# Secondary and university mathematics: Do they speak the same language?

## Project Manager

**Dr Jill Vincent**

**T:**8344 8532

**E:**jlvinc@unimelb.edu.au

**W:**Personal web page

**Location:**Level: 07 Room: 703, Doug Mcdonell Building, Parkville

## Project Details

The decline of tertiary enrolments and the low retention rates in mathematical sciences is a national and international concern.

The project will examine symbol use, a key aspect of students’ mathematical experience at school and university, and measure its impact on progression rates. Research, at secondary level, shows that mathematics symbols’ conciseness and abstraction can be a barrier to learning. Discontinuities in how symbols are used can make mathematics seem like a foreign language so students lose confidence. This project will explore the equivalent issue at the university level, when mathematics becomes more symbolic and its writing more subtle, requiring increased ‘flexibility’ from students. It will ascertain the impact on progression rates in mathematical sciences.

The project’s outcomes will include illustrated descriptions of similarities and contrasts between conventions and use of symbols in secondary and university mathematics and across mathematical sciences. It will provide evidence of links between students’ response to increased symbolic load and their confidence to continue studying subjects with high mathematical content at university, thus grounding potential teaching action plans to smooth secondary-university transition. The outcome will be innovative teaching practices to retain students in mathematical sciences, and hence increase the STEM workforce.

### Rationale

Mathematics derives much of its power from the use of symbols (Arcavi 2005), but research at secondary level has shown that their conciseness and abstraction can be a barrier to learning (Pierce, Stacey & Bardini 2010; MacGregor & Stacey 1997). We anticipate that many students have difficulty with the new and more intense ways in which symbols are used at university (these will be described below), with the consequence that they do not understand the mathematical content as well as they did before, which leads to a decrease in positive affect, which in turn discourages enrolment in further mathematical subjects.

## Researchers

**Dr Caroline Bardini**Leading Chief Investigator**A/Professor Robyn Pierce**Co-Chief Investigator**Emeritus Professor Kaye Stacey**Co-Chief Investigator**Dr Jill Vincent**Project Manager

## Collaborators

### Advisory panel

- Dr Deborah King (University of Melbourne)
- A/Prof Michael Page (Monash University)
- A/Prof Helen Chick (University of Tasmania)
- Dr Alasdair McAndrew (Victoria University)
- Dr Jason Giri (Federation University)
- Janine McIntosh (Australian Mathematical Sciences Institute)

With the collaboration of Victorian Secondary Schools

## Funding

The project has been approved by the University of Melbourne Human Research Ethics Committee and is funded by the Australian Research Council under the Discovery Project scheme for 2015 (DP150103315).

## Published Research

### Current publications

- Bardini, C. & Pierce, R. (2015). Assumed mathematics knowledge: the challenge of symbols. International Journal of Innovation in Science and Mathematics Education, 23(1), 1- 9.
- Vincent, J., Bardini, C., Pierce, R. & Pearn, C. (2015). Misuse of the equals sign: an entrenched practice from early primary years to tertiary mathematics. Australian Senior Mathematics Journal, 29(2), 28-36.
- Bardini, C., Pierce, R. & Vincent J. (2015). Contemplating symbolic literacy in first year mathematics students. In M. Marshman, V. Geiger & A. Bennison (Eds.), Mathematics Education in the Margins. Proceedings of the 38th annual conference of the Mathematics Education Research Group of Australasia, pp. 77-84. Adelaide, Australia: MERGA.
- Bardini, C. (2015). The reader and the writer perspectives or the subtleties of symbolic literacy. In K. Beswick, T. Muir & J. Wells, Mathematics education: climbing mountains, building bridges. Proceedings of the 39th Conference of the International Group for the Psychology of Mathematics Education. Hobart, Australia: PME.

### Prior related publications

- Bardini, C. & Pierce, R. (2015). Assumed mathematics knowledge: the challenge of symbols.
*International Journal of Innovation in Science and Mathematics Education, 23*(1), 1–9.- Bardini, C., Oldenburg, R., Stacey, K., & Pierce, R. (2013). Technology prompts new understandings: the case of equality. In V. Steinle, L. Ball & C. Bardini (Eds.),
*Mathematics education: Yesterday, today and tomorrow*(Proceedings of the 36th annual conference of the Mathematics Education Research Group of Australasia),

pp. 82–89. Melbourne, VIC: MERGA.

**Reconceptualising Mathematics and Science Teacher Education Programs through collaborative partnerships between scientists and educators:**