Jo Boaler and sense making in Mathematics

In my role, I am exposed to a lot of learning.  EQAO results will be released soon and I believe the trend continues where there is a province-wide decline in how our students are doing in Mathematics.  In the video I have posted below, Jo Boaler outlines an approach to Mathematics which really resonated with me.  

I have always been interested in the brain, its workings, and the relationship to learning.  In a screenshot from the video I encourage you to watch, you will see the parts of our brain that can be activated, once we change up and differentiate the way we deliver Mathematics instruction.

I made a note to myself to look up the difference between the two visual pathways, so I could have a more comprehensive understanding of them.  This is from the Wikipedia page.

"The ventral stream (also known as the "what pathway") is involved with object and visual identification and recognition. The dorsal stream (or, "where pathway") is involved with processing the object's spatial location relative to the viewer and with speech repetition."

The green is where and the purple is what

  

I bring this up because this information came rushing back to me while I was supporting some students in a Grade 6 classroom. There was an EQAO-like problem posed to the students which involved a fair bit of thinking.  In the following photo, you can partially see the question.  I will have to take a better photo, so I can comment on it more in-depth.

It was a great question but it was hard to understand and required the use of some reading comprehension skills.  In other words, the questions, before any Math was attempted, needed to make sense.  It required, to my mind, some annotating.  This might involve asking questions about the statements in the question or highlighting important aspects of the question; it might even involve drawing visual representations, in order to deepen the meaning of the question.

(But that will have to wait for another post because I am getting distracted from the original point!)

As I stood with the students around the chart paper, I realized that simply relying on a piece of paper and a few pencils were not enough to concretize and make sense of the question.  For Jo Boaler, some of her ideas for promoting Math Success (yes, I capitalized that), rest with using the visual, physical, symbolic, and verbal modes for learning.

The original question and initial paper response

To add a physical and symbolic component to the question, each 100 block represented 100kg in the problem.

Once we talked more about the question -- the verbal-- this student realized that 10x100 Base Ten items equal 1 large Base Ten cube.

I was not able to follow-up with the taking up of the question with the whole class.  This would be key to deepen the understanding of the 2 students I worked with and for the whole class.  In a subsequent post, I will get a hold of this question to highlight some possible annotation strategies that could be used to deepen the challenges that often accompany Math word-problems.  I will also make it a point to open up a conversation in the classroom about different ways we can support students' understanding of Math by using the different pathways available in our brain.