This article is adapted from the author's post of the same title on the University of Western Sydney's 21st Century Learning website, October 2010.

Skills in mathematical reasoning are becoming ever more important in the workplace and everyday living, driven in part by emerging technologies. Yet the last 20 years have seen a decline in the number of students taking mathematics at upper secondary level and beyond (see for example McGee, Ward, Gibbons & Harlow, 2003; Sullivan & McDonough, 2007).

The choice not to pursue mathematics has been seriously influenced by students’ attitudes towards, and performance in, the subject during the middle years of schooling (Year 5 to Year 8 in New South Wales). This is a time when young people are experiencing emotional, social, physical and cognitive changes, and these factors, along with wider societal influences, are often difficult to control from within the school.

However, students’ attitudes and academic performance are also deeply shaped by school mathematical experiences and the teaching they experienced in school (Boaler, 2009; Clarke, 2009; Nardi & Steward, 2003). Arguably teachers are one of the most powerful influences on students’ engagement with mathematics (Anthony & Walshaw, 2009; Hattie, 2003). Applying pedagogical content knowledge (Schulman, 1986), teachers can achieve high and consistent levels of engagement and effective learning.

So, what makes a ‘good’ mathematics teacher? There are several frameworks that address good teaching, including the Quality Teaching Framework (NSW Department of Education and Training, 2003) and the Standards for Excellence in Teaching Mathematics in Australian schools (Australian Association of Mathematics Teachers [AAMT], 2006).

Another way to examine the issue of quality teaching is to discover the opinions of students about their experiences of being taught. How do the frameworks compare to what students think about the qualities of a good mathematics teacher? As part of a longitudinal study on engagement in middle years’ mathematics I asked a group of twenty Year 6 students at a Western Sydney school to name the qualities that make a ‘good’ mathematics teacher. The students said a good maths teacher

• is passionate about teaching mathematics
• responds to students’ individual needs
• gives clear explanations
• uses scaffolding rather than providing answers
• encourages positive attitudes towards mathematics, and
• shows an awareness of each student's prior knowledge.

The study followed the same group of students into the first two years of secondary school. The students took part in individual interviews at the start and again at the end of the study, and in a series of focus group discussions at regular intervals across the three school years (Year 6 to Year 8). During these meetings students identified ‘good’ teachers: some of these teachers were then interviewed about their approach to pedagogy, and their classrooms were observed.

Students’ feedback highlighted the importance of teachers’ pedagogical relationships with students. When students felt their teachers were aware of and catered to their learning needs, they reported that their engagement levels rose. When the students felt disconnected from their teachers and felt the teachers were unaware of their needs, engagement declined. Positive student-teacher relationships provided a foundation on which teachers’ repertoire of pedagogical skills could be brought into play.

The central importance of student-teacher relationships also provides a context for understanding the impact of other educational factors operating at the school. The students were exposed to a new, integrated curriculum, and the school had in fact been purpose-built to cater for next-practice learning and teaching. However, one of the features of the curriculum was the rotation of Year 7 mathematics teachers between classes. This procedure gave them significantly less time to develop pedagogical relationships with their students, and drew critical comments from student respondents. Also in Year 7, a commercial website was introduced, providing tutorials and exercises as the central resource for teaching and learning mathematics.  Although it excited the students initially, they soon became dissatisfied, finding the site a distraction from class work.

In Year 8 the secondary school underwent some significant changes. The curriculum was no longer integrated. There was significantly less reliance on technology and a much heavier emphasis on direct instruction and the use of textbooks. The students began to build relationships with their teachers and, in turn, this saw their engagement in mathematics begin to build. The students spoke about how they now felt their teachers ‘cared’ about them and ‘knew’ them. As one student said: 'if you like the teacher, you’ll get maths more. You’ll know what’s going on more.'

Conclusion

The study identified the interpersonal teaching and learning relationships between teachers and students as the most important factor in optimising engagement with mathematics. The students engaged well when positive relationships with their teachers were in place, and curriculum arrangements were conducive to those relationships. By contrast, it was difficult for students to remain engaged in situations where they lacked positive interactions with teachers, even when they were being taught through a pedagogic approach, a curriculum, and a physical learning environment that could be widely seen as ‘best practice’.

Regardless of the school context, students in the middle years need positive teacher-student and student-student relationships as a foundation for engagement in mathematics. This relationship is built on an understanding of students and their learning needs. Unless such a relationship exists, other pedagogical practices, including the use of technology, may not sustain engagement in mathematics during the middle years.
 

References

Australian Association of Mathematics Teachers [AAMT] 2006, Standards of Excellence in Teaching Mathematics in Australian Schools, Australian Association of Mathematics Teachers, Adelaide.

Boaler, J 2009, The Elephant in the Classroom: Helping children learn and love maths,  Souvenir Press Ltd, London.

Clarke, D 2009, 'Mathematics teaching and learning: where to? Learning Matters, vol. 24, no.1, pp. 3-8.

McGee, C, Ward, R, Gibbons, J & Harlow, A 2003, Transition to Secondary School: A literature review, Ministry of Education, New Zealand.

Nardi, E & Steward S 2003, 'Is mathematics T.I.R.E.D? A profile of quiet disaffection in the secondary mathematics classroom', British Educational Research Journal, vol. 29, no. 3, pp.  345-67.

NSW Department of Education and Training 2003, Quality Teaching in NSW Public Schools, Professional Support and Curriculum Directorate, Sydney.

Schulman, LS 1986, 'Those who understand: Knowledge growth in teaching', American Educational Research Journal, vol. 15, no. 2, pp. 4-14.

Sullivan, P & McDonough, A July 2007, ‘Eliciting positive student motivation for learning mathematics’, paper presented at the Mathematics: Essential Research, Essential Practice, 30th Annual Conference of the Mathematics Education Research Group of Australasia, Hobart, Tasmania.