In this post, I look at a Year 8 Maths unit and demonstrate what a language conscious approach to teaching and learning looks like.
When collaborating with departments, I find that it helps to focus on particular schemes of work to show, very practically, how to develop disciplinary reading, writing and talk.
With my Maths department, I asked what age and stage they’d like me to focus on. The answer was Year 8, Autumn Term 2. While I spent some time working on three different units, I’ve decided to focus on only one in this post.
Let’s go…year 8 Maths
Come with me on a language conscious tour of a Year 8 Maths unit. Actually, to make it a whistle-stop, we’ll just drop in on one sequence of activities and see where it takes us. I’ll describe what I’m seeing and thinking as we go. It’s called this: Calculating: Fractions, Decimals and Percentages. (As you can see, word parts are jumping out at me and we’ve not even started.)
First stop – Mathematical language.
Scanning through the material, I’m seeing 12 words that occur frequently; I’ll sort them into a grid.
I expect that Year 8 students will have encountered most of these before but they may need recap and further reinforcement. I can see that there are specialist Maths words that might be pretty tricky such as ‘numerator’ and there are other words that will sound familiar but have a specific Maths meaning here, ‘mixed number’ for example. Yikes, there’s even a word from our local dialect which has an entirely different meaning when used in speech, ‘that was proper hard’ (where ‘proper’ is used to intensify the meaning). Ok, but what about a proper fraction?
Looking through the lesson materials it’s clear that these words are taught through the activity, in context. There’s a strong visual context and frequent repetition of the vocabulary as learners practise the Maths. They will certainly be hearing and reading the vocabulary through this practice.
But is this enough? How deeply will students process the language?
What about some explicit vocab activities to help embed meanings? Here’s what I’m suggesting and why.
- Etymology: specialist vocab in Maths often has a Greek or Latin root.
I’d want to do some quick and efficient work on word roots. Since the unit is all about calculating percentage, I could design a visual to illustrate the root, ‘cent’ and explore the word family. This is useful because it also brings in other Maths words and has rewards later on when new concepts such as ‘percentile’ are introduced.
Decimal is another key word in this unit so ‘deci’ is a useful prefix to teach. Could this be an opportunity to recap all the numeric prefixes – kilo, milli etc? Hang on, both of these prefixes refer to 1000. One must be Greek and the other Latin. I’ll need to explain this to students and do some digging to see if other prefixes double up in the same way. I think they will.
Before we move on, I’d like to add that ‘fraction’ is also worth a look. ‘Fract’ is a Latin root meaning ‘break’. Joined up thinking tells me that this will be helpful in Science – refract, fracture – so with a collegiate outlook, I’d be sold on explaining this too. Even better if there is a whole-school approach and the students arrive in Maths with this word knowledge.
Perhaps there’s a great wall display that can act as indirect reinforcement too?
2. Word games
Could our grid of twelve words be used for word games? I think so. Using talk for learning is extremely powerful because it gets learners to use vocabulary, explore concepts and develop understanding.
- How about a challenge? Learners take a key word and explain it to their partner without using the actual word. In 30 seconds, how many words can each pair describe and identify?
In my view, this approach has the edge on bingo because it puts the onus on the students to produce definitions and do the explaining. With bingo, the teacher tends to read out scripted definitions so although there is some good listening practice, students aren’t generating the meanings themselves.
- I’d also suggest that drawing the word, Pictionary style, could be a useful pair activity. Admittedly, this might work better with concepts from the next unit since it’s all about visualising and constructing, angles and triangles. Imagine the good noise in the classroom as students shout out their guesses – ‘it’s a numerator’, ‘an equivalent fraction’, or in the case of the next unit, ‘allied angles’, ‘corresponding angles’, ‘a transversal’. I’m wondering how often we hear our less confident students say these words aloud?
- Perhaps students could design some true / false statements with accompanying visuals. Is this an improper fraction? True / False. Explain your reasoning.
I’m also bringing in an oracy activity for Maths from Driver and Pim (2018). While it’s aimed at supporting EAL learners in the classroom, I’d like to highlight the authors’ statement, ‘It’s generally true that what is good practice for EAL learners is good practice for all learners.’
Divide up the cards around the class.
Second stop – tier one, or is tier two, or even tier 3 vocabulary? Um. Other words.
I’m going to create a semantic map of other vocabulary from across the sequence so that I can think about what the students will be reading and anticipate challenges.
Now, this is interesting.
- A lot of these words relate to real-world financial scenarios with which students may, or may not, be familiar. Maths staff will be old hands at explaining these concepts: VAT, service charge etc. Looks like there are different ways of saying more or less the same thing: a sale, a reduction, a discount.
