Visualization in Math to Increase Comprehension

We are working on our reading strategies.

And it's been easier to implement in the math classroom than I initially had thought!

Upon our return to school after spring break,

We reviewed the quiz on functions we had taken before we all went our separate ways for a week.

To do this, the students first analyzed where their strengths and weaknesses were.

Using the chart below from BTC, 

Students made notations to find any patterns.

While I was focusing on the horizontal rows of content,

I was surprised when a student piped up that he had mainly checkmarks in the Basic column,

But that he was missing most of the Intermediate and Advanced problems.

Interesting.

For me. 

As his teacher.

While it's important to start at the concrete, basic level,

This was a red flag for me to continue to push them to a higher level of rigor and increase in fluency.

At this point, I started in on how they visualized certain vocabulary words and statements.

We started with the word "Function".

What did they see in their mind when they read the word "function".

After all of my classes, 

I had a much clearer picture of what they were seeing when they encountered the word, function.

We discussed each visualization after they drew them up on the board. 

We again pointed out similarities.

We asked for justifications.

We found mistakes or misconceptions to revise the picture and ultimately, the understanding.

We did this again for the concept of proportional relationships.  

I loved how in each case,

All three representations were included!

I was expecting the graphs,

But not the equations, with them being the most abstract. 

One of the best realizations of this activity,

Was noting how many students do not have a picture in their mind 

when they encounter these vocab words.

My hope is that when students shared their images,

And our discussion followed,

That they students were able to now attach a visual to the word.