MERGA Submission to the Decadal Plan
The Mathematics Education Research Group of Australasia provides the following submission to the Decadal Plan for the Mathematics Sciences. The submission was prepared by Dr Tracey Muir (VP Development) following consultation with members who contributed via invitation to a survey to the following themes:
- Strengthening the supply and support of teachers of mathematics and statistics
- Closing achievement gaps in mathematics and statistics
Strengthening the supply and support of teachers of mathematics and statistics
Currently teachers are still coming to terms with the implementation of the Australian Curriculum, both in terms of content and assessment requirements. Knowledge of curriculum is especially challenging for primary teachers who need to be familiar with curriculum documents across a range of subjects. Statistical knowledge may prove to be particularly challenging for primary teachers, given that it has not had a huge focus in many primary schools in the past and their own content knowledge in this area may not be strong. In secondary schools, there is still an under-supply of specialist mathematics teachers throughout the country. There are a number of strategies that have been tried to address this shortage, but unfortunately perceptions of low status and demanding working conditions are not attracting people to the profession.
It is difficult to get accurate data on teacher supply because universities are not required to keep records of the secondary teaching areas in which their graduates specialise (and governments don’t ask them to provide this information), but recent surveys suggest that 20-30% of those teaching secondary mathematics (typically junior secondary) did not specialise in mathematics education in their pre-service teacher education program (Harris, & Jensz, 2006). The geographical distribution of out-of-field mathematics teachers is not even; schools in rural and remote areas report higher staff turnover and more difficulty recruiting qualified teachers than those in metropolitan areas (Lyons et al., 2006). This is especially worrying when PISA data show that the gap in mathematical literacy performance between students in metropolitan and remote schools is equivalent to about 1.5 years of schooling (Thomson et al., 2010).
Although some universities have students entering with a ATARs of ≥ 90, the majority have not taken mathematics to a high level in their final 2 years of study at High School and some (< 10) may not have taken any mathematics. Anecdotal evidence from mathematics education lecturers show that pre-service teachers’ experiences and attitudes towards mathematics are still quite negative, even for those who studied maths at higher levels. Lecturers did report, however, that quality teacher education programs along with quality entering pre-service teachers often means that they can increase their content knowledge and develop mathematical understanding. Some concerns were expressed about low level of entry standards (e.g., ATARS as low as 30) being accepted in some Australian universities. Concerns have also been expressed at the graduate phase of pre-service teacher education. Australian graduating teacher standards express clear expectations that graduates must understand the content they teach and be able to design and deliver lessons that meet curriculum, assessment and reporting requirements. However, graduating requirements continue to be a concern in relation to prospective teacher entry levels of mathematics (Anthony, Beswick, & Ell, 2012). Calls for a greater emphasis on subject matter knowledge in pre-service teacher programs, however, are only part of the solution as there are many different types of knowledge required for effective teaching (Frid, Goos, & Sparrow, 2009). Unfortunately, Australia didn’t participate in the international TEDS-M study, which measured the professional knowledge of nearly-graduated teachers of mathematics and investigated relationships between teacher knowledge and pre-service program structure (Tatto & Senk, 2011). The only Australian data we have about mathematical Pedagogical Content Knowledge comes from the ALTC CEMENT project led by the University of Tasmania (e.g., Beswick & Goos, 2012) and the only published results are for primary teachers due to the low numbers of secondary pre-service respondents.
Professional learning for practicing teachers of mathematics varies widely in terms of quality and process. It ranges from small-scale individualised teacher professional opportunities (e.g., Muir, Beswick, & Williamson, 2010), to small groups of teachers (e.g., Brown, 2009) and large-scale programs of professional development (e.g., White, 2010) involving off site workshops, professional reading and/or classroom support. Numeracy coaches (e.g., Anstey & Clarke, 2010) can also be viewed as a ‘tool’ or source of teacher knowledge, while other professional learning experiences have focused on tasks and students’ responses to these (e.g., Horne, 2008).
