On October 16th I presented at ResearchEd Surrey on Disciplinary Literacy in Maths and since then I have had many teachers get in touch who are also interested in this topic. I will therefore use this blog post to expand a bit upon my ideas and the research that I have come across.
As mentioned in my last blog on this subject, I reached an epiphany when I realised that we are not so concerned with literacy in maths, as the literacy of maths. As Draper (2015) says: “a text is really anything imbued with meaning”, and in the case of maths this may actually be a diagram, a pattern or an equation. For years we have struggled in maths to be part of “literacy across the curriculum” drives and sometimes this had lead us to shoehorn texts in to our curriculum to tick a box. What we should actually be doing I think is thinking hard about the communication of maths itself and teaching our students to be as fluent in this as possible.
Recently @JennyHillParker has worked with Pearson Education to develop a set of interesting guided reading resources to sit alongside the maths curriculum. These have different themes (famous mathematicians, engineering etc) and all help to broaden students’ knowledge and also to answer the question “why are we learning this?”. I am particularly interested though in the maths itself and how we teach students to become mathematically literate.
In my presentation I decided to break the topic down into four main areas: vocabulary and language, comprehension and understanding, talking mathematically and writing mathematically. In a similar way ReLeah Lent (2016) has a useful table breaking down the ways different subjects read, write and think. There is overlap between these areas but they do provide a useful starting point.
Vocabulary and language
My favourite joke is about a mathematician, a physicist and an engineer on a train to Scotland. I won’t tell it here but the punchline relies upon the extremely logical way that we work as mathematicians. We need to help our students understand this. When putting information in a Venn diagram a common misconception is that “53 people like cheese” means that they only like cheese, however actually it tells you nothing about their other likes or dislikes. This pedantry is a very mathematical trait. It also happens with many geometric problems – students tend to make assumptions about properties of shapes or diagrams from what the picture “looks like” which are not necessarily true. As mathematicians we know to rely only on what we are explicitly told, not what we think might be true. So as well as a vocabulary of words, within maths we have a vocabulary of notation: for example arrows for parallel lines, a square for a right angle etc.
Vocabulary itself has been written and presented on extensively over recent years (by Ed Southall, Jo Morgan, Alex Quigley, Sudeep Gokarakonda, Jo Locke amongst others) which can only be a good thing. Gone are the days of dumbing down language, particularly for slower grasping students and lower attainers, but we must take care to teach this technical vocabulary properly so that it can be accessed by all students. We first need to find the correct definition of a word, but we do also need to be aware that even within maths this definition may change. For example a factor divides exactly into another number and is usually a positive integer, however this definition becomes more problematic the more maths we do: in a recent lesson a vector proof we needed to take out a common factor of one fifth from an expression. Exam boards do also need to be aware of a more rigorous approach to definitions within the classroom – in our school a foundation student recently answered an exam practice question with all the negative as well as positive factors of 24.
The morphology (structure) and etymology (origin) of words can be useful aides for students. Understanding the root word can be really useful and help students to remember, for example factor and factory are both concerned with making things. Maths is full of prefixes: recently I observed a very grown-up and useful discussion between our ECT and his year 9 students on the prefix “bi-“ meaning two. I have recently learned that whereas previously I thought that “millimetre” and “kilometre” were just confusing, in fact milli- means “one thousandth of” and kilo– means “one thousand times” which now makes much more sense.
Instructional words also need consideration. It is a really good exercise to take a word like “evaluate” and have a discussion with colleagues across the curriculum about what it requires students to do in their subject. We really need to by mindful that students could come across the same word a number of times during the day, but their teachers could mean it in completely different ways. The Curse of Knowledge and being immersed in our own subjects could mean we forget to make these differences explicit and it is easy to see why students can get confused.
At Durrington we have taken time to identify Tier 2 words in maths and to make sure we are all explicitly teaching them in our lessons. We often use Frayer models in various ways, maybe by displaying a partially completed one on the board and having a discussion about the missing sections. I also like to write definitions on my whiteboard at the side along with a couple of examples and non-examples and leave them up to be displayed for the whole lesson so they students can refer back to them. It is really important to also review definitions regularly in recall starters so that students do not forget them.
Useful websites have been https://www.mathsisfun.com/definitions/index.html for a comprehensive maths dictionary; https://www.bossmaths.com/vocab/ for the background to many maths words; various presentations in https://www.resourceaholic.com/p/topics-in-depth.html for etymology of the keywords used and https://www.frayer-model.co.uk/ for a starting point for Frayer models of maths words.
Next time I will write in more detail about comprehension and understanding in Maths and I hope to be able to repeat my presentation at a conference in the new year.
Deb is a maths teacher at Durrington High School. She is also a Maths Research Associate for Durrington Research School and Sussex Maths Hub Secondary Co-Lead.