(for maths teachers at Ciputra)
In language teaching we try, where possible, to exploit a naturally occurring gap, for example an opinion gap. This was the approach taken by Pak Hasto in his CLIL lesson on social perspectives. And in the CLIL maths lesson that I taught on the first day, I was also able to exploit a naturally occurring gap; you all live in different places, and therefore you all live different distances from school, you travel at different speeds, and you need different amounts of time to get to school.
Fine. So even in mathematics there are naturally occurring gaps. However, the options for ‘communicative’ gaps in maths are relatively few. If there is to be a communicative gap, then there needs to be a communicative context for a gap, and unfortunately much of maths education is devoid of context, or at least a context with which high school kids are familiar.
Not to worry. Even if we cannot identify a natural gap, we may be able to create a gap artificially. If you all lived in the same building and traveled to work on the same bus, then we would have no variables for distance, time, and speed. In this case I could prepare for you all some fake variables, and we could run the same activity – pretending to live in the places I have assigned and to travel using the means of transport I have given. This is exactly what happens in a role play – perhaps you remember the dialogue between the fish seller and the customer?
Note that the motivation to communicate is much higher when we use real information (= ‘natural’ gap).
I have to admit that it was difficult to think of more information gap opportunities in maths – off the top of my head – and so I had a look at my son’s maths book, which is also where I got the idea for the distance, speed, time lesson. Flicking through the book, a few possibilities occurred to me.
- A lot of the maths in the book I’ve been looking at seems quite visual. There are 2 and 3-dimensional shapes, different kinds of triangle, different kinds of angle, and graphs. Anything graphic is easy to turn into an information gap activity. Student A names the shape he sees on his handout, Student B draws it, etc. At the end of the activity they compare handouts and make sure they understand the names of the shapes.
The same activity works well with line graphs, as there is a lot of useful language involved, and plenty of repetition. Describing graphs also brings into play more cognitive engagement, as Ss inevitably have to identify and describe trends, and look for patterns in the information.
- Staying with visuals, a more kinesthetic application of the previous activities would involve groups of students describing a graph to their friend at the whiteboard, who then has to draw it. Conversely the student at the whiteboard can elicit from team members vocabulary items (e.g. “polygon”), or graph descriptions (e.g. “the temperature increased steadily from 0 to 100 degrees”). Peter used this kind of activity – called ‘pictionary’ – in a lesson he shared with Syafrina, to elicit visible and invisible items.
- At a more advanced level, linear equations(!) are ideally suited to information gap activities. There’s a nice example in Teaching Maths through English, which provides data about 2 mobile phone companies, PURPLE and BLUE (I hope you can smell a role play!), and some associated tasks: I make 90 mins of call each month, which phone company is cheaper? When is it cheaper to choose BLUE mobile phones? Odd that the writers do not mention roleplay here, although they do underline other advantages of this kind of task, namely that it is personalised (all students use mobile phones), and personalisation obviously helps to make abstract concepts concrete.
- Finally, in language training we always give students an opportunity to find solutions for themselves before we ‘give’ them the solution. This approach involves deeper thinking, and to some extent negotiation, with students collaborating to find solutions. In my school the maths teachers never gave us a chance to find solutions by ourselves, and I sincerely hope that my son’s teacher is challenging his students, because the book he is using does not reflect this approach at all.
For example, one day my maths teacher asked us to calculate the volume of water needed to fill a swimming pool. He drew a diagram of the pool on the blackboard, with dimensions:
We were to work individually. We had been studying trigonometry, and I guess he wanted us to calculate the area of the triangle formed by the pool bottom, the shallow end and the deep end, and to figure this into our calculations. But I could see a much easier way. I could see that if the pool is 1m deep at the shallow end and 2m deep at the deep end, then the average depth was 1.5m. I finished the task very quickly, which seemed to upset my teacher. “Have you finished already, Bolton?” “Yes sir.” He asked me to describe the stages in my calculation and his face turned red with rage when I told him about the average depth. What an asshole.
A better approach would have been to put students in groups and get them to figure out possible ways to calculate the volume of water in the pool. After a few minutes, re-group the students so that they can share their ideas (= information gap), and ask them – collaboratively – to decide which method is best. Finally invite each group to explain their choice, and take a vote on which method is best. If somebody says, we think the best way to measure the volume is to fill it using 1 gallon buckets and keep count of how many buckets it took, then praise them, but appeal to their sense of reason by eliciting from another student why this might not be practical.
Anyway those are just a few ideas. If you need anything more specific, send me some pages from your coursebooks, and I’ll see what I can do.
