Week 5: Developing mathematics pedagogies ACTIVITY (Post 1 of 2)

ACTIVITY: Hasan, Grabowski, and Hawthorne (2017)

(LINK to Google Doc for better quality)

For this week’s activity, I definitely felt ‘anxiety’ when I watched Chase’s video on rhythmic movement to different sequences. Somedays, I feel I can barely clap my two hands together, so for my brain to command different parts of my body to move in different directions, with different combinations, I could feel my heart racing! Though I appreciate her breakdown at the end of video indicating that this type of learning could reduce anxiety because learners become so focused they do not worry about what they look like, I think that may be applicable if the learner has some basis of coordination. For someone like me, I would panic!

So I gravitated towards Hasan, Grabowski, and Hawthorne’s (2017) extension of the Binary Code. I found the video and the description a little overwhelming, so I embraced what a student would feel and ‘made it my own’.

What resulted was a game, because I enjoy the attributes of ‘play’ and the creativity of turning a task into something playful. Keeping in mind the objective of using combinations, colours and arithmetic, I designed a system where students would have to determine ‘targets’ to generate points. The basics are:

Colour	Point Value	Position	Point value
White	1	Outer ring	1
Black	2	Middle ring	2
Red	3	Inner circle	3

The value of the overall target is dependent on a) the colour(s) used and b) their positions.


For example, the lowest possible “target” value is:

Then integrate the next lowest point colour (BLACK) into the outer ring. And calculate the point total.

Third lowest target point total:

If the pattern continued…

The next question that could be asked is, could more points be generated by repeating the same pattern with RED? Or to add black to the next ring layer?

So wait…could there more configurations with 9 points? 8 points? This would be a great task to figure out! While doing this, we can integrate the concept of BEDMAS, communication and patterns…etc.

And if we arrange all those ‘targets’ into a table…this is what we get!

As I was completing this table, I knew I was missing certain targets. But by observing the patterns, such as the rings, the values, I started noting trends in the diagonal direction. From there, I was able to figure out which images I was missing, and could PREDICT their points value even before I did the calculation. Playing with the targets in each column (point values), I’m certain there are other patterns that could come out of this as well.

This took A LOT of concentration. I could see how one could become so immersed in the combinations and arrangements, especially if more colours were introduced, or if a different point system was created, for example, finding the sum of RING + COLOUR instead of the product of RING x COLOUR.

Colouring by hand would be hands-on, but I liked using this format because I could move and arrange with ease. This would be good to do for students as individual sheets, or if collectively, students each created their own and could organize this into groups, etc.