Professional associations generally do a good job of providing quality professional development, but often they are preaching to the converted and do not really reach teachers who would benefit most from updating their professional knowledge. In Queensland, for example, it is now compulsory for teachers to undertake a specified number of hours of PD annually in order to maintain their professional registration, but there is no quality control of this PD and costs vary widely. It is too expensive and time consuming for the teacher registration authority to monitor quality or develop approval processes for PD providers. Apart from staying registered, there is no other incentive for teachers to participate in professional learning: no increase in salary or improvement in working conditions, no change in career path.
We would recommend that support for current mathematics teachers involves professional learning that is situated in classroom practice, is sustained, with teachers given time to attend and follow up, and is endorsed by school and district leaders. Different approaches to professional learning need to be considered that are more individualised and encourage teachers to implement new practices and reflect upon their effectiveness. Further support also needs to be given in terms of making the professional learning affordable and accessible to all teachers including those in remote locations.
Members identified that the main challenge facing mathematics teachers today is the lack of time – to both attend professional learning and to reflect on their practice and how to do it more effectively. There continues to be a concern with the engagement of middle years’ students in mathematics – this could be partly addressed through ensuring that they receive mathematics teaching from qualified and enthusiastic mathematics teachers. The Decadal plan might also be an opportunity to look at providing specialist mathematics teachers within primary schools, particularly in the upper grades.
Assuring the supply of qualified and high quality teachers of mathematics is not a simple issue, and it’s connected to other issues of concern such as decreasing enrolments in advanced mathematics in school and low participation in university mathematics. No single strategy is going to solve all these problems, so it will take courage and vision from governments as well as cooperation between the main stakeholders (university education faculties and schools, university mathematics schools, teacher professional associations, etc) and a commitment to long term planning rather than quick fixes to make any difference. No amount of legislation can make teaching a more attractive career for university mathematics graduates, who can typically earn more money and find more supportive working environments elsewhere; just raising entry standards for pre-service programs is not going to change this.
Closing achievement gaps in mathematics and statistics
A recent review of Australasian research 2008-2011 (Gervasoni, Hunter, Bicknell, & Sexton) provided insight about powerful pedagogical actions to maximise learning in school mathematics. The review found that the findings centred around three themes related to powerful pedagogical actions: (a) creating powerful learning environments; (b) selecting tasks and models that promote deep learning; and (c) knowing and using pedagogical knowledge.
A number of studies (e.g., Bautista & Mulligan, 2010; Niesche, 2009) addressed effective pedagogy for teaching mathematics in diverse classrooms. Such studies, in contrast to taking a deficit view, direct attention to how student learning opportunities and engagement increase when teachers use socially and culturally responsive pedagogical actions. Studies include utilising students’ social relationships, cultural understandings, and home languages, within relevant and engaging curricula. These studies open a pathway for Australasian and international researchers to listen to, and work with, Indigenous communities in developing powerful pedagogical actions for all.
Another way in which the achievement gap can be addressed occurs when teachers demonstrate their pedagogical knowledge through their selection of rich tasks and models that cater for multiple entry points (e.g., Grootenboer, 2009). Tasks need to be sufficiently problem-based to provoke collaborative and interactive group work within extended dialogue premised in the discourse of inquiry and argumentation (Gervasoni, et al., 2012). Studies of problems, tasks, and models suggest that these need to: (a) involve visualising, modelling, and practical experiences; (b) be challenging enough to extend learning; and (c) be engaging and authentic for students.
Learning trajectories and growth point frameworks can be used to identify achievement gaps and then used for planning instruction. One-on-one interviews have been found to be effective assessment strategies that provide for further exploration and elaboration of students’ explanations.
Technology, in its role as a pedagogical tool, holds significant possibilities for improving learning and teaching. It was clear from the reviewed studies that teachers play a critical role in determining the way that technology is used in mathematics classrooms (Gervasoni, et al., 2012). Studies showed the significance of ICT as a motivational tool and how it can be a spring-board to prompt mathematical learning during all phases of mathematical activity. However, caution needs to be used because there are indications that without expert pedagogical actions students may only attend to surface features of the mathematics rather than making connections across broader understandings. Similarly, teachers influence the role IWB hold in a classroom as a pedagogical tool. Studies note their motivating features but recognise the potential these have to default to teachers using more transmission modes of teaching. We would recommend therefore, that the use of ICT be fully explored as a way of both engaging students and improving teachers’ pedagogical practices.
