This evening I took part in a #mathscpdchat discussion on Twitter about “Using Correct Mathematical Language”. Full details to follow here: (link when available)
Every Tuesday 7pm-8pm, the @NCTEM hosts #mathscpdchat with a variety of topics and “conversation navigators” to guide us through the discussion, This week was the turn of the Association of Teachers of Mathematics twitter account, @ATMMathematics.
The setup: Jemma Sherwood, Head of Maths at Haybridge High School, Stourbridge, thinks it does matter, and she’s explained why in a recent blog, The Importance of Vocabulary. https://jemmaths.wordpress.com/2017/01/08/the-importance-of-vocabulary/
Twitter users were invited for their views for or against Jemma’s thesis.
The main part of the discussion: But does it matter? Should we insist on correct use of formal mathematical Join
Before the chat had even started people were already engaged in the discussion. @ATMMathematics had tweeted that they would be online between 7pm-8pm and added “Be there or be a “quadrilateral” – Twitter was quick to point out the missing word “regular” as being important. 140 characters on Twitter I think MOST if not ALL knew exactly what was meant.
We were invited to think (about 5 mins) before #mathscpdchat.. “Do you give a definition from a textbook or a dictionary?”
I found myself this morning with class in front of me (Top Set Year 8) trying to define Circle, Diameter, Radius, Circumference and even Area in a way that students could / would understand. I did not anticipate that this was going to create such a discussion and for next lesson vocabulary is going to be far more important. As it happened I ended up drawing on the board a few ‘real’ shapes and diagrams on the whiteboard – students were quick to comment on the accuracy of my free-hand circle but they knew what I meant !! Or did they? Should I have prepared a better image. I think on this occasion I got away with it – JUST !!!
I think that allowing students to ‘pick it up’ (the mathematical language) through hearing you (as teacher/professional) use the word that they will end up identifying the word and eventually using it correctly. Should we have strategies to help students learn the spellings etc – of course we should. As maths teachers, we need to think about how we structure an approach to the T&L of maths vocabulary. #mathscpdchat received many contributions around this and decided it was always helpful to derive the word and to then think of the origins of the word. One example given, century, cent, centimetre, centurion, c in Roman numerals. Others suggest that they introduce the word, spend time on the pronunciation & ‘maths’ meaning. It was clear that providing examples throughout a lesson or unit was helpful but also that non-examples were also just as useful. It was made clear that it is important to review the meaning of word throughout to make sure students fully understand.
It was suggested that the simplistic view was that as teachers we frequently use ‘language’ to refer to ‘vocabulary’. I am sure that a linguist will identify the many differences and it is important that these are considered. As maths teachers do we spend enough time exploring the social role of language, such as in establishing relationships? Another question to think about and perhaps some keen readers might want to blog a longer response to is: “How do we use spoken and written language in our teaching?” / How does the social aspect of language use relate to mathematics teaching and learning in our classrooms?
One of the issues with Mathematical Language is thinking about the language for learning and thinking. One example of how this is an issue is disadvantaged children with slower language development. It is also important that students’ informal language emerges first (because then it has meaning) and for the teacher to then introduce the additional maths vocabulary. Given the precise nature of mathematical language it was argued that there is no ambiguity because as teachers we know certain words (for example numerator) have specific meaning.
The accurate use of correct terminology is important in communicating effectively and efficiently. The discussion then went on to discuss how in a primary school that all (I think a slight exaggeration and they mean some) pupils know the correct words for dinosaurs, but when asked they do not or can not remember the correct mathematical language. Students can remember big words when they are interested in what they mean! I think this is true across all subjects and not just when learning mathematics.
The question was asked, although a definitive answer was not forthcoming about the use of Mathematical dictionaries. It appears that most maths teachers have come across them and their use but it is not many that have class sets of such resources. Perhaps if we are to embed the use of mathematical language in the classroom we should encourage our students to use a Mathematical Dictionary in the same way they would in other subject areas. The NCETM has a useful glossary (KS1 to 3) here: https://www.ncetm.org.uk/resources/42990 You have to scroll down to find the Glossary but it is useful.
We should end this blog with this:
Do you have a favourite mathematical word?
If so, what is it and why?
Thanks again to @NCETM for Tuesday night’s #mathscpdchat . Join the discussion on a Tuesday 7pm-8pm
Dates and topics can be found here: https://www.ncetm.org.uk/resources/41729