# Developing understanding in Mathematics

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## Learning mathematical language

Like all discipline areas, Mathematics has specific language that students must understand in order to make meaning and develop their knowledge. Being able to interpret language in a range of mathematical contexts and for different purposes is fundamental to mathematical problem solving.

Di Gisi and Fleming (2005) describe three types of vocabulary that students need to be able to solve word problems:

- mathematics vocabulary
- procedural vocabulary
- descriptive vocabulary

There are multiple semiotic or meaning-making systems and grammatical patterns in Mathematics (Schleppegrell, 2007).

In terms of meaning-making systems, students must move between written language, oral language, symbolic notation, and graphs and visual displays. They must also become familiar with mathematical grammatical patterns relating to technical vocabulary, use of synonymous verbs, and implicit logical relationships.

### Strategies to develop an understanding of mathematical language

The strategies below demonstrate ways teachers can use literacy to support student understanding of mathematical language.

- Translating from words to symbols
- Understanding mathematical terms and notations
- Everyday vs mathematical language
- Technological terminology
- Using morphological matrices with measurement units
- Introducing new mathematical terminology
- Reading and discussing operations for meaning
- Using cognitive conflict to promote precision of definitions
- Language for graphs and statistical displays

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### References

- Adams, T. (2003). Reading mathematics: More than words can say. The Reading Teacher, 58(8), 219–234.
- Adams, T.L., Thangata, F., & King, C. (2005).“Weigh” to go! Exploring mathematical language. Mathematics Teaching in the Middle School, 10(9), 444–448.
- Armstrong, A., Ming, K., & Helf, S. (2018). Content area literacy in the mathematics classroom. The Clearing House: A Journal of Educational Strategies, Issues and Ideas, 91(2), 85–95.
- Bowers, P.N., & Cooke, G. (2012). Morphology and the common core building students’ understanding of the written word. Perspectives on Language and Literacy, 38(4), 31–35.
- DiGisi, L.L., & Fleming, D. (2005). Literacy specialists in math class! Closing the achievement gap on state math assessments. Voices from the Middle, 13(1), 48–52.
- Gough, J. (2007). Conceptual complexity and apparent contradictions in mathematics language. Australian Mathematics Teacher, 63(2), 8–16.
- MacGregor, M., & Stacey, K. (1997). Students' understanding of algebraic notation: 11-16. Educational Studies in Mathematics. 33(1), 1–19.
- O’Halloran, K. L. (2000). Classroom discourse in mathematics: A multi- semiotic analysis. Linguistics and Education, 10(3), 359–388.
- Pierce, M. E., & Fontaine, L. M. (2009). Developing vocabulary instruction in mathematics. The Reading Teacher, 63(3), 239–243.
- Rozzelle, J., & Scearce, C. (2009). Power tools for adolescent literacy: Strategies for learning. Bloomington, IN: Solution Tree.
- Schleppegrell, M. J. (2007). The linguistic challenges of mathematics teaching and learning: A research review. Reading & Writing Quarterly, 23(2), 139–159.
- van Vondel, S., Steenbeek, H., van Dijk, M., & van Geert, P. (2017). Ask, don’t tell; A complex dynamic systems approach to improving science education by focusing on the co-construction of scientific understanding. Teaching and Teacher Education, 63, 243–253.
- Victorian Curriculum and Assessment Authority (VCAA). (n.d.) Learning in Mathematics. Retrieved from Victorian Curriculum - Learning in Mathematics
- Zevenbergen, R. (2001). Mathematical literacy in the middle years. Literacy Learning: The Middle Years, 9(2), 21–28.

## Using literacy to support problem solving

Language is fundamental to teaching and learning mathematics. Often, students must apply literacy skills to read and interpret worded problems. However, literacy errors related to problem solving can occur before students attempt to apply their mathematical knowledge.

These literacy errors related to problem solving include: reading, comprehension and transformation (Newman, 1977; Clements, 1980; Clarkson, 1983).

The importance of literacy in mathematical problem solving processes was reiterated by Doyle (2005, p. 40), who maintained that "the more students understand information, the greater chance they have of participating and developing mathematical skills."

### Strategies that use literacy to support problem solving

The strategies below demonstrate how teachers can develop students' literacy skills to support their mathematical problem solving.

- Close reading: Identifying key information in a problem statement
- Identifying a simpler, related problem
- Drawing a diagram
- Using an organised list
- Identifying a pattern
- Linking count nouns and mass nouns to variables in statistics
- Investigating a concept from multiple perspectives
- Explicitly teaching counter-examples
- Developing students' question posing

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### References

- Clarkson, P.C. (1983). Types of errors made by Papua New Guinean students. Educational Studies in Mathematics, 14, 355–367.
- Clements, M. A. (1980). Analyzing children’s errors on written mathematical tasks. Educational Studies in Mathematics, 11, 1–21.
- Doyle, K. (2005). Mathematical problem solving: A need for literacy. In Bartlett, B., Bryer, F., & Roebuck .D., Stimulating the ‘action’ as participants in participatory research. International Conference on Cognition, Language and Special Education, 2, (pp. 39–45). Brisbane: Griffith University.
- Fang, Z., & Schleppegrell, M. J. (2010). Disciplinary literacies across content areas: Supporting secondary reading through functional language analysis. Journal of Adolescent and Adult Literacy, 53(7), 587–597.
- Fisher, D., Frey, N., & Hattie, J. (2016). Visible learning for literacy, Grades K-12: Implementing the practices that work best to accelerate student learning. Thousand Oaks, CA: SAGE Publications.
- Johnson, H., & Watson, P. A. (2011). What is it they do: Differentiating knowledge and literacy practices across content disciplines. Journal of Adolescent and Adult Literacy, 55(2), 100–109. Newman, N. A. (1977). An Analysis of Sixth-Grade Pupils’ Errors on Written Mathematical Tasks. Paper presented at the 1st Conference of the Mathematics Education Research Group of Australia, Melbourne.
- Stacey, K., & Groves, S. (2006). Strategies for problem solving: Lesson plans for developing mathematical thinking. Berwick, Victoria: Objective Learning Materials.
- Victorian Curriculum and Assessment Authority (VCAA). (n.d.) Learning in Mathematics. Retrieved from
Victorian Curriculum - Learning in Mathematics

Last Update: 04 October 2021