective Teacher-initiated Teacher-pupil Dialogue to Promote Conceptual Understanding in Mathematics Lessons in England in Key Stages 2 and 3? In: *Research Evidence in Education Library. *London: EPPI-Centre, Social Science Research Unit, Institute of Education.

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