Creating a Culture of Math: Conversations, Part I

As our children enter the world, their first experience of culture comes from their household, the people who spend the most time with them, usually their parents.  We know that modelling is extremely important in showing our children how the world operates.  We don't talk much though, in my experience, about showing children what is valued through our engagement and conversations with them.  Conversation is a wonderful way for a parent to be truly present with a child, create pleasant memories, play with ideas, and learn about one another.  It is through pleasant memories and engagement with important adults that children learn to value particular types of experiences.

When I first started reading novels with my daughter, I struggled to talk with her about the parts of the story.  She could tell me that she enjoyed the story, and I could say that I liked the story, but the conversation kind of halted there.  I would try to think back to my school days and I would remember things like foreshadowing and point of view, but she wasn't really there yet.  What I lacked was a knowledge about how learning about stories develops so that I could meet her where she was.

Conversations about math are the same as any other conversations in that we meet one another in a place of commonality and each add something in turn.  We add our observations, our reactions, our wonderings, and our suggestions for action.  We talk and we also really listen, and we always try to keep some common ground. 

So, what is there to talk about?  Here are a few key things we can try:

1) Make observations and ask for a response - At some point, each of my children enjoyed making shape patterns with counters.  For example, my son would bring 12 counters into the kitchen and arrange them into a rectangle.  "I see a rectangle," I observed.  A smile.  He knows I am paying attention and willing to engage. 

"How many are there?" he asks.  I know he is already proficient at counting by ones but hasn't gone on to skip counting yet, so I insert a new idea into the exchange. "1, 2, 3, 4, 5, 6, 7, 8 , 9, 10, 11, 12," I count.  

Later on, we would count, "3, 6, 9, 12."  Or when he was exploring multiplication, I would count 12 and then conclude, "3 x 4 = 12.  (pause)  I wonder if we could arrange the counters in a different way." 

Sometimes, he would bring more counters to continue the game with a new number.  If we had 7 counters, he would spend some time trying to make it into a rectangle and find that he could only put them all in a long line.  "I can only arrange them this way," he'd say.  "Yep," I agree, "7 only makes a long, skinny rectangle.  7 is prime."

Here, I want to emphasize that inserting a new idea is part of a conversation.  Just as in everyday conversation, we would not insist that the other person agrees with us when we share our point of view, in an exchange about mathematics, we would not insist our child absorbs our 'new idea,' understands it, or agrees with it.  Of course, if asked for an explanation, we can give one.  Just keep the conversation balanced.  You both have something to add.

We can start conversations too.  We make an observation, see if our child is interested, and if so, invite them to engage by asking a question or suggesting a course of action.  For example, 

• That pattern looks familiar...  It looks like Pascal's Triangle.  Does the next line agree with that?
• It looks like these numbers go up by 4 each time.  What is the next number?
• I see a lot of triangles in this building.  What do you see?
• It's colder today than it was yesterday.  What's the temperature today?
• The forecast says tomorrow will be -20 degrees.  Brr!  It's going to be cold!
• We got different results.  Let's figure out why.
• The story says it was late in the afternoon, but they didn't have clocks back then.  I wonder how they knew what time it was.

2) Talk about processes - There is a widespread bias for results and constancy in mathematics.  In school, either we are marked on getting the right answer or we get marks for the answer and for doing things the way we were taught.  When we do look at the process, it's usually to figure out what we did wrong.  I submit that there is far more to share and enjoy in exploring processes when learning math.

There is almost always more than one way to solve a problem.  We can find our curiosity about how our child chose to solve a problem. 

Understand their method and talk about your observations:  "I notice you grouped the numbers into smaller chunks before you put them all together." 

Ask questions:  "Just now you looked like you were looking at a mental picture.  Did you draw the fractions in your head to add them together?" 

Relate:  "This one is more complicated, isn't it?  We need to think." 

Share:  "I did it the same way.  I like this way because it's so simple.  I don't like too many steps."  Or, "I did it a different way.  Would you like to see?" 

Explore:  If you can think of several ways to solve a problem, you can talk about which method you would choose to use for future similar problems.

A couple of useful phrases when talking about methods and algorithms:


"Elegant Solution" - Mathematics values simplicity.  We don't like a lot of clutter, a lot of calculations to wade through and possibly make a mistake in.  It is or it isn't, and the more easily you can prove it to me, the better.

"Powerful Method" - Mathematics values methods that work for many problems.  A method that can be used for all rational numbers (fractions, decimals, whole numbers, positive and negative) is more powerful than a method that only works while dealing with whole numbers.  For example, using a number line is a more powerful method than using the concept of "take away."


Whew, these posts are taking longer to put together than I expected.  And summer is busier!  This is part I of "Conversations."  Stay tuned for Part II...