This is the final post about the Maths behind the Concrete Project. In a previous post I described how we used graphs and words to describe relationship between variables (such as distance to factory) and how dirty the air was.

The next step was to move from a graph (which gives information as you move along a 1-dimensional line) to a map (which gives you information as you move about a 2-dimensional plane).

I, in my role as mathematician, created a whole load of data for the students to plot on a graph. A year ago I would have thought that this is cheating, but now I focus on the purpose of the project. The aim was not for the students to use Excel to efficiently **calculate**, but to understand how to **plot** information and draw **conclusions** from graphs. Leave the boring stuff to the teacher.

We spent a two double lessons on this. The first lesson was a complete success because:

- The numbers involved were easy to understand (we started with lots of simple examples, with made-up numbers)
- Colouring is fun! The exercise was novel
- I poured a lot of energy into the atmosphere of the class
- There were four adults in the room
- I modeled the process very clearly on the board

The second lesson was a complete failure because:

- The numbers were now very small. (I toyed with multiplying all of them by a factor of 10 to make more manageable, but wanted the students to get a sense of just how small the concentrations in the air were. Maybe this was a mistake, understanding 2.3 x 10^-19 might be too challenging)
- The students were gradually losing motivation in the project. The concrete factories were no longer going ahead – so why should we continue to work on this project? Fascinating issue, which clearly highlights a potential pitfall of PBL – it could encourage students to only learn when they are solving a genuine problem.
- There were a number of students who were very vocal that “this wasn’t really maths”. Because the maps are unfamiliar and involve colouring, there surely musn’t be much deep learning going on. Students often surprise me with their very traditional opinions on what learning looks like.

In the end, teachers followed students. There was no genuine need for the maps to be completed, so we didn’t push for them. Instead, we learnt about sequences and finding the nth term – back to the worksheets that the students recognise as “proper maths”.