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.

4) Take a Different Perspective - One of the times people often get stuck in math (and in conversation!) is when two people are looking at the same idea or problem from different points of view, and neither wants to budge.  Both want the other to understand their point of view.  And just as in any other discussion, understanding another's point of view is a good way to broaden one's understanding of an idea.  In fact, understanding a concept from many points of view is a good way to deepen one's own understanding; it's a good way to make connections to other ideas; and it's a good path to new ideas.

So what does it look like to explore an idea from more than one point of view?  Suppose your child understands that in order to add 3 and 2, she has a group of three objects and a group of two objects, and she counts the objects in both groups to get five.  What other ways can we look at this? 

• We could look at it as a 'count' instead of a group.  Make a number line (on paper, on stairs, along the floor...) and count up 3, and then count up 2 more.  (introduces the idea of a number line, direction of a count) 
• Take a time when she has 3, say, carrot sticks, and she wants more.  Ask, how many more?  She asks for 2.  Give her 2, and observe, now you have 5.  (application of addition in a situation that has meaning for her)
• Suppose she has 3 carrot sticks, but she says she wants 5.  Ask, "Oh, you want 5?  Okay, how many more do I need to give you?"  (The key here is to avoid hovering as she thinks it through.  Be busy doing something and let her do the work.)  (introduction to algebra)
• Play with manipulatives, which can be counters, snacks, toys, whatever you want to use.  Observe that you have 5 cookies, say.  Suggest (in a playful manner) that you divide them up in this way:  "2 for you and 3 for me!"  (2 + 3 = 5)  Let this evolve into 3 + 2 = 5, 4 + 1 = 5, 5 + 0 = 5, 2 1/2 + 2 1/2 = 5 ...  (there are many ways to add up to 5, the number 5 can be broken down in many different ways)
• Does your child like music?  This one is easier with 3 or 4 than with 5, simply because most beginner music books use 3/4 time or 4/4 time.  Notice different ways to making enough beats to fill a bar exactly.  (again, many ways to add to the same number)
• Notice that 5 "take away" 2 is 3.  (addition and subtraction are related)
• Suppose she "sells" you an ice cream cone for $2.  Tell her you only have a 5 dollar bill and let her make change.  When children are first introduced to the idea of change, it is often helpful to show them, as in this example, the change ($3) and note the ice cream cone is worth $2, so together they add up to $5, which is what you gave them.  The trade is fair.  (application)

4)  Know When to Let It Go - Sometimes your child doesn't grasp an idea the first time.  That's okay!  They didn't figure out how to say 'mama' the first time they tried either.  The key is not to turn them off trying.  Introduce an idea, pursue it if there is interest, don't if there isn't.  But don't be afraid to introduce it again, later, perhaps in a different way.  Often, they will introduce topics themselves, perhaps not in the way that you expect, and perhaps not in the sequence that you expect. 

Many of us carry baggage from interactions with someone trying to explain to us something mathematical.  The worst is when you don't understand and the person explains it EXACTLY the same way, only LOUDER.  But, explaining a hundred different ways isn't always helpful either.  Like advice, only explain when your child indicates an interest in your explanation.  Unwanted lecturing is a good way to get your child to shut down.  If they don't understand and don't care, let it go. 

If they don't understand to the extent that you think they should, but they have been trying to understand, it might still be a good time to celebrate what they did learn and leave them to mull over the rest.  More math is done in the "right brain" than most people think.  It takes time to make associations and put concepts into context.

5) Play with it - Again, many of us are used to being told "correct ways" of dealing with math.  This is not math!  There is always more than one way to do things.  There is always more than one way to look at things.  The kids that have trouble in middle school to higher math are the ones who memorize the steps without understanding the concepts.  Steps can be learned in a short time if the foundation concepts are there. 

And how do children understand concepts?  How do they make sense of the world?  They play!  Together with your child, play with math.  Make connections -- goofy ones, artistic ones, logical ones -- make connections to the rest of your world.  Don't be afraid to talk about big ideas:  levels of infinity, closed spaces, exponential growth.  You don't need to calculate to explore big ideas.  Give numbers personalities.  Imagine them in our world; imagine yourself in theirs.  (Watch Donald Duck in Math Magic Land.)  Sing silly songs to remember facts.  Look for patterns.  Play games.  You've heard it before:  Playing is learning!


To best let these conversations add to the culture of math in your household, be open to holding them in any situation, not just while "teaching math."  You may have heard people say, "Math is everywhere!"  It really is.  I don't mean to say that we should go looking for math and speak about it every chance we get.  But do try to make connections between conceptual math, everyday math, and the rest of life.  Look for and share in the beauty of patterns; use math to solve problems and make decisions; celebrate Pi Day; explore math in history and culture; use math to understand the world.  Model these conversations with other adults if you can -- talk aloud to yourself if no one is available --  and include your child when you can.  Keep it positive and show no fear.  :)