Analysis of Australian children’s mathematical knowledge highlights that a significant number are mathematically vulnerable. This calls very for a variety of instructional approaches, including classroom instruction, specialised short term intervention programs and ongoing specialised assistance for those with complex learning difficulties. In all cases this calls for teachers with specialised knowledge who can assist with diagnostic assessment, professional learning provision and advice for classroom teachers and provision of intervention programs. (Approaches such as the Extending Mathematical Understanding and Maths Recovery are useful in this regard).
Anstey, L., & Clarke, B. (2010). Perceived professional learning needs of numeracy coaches. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 45-52). Fremantle, WA: MERGA.
Anthony, G., Beswick, K., & Ell, F. (2012). The professional education and development of prospective teachers. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, J. Greenlees (Eds.), Research in mathematics education in Australasia 2008-2011 (pp. 291-312). Rotterdam, The Netherlands: Sense Publishers.
Bautista, D., & Mulligan, J. (2010). Why do disadvantaged Filipino children find word problems in English difficult? In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 69-76). Fremantle, WA: MERGA.
Beswick, K., & Goos, M. (2012). Measuring pre-service primary teachers’ knowledge for teaching mathematics. Mathematics Teacher Education and Development, 14(2), 70-90.
Brown, J. P. (2009). Concept maps: Implications for the teaching of function for secondary school students. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia, pp. 65-72). Palmerston North, NZ: MERGA.
Frid, S., Goos, M., & Sparrow, L. (2009). What knowledge is needed for effective teaching of mathematics. Mathematics Teacher Education and Development, 9, 1-3.
Gervasoni, A., Hunter, R., Bicknell, B., & Sexton, M. (2012). Powerful pedagogical actions in mathematics education. In B. Perry, T. Lowrie, T. Logan, A. MacDonald, J. Greenlees (Eds.), Research in mathematics education in Australasia 2008-2011 (pp. 193-218). Rotterdam, The Netherlands: Sense Publishers.
Grootenboer, P. (2009). Rich mathematical tasks in the Maths in the Kimberley (MITK) project. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia, pp. 696-699). Palmerston North, NZ: MERGA.
Harris, K. & Jensz, F. (2006). The preparation of mathematics teachers in Australia. Report prepared for the Australian Council of Deans of Science. Melbourne: Centre for the Study of Higher Education, The University of Melbourne.
Horne, M. (2008). Using educational research to inform mathematics teaching in a school. In O. Figueras, J. L. Cortina, S. Alatorre, T. Rojano, & A. Sepulveda (Eds.), Mathematical ideas: History, education and cognition (Proceedings of the joint meeting of PME 32 and PME-NA XXX, pp. 81-86). Morelia, Mexico: Cinvestav-UMSNH.
Lyons, T., Cooksey, R., Panizzon, D., Parnell, A., & Pegg, J. (2006). Science, ICT and mathematics education in rural and regional Australia: The SiMERR national survey (Abridged report). Retrieved 16 September 2010 from http://www.une.edu.au/simerr/pages/projects/1nationalsurvey/Abridged%20report/Abridged_Full.pdf.
Muir, T. , Beswick, K., & Williamson, J. (2010). Up, close and personal: Teachers’ responses to an individualised professional learning opportunity. Asia-Pacific Journal of Teacher Education, 38(2), 129-146.
Niesche, R. (2009). The use of home language in the mathematics classroom. In R. Hunter, B. Bicknell, & T. Burgess (Eds.), Crossing divides (Proceedings of the 32nd annual conference of the Mathematics Education Research Group of Australasia, pp. 704-707). Palmerston North, NZ: MERGA.
Tatto, M. T., & Senk, S. L. (2011). The mathematics education of future primary and secondary teachers: Methods and findings from the Teacher Education and Development Study in Mathematics. Journal of Teacher Education, 62(2), 121-137.
White, A. L. (2010). Counting on in the middle years. In L. Sparrow, B. Kissane, & C. Hurst (Eds.), Shaping the future of mathematics education (Proceedings of the 33rd annual conference of the Mathematics Education Research Group of Australasia, pp. 610-617). Fremantle, WA: MERGA.