- The key words ‘increase’ and ‘decrease’ change their word class and appear in different structures. They are verbs, ‘increase an amount’, ‘increases’ or part of a noun phrase, ‘percentage increase’, ‘a 10% increase’.
What can we do with all this? I’m thinking:
1. Take every opportunity to build in quick active reading tasks to make learners think explicitly about language. Gap fill tasks are quick to make and do with students. Tinker with an existing slide to produce a cloze activity.
2. Make links between related terms.
3. How about some quick-fire question and answer to get learners to link concepts to real-world scenarios? These examples might encourage some exploratory talk.
- Would you rather make a percentage profit or a percentage loss?
- Who would like a percentage profit? Who might want a percentage decrease?
- When would you like something to have a 10% increase in value? Or a 5% decrease in value?
- Would you rather have £8 off or 10% off or 20% extra free?
- When do you get the bill? Or a voucher?
- Would you rather buy or sell second hand cars?
- Would you rather collect your wages every week or receive your earnings every month?
Idea adapted from Amadi (National Literacy Trust resource).
Third stop – word problems.
Hopefully, there’s been some groundwork in year 7 on how word problems work (I’ve written about this here) so we can build on this now with year 8.
Again, I can see that there are well-designed visuals on the slides which allow students to practise the Maths without the words.
Once the Maths has been practised, students could word it up! Write the question that would go with the scenario.
A model with margin prompts would be a useful scaffold and reminder of how word problems work. It would be easy to change the visuals and ask students to write a new question. A word bank similar to my semantic map (above) might also be a handy support.
For further challenge, perhaps students could write their own questions without any visual prompts.
- Choose the Maths operation first (percentage decrease or a percentage increase question) then decide what scenario would work. Is it going to be discount shopping, wages and overtime, buying or selling cars? Will it involve phones, cereal packets, costly coffees…..?
- Write it.
- Use margin prompts as a peer or self- assessment tool.
- Do the Maths. If the operation has been understood, the answer should be convincing.
Before we leave word problems, I’d like to make a sequencing activity that models to students how Mathematicians read and reread very carefully. To solve this puzzle, students need to find linguistic clues and patterns, justifying their final answers. Finish by doing the Maths.
Fourth and final stop – Mathematical reasoning
Ok, we’re almost at our destination. Now, through this sequence, I can see a strong emphasis on reasoning skills. Reasoning is an important disciplinary process in Maths. I’m picking out some of the sentence stems that I can see peppered across the unit.
Whether explanations are completed orally or written down, I know that good mathematical reasoning requires students to use mathematical language confidently so this is something I need to model and scaffold. I’d identify relevant subject vocabulary and handy discourse markers such as ‘because’, ‘so’ and ‘therefore’. Then I’d provide a model, or construct it jointly with the class.
I’ve seen some really impressive examples of students’ detailed, written explanations from David Dowling, a Maths Consultant at the National Literacy Trust. He uses sentence stems, agreed vocabulary and diagnostic questions (from @mrbartonmaths) to develop students’ writing. He also embeds that all important metacognitive tool of peer assessment. I’d want to use this strategy.
If this was an oracy activity, I’d build in a listening task by asking one student to record the examples of mathematical language they heard their partner use. That way, there’s an explicit focus on language.
The End, or is it the beginning?
As a strategy, taking a unit and looking at it in a language conscious way is really valuable. It shows how language constructs disciplinary thinking and doing for our students. It shows that we can and should plan explicitly for this.
But what it reveals, which is even more powerful, is that curriculum planning is the key. Teaching and learning tools that are outlined on this tour will be just as relevant in year 7. We might ask ourselves, for example, where do we want to teach numeric prefixes and how do we revisit? When will we focus on the language of word problems? What will feed forward into next term, or next year?
So, here we are at our destination. We may have reached the end of this tour but, for curriculum planning and staff development, this is only the beginning of a new, fascinating journey.
A copy of the slides embedded in this post can be found here. Feel free to adapt and use for CPD if you wish but please include the references.
References
Driver, C. & Dowling, D. (2020) ‘Literacy in Mathematics’ National Literacy Trust workshop.
Driver, C. & Pim, C. (2018) 100 Ideas for Secondary Teachers. London: Bloomsbury Education
I’ve adapted an activity from Amadi, C from the National Literacy Trust website. You need Premium membership to access it.
Several of the Maths slides I adapted are from http://toolkit.mathematicsmastery.org, originally accessed by my colleagues.
