Grapes of Math: Working Awareness

I left off last time with my musings of my own growing mathematical awareness.  I remarked that experience is the best cultivator of awareness, and group discussions can speed things along as well.  Dave Hewitt discussed more on the techniques that a teacher could employ to work with a student’s awareness, but the reality is becoming aware is the work of the student.  The teacher cannot do this job for the student.  They can though provide opportunity.

As Grapes of Math was staring at me, I thought how fitting.  Combined with Cuisenaire Rods, this book could certainly create opportunity needed to see where the student’s awareness was at, and then allow the teacher to work with the student’s awareness.

Grapes of Math, written by Greg Tang, is a fun rhyming picture book that encourages the reader to employ strategies to help them count items quickly.  I have always found the book fun to read to my children, but they were never interested in trying to employ the strategies.  It requires a bit of thinking and manipulating the items in your mind which most children find uncomfortable.  The reality is they are just not that aware but the benefit of a manipulative like the Cuisenaire rods is awareness is heightened.

For children who have been playing with Cuisenaire rods for a while, they have a heightened sense of awareness to color patterns and shapes.   I decided to sit down with my children, and allow them an opportunity to use the Cuisneaire rods to work out strategies to count the items quickly.   My goal was to be careful what I offered the children in information.  I was instead going to employ specific questions that would help me to see what they were aware of and how they were thinking.

Now, Greg Tang provides hints within the poems to direct the child to a specific strategy.  The truth of the matter is that more than one strategy exists for each problem provided, so that the child might not choose the strategy that Greg Tang had purposed it for.  Because Cuisenaire Rods have a “show me” quality about them, this exercise would provide me the opportunity I needed to discover the thinking of my children.

Without a doubt, I knew from experience that my children would provide differing strategies, and that is why I found the book such an excellent opportunity to use for this work.   This would not be a routine task in which they could merely rely on “received wisdom.” Instead they would be dependent on their awareness to help them with the task.

Hewitt emphasizes that a routine task does not reveal a student’s awareness, and we have to be sure to provide tasks that force the student to utilize his/her awareness instead of depending on a formula to find the answer.  Exercises that focus on developing a process to find the answer is key in allowing the teacher to see a student’s awareness.  Avoid tasks in which the student can depend on “received wisdom” formulas which varies based on the experiences of the student.

For my children, I thought I was aware of their individual awareness.  As we play with Cuisenaire rods, I found that they are very much aware of things I did not think they were aware of as well as not aware of things I was certain they would be aware of.  As I prepared the materials for our exploration, I was quite interested to see how they would complete each task provided in Grapes of Math.  Questions that I would focus on asking would be:

• How do you think you can count this quickly?
• Is there another way?
• Which way is faster? Why?
• How do you know?

As I have grown in my understanding, I know not to look for a certain response from my children but to instead work with the response they give me even if it is far from the response I am looking for from them.  The main reason is it doesn’t cultivate their thinking.  I want to give my children an opportunity to think it out for themselves rather than me to think it out for them.  I can tell them their answer is wrong but I’d rather they would come to the conclusion themselves.

This takes a bit more time, and so I have learned more patience.  I have also learned that deeper thought in a short time span is much better than mindless movement through algorithms.  There are days that I feel we haven’t accomplished much, but I forget that awareness is much more usable in the long term than mindless processing of algorithms.

Tomorrow I will share what happened when my kids used the Cuisenaire Rods to solve the Grapes of Math riddles. It was fascinating to see their progression of thought as they used their awareness to discover different strategies to add quickly.

What opportunities have you found to discover your student’s awareness? Comment below and let’s share in this journey together.

This post is linked up at Homeschool Link Up found HERE.  Check more fun resources there.