Creating a Culture of Math: Conversations, Part II

... continued from Part I

3)  Introduce Vocabulary -  When things or ideas are important in a culture, we name them so that we can talk about them.  Children intuitively understand that when we have a name for something (particularly if there are names for nuances of an idea) it is important to us.  Using math vocabulary communicates the value of math.

Often in a setting of structured learning, children are introduced to vocabulary at the beginning of a unit so that they understand concepts and details taught during the unit.  In an unstructured setting, I have found it works much better to introduce vocabulary after a concept is broached.  Just as when we first learn to speak, first we see the object, action, person, etc., then we want the name for it.  The name now has meaning.  For example, I observe (to myself) that my child is frequently adding 2+2+2+2.  I can then find an opportunity to observe aloud that yes, 4 twos is 8, and inject, 2 times 4 equals 8.

Creating a Culture of Math: Toys and Games

Children are naturally interested in the things that surround them, especially when those things are being used by Mom and Dad.  We'll address tools that adults use to go about daily life in subsequent posts, but in this post, let's consider things that children have free access to.  Children love toys.  While it may be true that they don't need many or complicated toys, what they have access to, they will play with and learn about.  Math may or may not come naturally to a particular child, but toys made available give them opportunity to explore and speak to what their family culture values.

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."