Visualising Thinking.

The next topic for the year 8 maths class is 'relational thinking'. For those of you not maths trained, the idea behind this kind of learning area is to get the students making connections and looking at the relationships between sums on either side of an =

An example question is 24+14=?+16

The idea being that you are not supposed to work out what 24+14 is on the path towards working out what number the ? represents but instead look at the overall relationship between the two different sums. One way of looking at it is that if you add 2 to the 14 to get 16, you must take 2 off the 24 to get the ?

Now relational thinking, in terms of what I need to teach the students, applies not only to addition but to  all four basic operations.

So I have a couple of students, very bright students, who have completed the work for the current topic, so I took them aside today, gave them some of these types of questions and requested that they work together, next to me, so that I could listen to their discussion as they tried to complete these questions. There were 4 sheets, each one with a different basic operation on it. I suggested that they begin with the addition sheet, and let them attempt the first few before giving them a friendly nudge to look at the relationship between the 2 sides rather than calculating the answer, as it would be easier for them.

Once they had the relationship down, we sat at my computer, in a Minecraft world and discussed a way of visualising that relationship with blocks. Once we had agreed on a way that it would work, they continued onto the subtraction questions while I recorded a quick video, while it was still fresh in my mind, detailing the way of visualising that relationship. Rinse and repeat for all four operations and I now have a student approved, teacher certified way of visualising the relational thinking processes in Minecraft. The next step is to work out a classroom implementation of it, in a fun and engaging way.

I am also running this by the Numeracy guru at my school to see if she agrees that the visualisation is correct, and also to ask for her input into any other ways of visualising the relationships.

As always, thanks for reading and feel free to leave a comment below. I will be publishing the video to youtube shortly, so if you are interested please keep an eye on my youtube channel.