Talking math with your kids #tmwyk

One of the wonderful privileges of being a parent is that we get to train our children in so many ways. One of my ways to nuture my children is through talking to them about mathematics. Sadly, for many who have had bad experiences with mathematics, this idea of talking math with children can cause anxiety.  This does not have to be the case when we see math as the flexible, usable, adaptable, enjoyable beauty that it is.  

On Twitter there is a hashtag, #tmwyk or talking math with your kids. This hashtag was created by Christopher Danielson. Christopher is very active on Twitter and quite responsive to individuals who post with the #tmwyk hashtag.  You can check out Christopher's website here.   

Over the last year or so, I have posted a number of interactions with my oldest daughter to the #tmwyk hashtag.  

 

Using the Chromecast to #tmwyk pic.twitter.com/9yGWvLc9hu

— Adam Paape (@Adapaa) March 21, 2015

My kiddo and I were playing, "Which one doesn't belong?" in this tweet.  Christopher Danielson is responsible for the "Which one doesn't belong?" game.

Fun work with multiples of three based on this glass of milk. 5 year old loves it. #tmwyk pic.twitter.com/FszNjPMtZP

— Adam Paape (@Adapaa) November 2, 2014

Here we had a wonderful conversation about multiples that she started by noticing the threes.


This morning my daughter and I spent some time playing a card game. I found this card game here. The basic idea is that you lay down 7 cards and then the kiddo tries to find two cards that add up to 10.

The child continues to find pairs of 10s until there are no more pairs.  When there are no more pairs to be made, the parent puts down seven more cards and the child tries to find pairs of 10s again.

In our first attempt at this game, my daughter was clearly excited. We had a really nice conversation about an Ace (1) plus 9.  We discussed whether or not 1+9 was the same as 9 + 1.  Talk about a great way to think about the commutative property of addition. My daughter said, "Yes Daddy, they are the same."  I said, "Why are they the same?"  At first she said,  "Well, just because they are." But then she gave me a counterexample.   "Dad, it isn't 9+2."  I said, "That's really good kiddo. Thank you for your thought and thank you for making me think."

 After a little while we put down 7 more cards.  An interesting thing happened with this sequence.  Take a look.

 I asked her, "What do you notice." I was expecting that she would identify the patterns of the Aces and the 9s.   However, she had a very different thought in mind.  She told me, "Well Dad, these two are the only two that are black."  I said, "Wow! You noticed something I didn't even see." She looked at me with a huge smile.  She was so proud to have noticed something that Dad didn't see.

I love activities like this where there are many possibilities for different perspectives on the math.  On this particular sequence of seven cards, I thought that she would just pick up all the Aces + 9 to get her 10s, but she didn't do that.  She remembered that there was another 5 that was hidden under one of the 9s, so she worked to get an Ace plus 9 so that she could get to a 5 + 5 because, as she said, "I know 5 + 5 is 10." Wonderful, this is why we talk math with ours kids.  They will show us things that we didn't even think about.   Kids will create strategies that are all their own and it is one of our jobs to get them to justify their reasoning behind these wonderful, kid-created strategies and thoughts.  So, let's keep the #tmwyk movement going - the payoff is huge!

Growth mindset in the classroom

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A number of weeks back I had the pleasure of listening to Jo Boaler speak at the Wisconsin Mathematics Council annual conference. She spoke to us about many aspects of best practices in mathematics education. One of her main points was that we need to make a transition within our students from a fixed mindset to a growth mindset. Boaler referenced Carol Dweck's research on mindset. Dweck makes the point that students need to realize that their brains literally grow when they are challenged in the classroom. When a child is given a complex problem, the teacher needs to encourage the students that they can do this and that this challenge will grow their brains- the challenge is good. Dweck highlights the idea of "not yet" as an important way for teachers to think about assessment of students. She mentions that students who have a growth mindset really do see learning as a valuable endeavor.

 See Dweck's Ted Talk on "The Power of Yet" below.  

As I think about this growth mindset and the idea of not labeling students as smart or dumb, I feel like this is something we ought to be doing already. However, it really isn't the case.  And, I'm sure that I am guilty of unknowingly labeling my students in the various ways that I treat them.  Many students see themselves as smart or as dumb (fixed mindset).  Teachers need to be intentional in articulating to students that the lessons teacher's design are meant to be challenging and that hard work does pay off through perseverance and persistence. Within the Common Core Standards for Mathematical Practice, there is a standard (SMP1) that highlights the benefits of perseverance in problem solving. Any teacher of mathematics ought to realize that persistence in problem solving is a valuable trait, but often times we really struggle to get this trait to be manifest within our students.  Therefore, this intentional focus on perseverance is something that a teacher needs to purposefully cultivate in his or her classroom practice.

I have spent quite a bit of time with my 6-year old, helping her to see the value of hard work both in her reading and in her work with mathematics. The other night we were working on her leveled readers and she was working hard and struggling, but I told her, "Sweetie, you can do this. It is hard work, but hard work pays off.  Let's keep trying."   Eventually, after working really, really hard on a lot of words, she said, "Dad, I can do this!  I can read!" She was so proud of her hard work.  She experienced "not yet."

The other day we received a document from her school of a self-analysis that she did within a book called, "If I lived in a castle."  You can see the image below.  She identified herself as "Lady [her name] the Smart."  I'm not too concerned about this, but I do find it interesting that she is already labeling herself "the smart."

So, take another look at Carol Dweck's video and think about the idea of a fixed mindset versus a growth mindset.  As an educator, my goal for my students and my children is that they have growth mindsets. It is work, but it is worthwhile work that pays huge dividends in learning and brain development.