This post was inspired by “What’s the best way to teach vocabulary?” written by @Mr_Bunker_Edu. I’m procrastinating whilst marking books and this post made me think about how I introduce key words to my students in Mathematics. For the purpose of reflection, I’m just going to think out loud on this one, so please excuse my, not so perfect writing style.
The more words my students can read and understand, the more complex and challenging texts they can access
The above quote is taken directly from the aforementioned post and I feel it applies across the board, albeit Maths, English, Science, PE or any subject. Some folks would question the need for students to understand complex words in Maths because Maths is all about numbers right?! Wrong; we use words too!
In every Maths lesson I get students to read their answers to the class, read questions / statements to each other and expand on what the previous person has said – one of my favourite things to do! This helps to remind me of a students ability to read whilst allowing me to gauge the level of differentiated task/activity that a particular student should be working on. It also provides an opportunity for students to lose their inhibitions in class and gain the support of their peers. Generally speaking, students don’t laugh at their peers if they can not pronounce a new word, they will actually say it for them, help them out. Reading together, part of a question at a time, can really focus learning too.
If we think about this in the context of an exam question, the problem becomes apparent. If a student is able to read and understand the examination question, they will know what the examiner is asking and they have a good chance of actually answering the question; as opposed to laying out a short waffling sentence and a string of numbers in the hope that some combination will be correct. This may seem like common sense as many students can read the examination questions but unfortunately, they hit a hurdle when it comes to understanding and interpreting the questions.
The same is true of any classroom textbook. Some books are more suited to students with a higher reading age and others have much less text, more pictures/diagrams and simple questions. Key words tend to be highlighted, in bold and usually in a box somewhere on the page (not all Maths textbooks have a glossary).
If students struggle to read, then they have very little hope of interpreting the question, knowing what the examiner is asking them to do. So, with my teacher of Mathematics hat on, how can I help my students to understand the question? How can I help them to interpret this problem? They need to understand what words mean. And, they really need to understand that some words sound the same but have a slightly different spelling (e.g Compliment and Complement)
In Mathematics lessons at our school, key words are introduced with the learning objectives and returned to throughout the lesson.
I have had conversations with staff at different schools, who think that this form of mild immersion leads to students knowing and understanding new key words but this is superficial. Having the words displayed on the board and around the classroom is excellent, but can tend to become a form of wallpaper; the students see the words but they do not think about the meaning of the words. Displaying key words is useful in the short term, but can be useless in the long term unless they are reinforced and regularly revisited
I have found that the following works well for me and my current classes;
- Returning to key words in later lessons (useful when “Cold Calling” – see Teach Like a Champion Technique 22 – Doug Lemov)
- Using the words in mini spelling tests
- Creating word-searches (occasionally)
- Having a Q&A session or plenary to check understanding
- Encouraging students to use these key words when making their own questions, as part of assessments.
The above, can lead to a greater depth of understanding, both in terms of the key word and in terms of subject knowledge. These methods may not necessarily work for all teachers nor for all classes. However, these methods can work for students who have weak literacy skills.
(see “The essential guide to lesson planning” by Dr Leila Walker for further hints and tips)
This is the part of Mathematics that you either love or hate, can do or are simply scared of. If (you or) your students’ numeracy skills, ability to manipulate numbers / equations, level of reading and understanding is excellent, then you are in a position to tackle some of the most challenging problems (www.Brilliant.org). Take a look at this problem from the UK Intermediate Maths Challenge 2013 which is aimed at students in years 9 to 11:
Irrespective of the Mathematics involved, you will notice that if you do not understand or know the words congruent, trapezium, parallel, diagonal or ratio, you are already experiencing problems. Even if you are able to ‘do the Maths’ (simplify a ratio or express the shaded section as a fraction), with a limited vocabulary, you will struggle. Can you see what I mean?
