To develop excellent secondary maths teachers we need space in the curriculum for critical reflection

Pete Wright.

Mathematics teacher educators face strikingly similar challenges to secondary maths teachers. Both groups face the seemingly impossible task of enabling students to achieve depth of understanding whilst being expected to cover an overly prescriptive core curriculum.

The Government’s plans for reforming initial teacher education look unlikely to have a positive impact on maths teaching. What would improve the situation?

I have highlighted elsewhere the growing consensus amongst mathematics educators that the school curriculum needs to focus more on developing conceptual understanding. Students need to progress beyond learning mathematical procedures without appreciating what they are used for. They need to develop confidence in applying these procedures to solve real life problems similar to those they will encounter in their lives. This means students need to be given opportunities to explore challenging mathematical problems where it is not immediately obvious which procedures to apply. Students should be encouraged to reflect on the reasons why mathematical procedures work, how they were developed, and which situations they are best applied to.

And yet too many mathematics lessons are typified by the teacher explaining a procedure, demonstrating its use in solving a closed problem, before setting students a series of almost identical tasks. In 2013, the government introduced a new mathematics curriculum which, it claimed, would place greater emphasis on mathematical reasoning and problem solving. These two objectives were incorporated, alongside developing fluency, as overarching aims. Paradoxically, however, the new curriculum included even more subject content than the previous one. This was despite calls for less content, enabling each topic to be tackled in greater depth and with greater emphasis on developing conceptual understanding. Not surprisingly, the new curriculum has had little impact on the way mathematics is commonly taught in schools.

Fast forward to 2019 when the government introduced the Core Content Framework (CCF), which was presented as a minimum entitlement for student teachers. The CCF has been criticised for ignoring the importance of subject specificitywhich, at UCL’s Faculty of Education, we see as a central element of ITE provision. Teacher educators now face the same pressure as teachers in schools to cover core content, since adherence to the CCF is closely monitored by Ofsted and will be an important factor in universities gaining re-accreditation for their ITE courses before 2024. The fundamental issue here is that the CCF places too much emphasis on generic knowledge and practice within the ITE curriculum and leaves insufficient space to address subject-specific demands.

Developing excellent secondary maths teachers requires addressing a combination of issues which is unique to the discipline. Firstly, mathematics is one of the oldest disciplines, arising from humans striving to make sense of the world around them to survive and prosper. Whilst new mathematical knowledge continues to be generated out of a need to solve current day problems or resolve unanswered questions, the vastness of the discipline has often led to the original rationale for older mathematical ideas being forgotten.

Genuinely powerful mathematical knowledge requires an appreciation for how new knowledge is generated by mathematicians. This necessitates students investigating open-ended problems, engaging in mathematical argumentation, working collaboratively, posing their own questions and comparing solutions. Most student teachers are initially unfamiliar with these ways of working, having experienced the traditional approach described above. Reflecting critically on their own learning experiences and interrogating their own prior assumptions about mathematics are essential if student teachers are to become effective teachers of mathematics who can challenge and improve on existing practice in maths teaching.

Another unique aspect of mathematics is the extent to which it evokes high levels of anxiety, alienation and disengagement amongst some learners. These are partly attributable to the high-stakes nature of assessments, with maths qualifications often determining opportunities for future study and employment. Research also suggests they can result from implicit messages that are transmitted, often unknowingly, by teachers in the mathematics classroom. For instance, the way in which teachers respond to students’ errors, or praise their achievements, can result in a fear of failure and value being attached to ‘answer-getting’ rather than ‘meaning-making’. This highlights the importance of encouraging student teachers to engage with theory and research, enabling them to better understand the difficulties faced by learners of mathematics and why some teaching strategies are more effective in overcoming barriers to learning. Such critical reflection on practice can be likened to developing conceptual understanding in school mathematics, and both require more space within the curriculum.

Photo by Alliance for Excellent Education, via Creative Commons