# : How to develop disciplinary literacy in maths How to develop disciplinary literacy in maths

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## How to develop disciplinary literacy in maths

### How to develop disciplinary literacy in maths

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by Tudor Grange Research School

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#### Elizabeth Bridgett

Elizabeth is the Trust Lead for Maths at Tudor Grange and has been working in maths education for over 20 years. Formerly an advanced skills teacher and specialist leader of education, Elizabeth is also an NCETM Teaching for Mastery Specialist. She has a degree in mathematics and a masters in School Improvement and Educational Leadership.

As I started my journey into the disciplinary literacy of maths, two images emerged in my mind. The first is the Golden Record on Voyager 1 which was sent out into the universe in 1977; it contains information, including numbers and calculations, in order that extra-terrestrial lifeforms can learn more about us. The second image is a meme that represents bewilderment which is commonly referred to as “confused math lady” – a confused looking person surrounded by maths symbols.

Let’s contrast what these two images are saying. Firstly, maths is a language literally so universal that it may be one of the only ways in which we could communicate with alien life form. Secondly, our notation is so difficult and so impenetrable that it’s used across social media as a joke – a sign of confusion and difficulty. And therein lies my problem as a maths teacher. Our notation is liberating and powerful; it is a tool with which we manipulate, investigate, ponder and communicate. But it can also be a way in which students are excluded and disenfranchised. Our disciplinary literacy does not necessarily sit in the realm of words and sentences but it’s crucial to our subject.

Research evidence.

My journey began with Beth Woollacott’s work and I can honestly say, it blew my mind! Reading maths is not like reading words. Consider the table below and focus on your eye movements. Are you going from left to right or something else? Is the reading direction something that we explicitly teach or something that we assume?

David Pimm’s work also discusses reading mathematical notation and how it differs to words; we have no way of decoding a symbol if we don’t know what it means. Our highly condensed symbol system interacts in different ways; consider the difference between

How do the symbols carry the meaning? How does the pronunciation carry the meaning – if at all?

Mathematics Teaching, the journal of the Association of Teachers of Maths, is a wonderful source of inspiration and information. Watson (2009) reflects on notation and states that it is powerful when:

- “it reveals more structure than was used to devise it.
- it enables communication with self or other learners.
- it becomes a means of expressing and crystallising thoughts.”

The idea of mathematical structure and how to reveal it is a theme that runs through the NCETM’s ideas of Teaching for Mastery. Watson, Stratton and Ollerton (2019) discuss how our symbolism and diagrams have developed over hundreds of years to reduce cognitive load – a brain on the page that we can look into. So, whilst we need to carefully manage how the notation may obscure meaning or hinder learning, we need to consider how we can empower students to communicate, articulate and solidify their thoughts.**Evidence into action**

There is so much to consider that it was difficult to know where to start. But here are some of the things that we worked on across Tudor Grange Academies Trust through our curriculum and collaborative structures.

We started with the language and vocabulary of maths using Frayer models and an insistence on precise mathematical language. Opportunities for discussion and articulation were built into our curriculum. For example, a Frayer model for standard form is a great way to discuss the conventions of the notation; asking if a statement is always true, sometimes true or never true provides the means to spark a debate and explore the differences between demonstration and proof.

We explicitly teach notation, pronunciation and reading direction as well as the mathematical concepts they describe. E.g. is seven squared and the square of 7 and and the area of a square of side length 7. Teachers are helpful by nature and often want to do all of the reading of notation for students; it’s not always easy to remember to stand back and pause for a moment.

We have embedded representations to reveal mathematical structure and draw out the meaning of the symbols. For example, the ubiquitous bar model is a wonderful tool for revealing the structure of equality and manipulating equations.

We were inspired by the “contrasting cases” work of Star and Rittle-Johnson in which learners are invited to critique two students’ approaches to a problem. This presents an authentic and meaningful way to engage with mathematical writing and notation. For example, contrasting different written methods solving

**What next?**As a trust, we are trying to build mathematicians and so we are keen to develop students’ mathematical thinking as well as their proficiency with notation. So, what are our opportunities to present problems in which students can become creators who use the conventions of notation as part of their toolkit? How can we move from informal writing when solving problems to formal written solutions that can be understood and appreciated by peers? This is an enormous journey and we have only just begun to discover the subtleties, nuances and difficulties that lurk within it. And the question that is forever at the back of my mind is, how do we draw the distinction between the marks on the page and mathematics?

**References**

Contrasting cases (no date) Home. Available at: https://scholar.harvard.edu/co… (Accessed: 26 April 2024).

Ollerton, M, Stratton, J, Watson, A (2019) Inquisitive about inquiry? Loaded with cognitive load? Part 1 Mathematics Teaching (270) pp. 32 – 36

https://atm.org.uk/write/Media…;

Pimm, D. (2018) Speaking mathematically: Communication in mathematics classrooms. London: Routledge.

Woollacott, B. (no date) Professional development, ‘Reading Maths is Hard’ | LUMEN | Loughborough University.

Available at: https://www.lboro.ac.uk/servic… (Accessed: 26 April 2024).

Watson, A (2009) Notation Mathematics Teaching (213) pp. 35 – 38

https://atm.org.uk/write/Media…

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