Soooo, problem solving, the higher level work in Mathematics, the Gold or Platinum level of worksheets, is only really accessible to students whose reading and comprehension is very good. Is that really right? I can’t say with 100% certainty that this is true but I have noticed that the students I have taught who struggle with problem solving nearly always need the problem broken down. This is where those long weekends come in handy…ah yes, the time we have to devise a set of worksheets with more clues for some and less clues for others; differentiation! (This is another discussion that will simply run and run…)
All teachers need to find ways to support each other when helping students to be the best that they can be. In English or History for example, a student could be asked to “…draw a graph showing the mood or intensity of the story as it proceeds” (pg 97 Dr L Walker) to incorporate numeracy.
In PE a student may be asked to complete written work using connectives and sentence openers to guide them;
With all of this in mind, I’m thinking about the ways in which I can support my colleagues in the English department in broadening the vocabulary of our students. For starters, I need to increase my vocabulary and understanding of words, as well as give the students the opportunity to do more writing in Mathematics. Next week I’ll get students to be creative and write a short story using key words in an attempt to help them remember and understand. I think I’ll even get them to write numbers as words instead of digits, because they need to (and it often comes up in exams!)
It’s one thing to have a little song to help students remember a formula but we, as teachers need to consider looking at the etymology of words every now and then. We should also try to find a few more interesting stories to keep them hooked, help them understand and ultimately expand their vocabulary.
If you have any quirky (or not so quirky) ways of introducing and helping students understand key words in your lessons, please share. I’m always keen to try something new.
Reblogged this on The Echo Chamber.
Hi Sharon, thanks very much for the name-check here, I’m most flattered!
I’ve been thinking for a while (4 days?) about your blog and how within a word like ‘congruent’ might best be taught in Maths. As a non-subject specialist, I may obviously be way off the mark.
With congruence, as I;m sure most people do, it would be pretty obvious to start by discussing the definition, and using examples of shapes to show congruence. I think though, what might be really beneficial for the vocabulary to become deeply embedded would be an additional step, whereby students had to write a couple of sentences in response to the displayed shapes. The sentence forces them from ‘getting’ the meaning to be able to express it in a complete thought. It could be modelled like this:
Because….. (student writes explanation), they can be correctly called ‘congruent’.
Then you might give another more complex example, say with two congruent shapes and an additional shape, but on a smaller scale and get another sentence:
Although….. (student explains how shape ‘C’ is similar), it cannot be called ‘congruent’ because….. (student writes explanation)
Then for golden sentence number three, they could draw their own example,
As you can see from my drawing…………….
In don’t know if this is completely obvious / already done in Maths lessons. It might also be nonsense. Thinking about it has helped me learn the meaning of congruence anyway!
Dave, You are spot on.
The way to embed new words and ensure that students understand the meaning of the words, is to play with the language. I’m keen to have discussions in my lessons and often stop class work to do so (I am aware that this does not suit all teaching styles).
I do not, however, have this elegant a form of sentence starter (writing frame? prompt?) but I really like the model you have provided and will be adding this to the shared planning on this topic. I’ll have to catch up with you at some point this term or next, to look at ways of wording similar models. You’ve got me thinking about making a bank of sentence starters…
Thanks for taking the time to respond.
Great post! Thanks for sharing. I think we need to build up vocabulary in maths in order to enable higher level thinking and mathematical discussion. I’ve blogged about it before: http://wp.me/p2z9Lp-3Z
I love the trapezium question too!
Back in the day – I used a “word splash” brainstorming activity to open a unit and also as a vocabulary review – great way to activate prior knowledge and uncover student misconceptions. My personal twist was to have students generate sentences either solo or in pairs and then circulate around the room and “borrow” one they liked from another student/group.
Great resources here too: http://www.oame.on.ca/main/index1.php?lang=en&code=ThinkLit
Norma, this is a really nice idea; something I could share with NQTs (& other staff!)
Thanks for the link to the resources too!