5 Ways to Build Math Minds

Last summer I left the job that I had for 7 years and have slowly been transitioning out of it (they kept bringing me back in :).  With that job I was always busy during the summers doing trainings for teachers, but this summer and most of last summer I’ve gotten to be home hanging out with my 4 kids (YEAH! and EXHAUSTING!).  To be honest, I started writing this post a year ago, but never finished.  Thanks to @JamieDunc3 for pushing me to actually finish it. 🙂

One thing I’ve noticed being home more with the kids is that I probably do some mathematical things with my children that others do not (don’t ask me about my literacy endeavors with them).  Or maybe you do them, but don’t realize the powerful mathematical foundations you are building with them.  What I realized as I began writing this post was that these 5 things are not just for parents, they apply equally to the early elementary classroom and to preschool classrooms.

So, here are my top 5 Ways to Build Math Minds, that I do with my personal children:

5. Count everything and nothing

Most of the time we think of making kids count sets of objects, which is important, but I’ve found so much power in just counting NOTHING.  We live in a small town and so if we want to go anywhere it’s a long drive (like 45 minutes to get to a pool for swimming lessons).  On our drives there is lots of counting, but we often don’t have objects to count (on our drive to swim lessons we were lucky to see 10 vehicles along the way).  So, we just count to count.  They count to see how high they can count, they count to a specific number, and they count to 60 for every minute we have left until we reach our destination as we get closer.  I’ve noticed how much the kids are discovering the patterns.  They have been able to transfer the 0-9 into the decades of 10-90 and on into the hundreds.  However, my five year old, still battles the transition into the next decade and says sequences like “Twenty-eight, twenty-nine, twenty-ten, twenty-eleven.”  It’s actually really cute and I LOVE that he is getting that connection to the counting sequence.

Counting isn’t just for young kids, either.  All kids should be counting.  Have you ever had kids count by 2/3, 0.6, or 2x+4?  Or, how about instead of just counting by 2 starting at 37, try counting by 2 minutes starting at 12:17pm.  As kids count they begin to notice patterns and math is built on seeing & understanding patterns (see #2 below).

4. Make kids do chores to earn money

I know this doesn’t sound like it would apply to the classroom, but hear me out.  Since the time my oldest was three we have been paying him a quarter for each chore he did (and we continue to do it with all of our children).  That may seem ‘rich’ to some, but I had some goals in mind that using quarters helped me achieve but you could do this with dimes or nickels, whatever you want.  Here are a few things I noticed and focused in on with him.

• *He had to develop his one-to-one correspondence.  Meaning, he put one quarter on each square of his chore chart that he completed.  This is a big thing for little kiddos!
• *He learned to subitize up to 4 really quickly because he wanted 4 quarters so he could exchange for a dollar.  He could tell instantly when he had enough on his chart to make a dollar, because he could “see” 4…which is why I went with quarters instead of dimes.  It’s harder to see 10 for little kids.
• *He started to unitize…he understood that 4 quarters = 1 dollar.  This is HUGE when it comes to money.  It’s very difficult for kids to understand that they get 1 thing but it’s the same as these 4 things.  This is epitomized in Shel Silverstein’s poem Smart, where the boy trades his 1 dollar for 2 quarters because 2 is more than 1 and then continues on until he has just 5 pennies, because 5 is more than the 4 nickels he had.  My son understood unitizing quickly, my daughter took a bit longer because she felt the same way as the boy in the poem.  Every time my son would want to exchange his money, she would choose not to because she wanted to keep all her many quarters instead of having just a few dollars.
• *As the kids really got into exchanging for dollars, it also started helping them with some of their ‘math facts’ and the benchmarks of 5 & 10.  They started to know instantly how many more dollars they would need to be able to exchange for a $5 bill and then a $10 bill and then a $20 bill.  I remember a time before my son entered Kindergarten that I asked him what 10 + 9 is and he instantly knew it was 19.  His explanation was “because 10 and 10 make a 20, so it’s just one under.”  This comes from him constantly wanting to get to a $20 bill and know how many more dollars he needed and how much he had at the time.

So, in a classroom you can do the same thing by implementing a classroom store.  There are all kinds of posts out on the internet about teachers who have implemented systems in their classrooms where students earn money for doing things in the room.  Then you can have them do the exchanges mentioned above, but also they can purchase items from their classroom store.  At home, I have my kids save up their money for toys or electronics they want.  This gives you lots of opportunities to work on addition & subtraction along with learning about money.

3. Play games

Now, if you have followed me for any amount of time I hope you have seen what a big fan of games I am (check out my free Evergreen Games!!).  I grew up in a game playing family and any chance we have we play games with our kids.  Any card game, board game, dice game, or dominoes builds powerful math ideas.  Often when you play games kids may not attend to the mathematics involved.  So, of course I’m always talking to my kids about it.  For example, when we are playing Chutes & Ladders, I will ask them questions like “How many do you have to roll to make it to that ladder?” and  “What do you NOT want to roll?” when they are close to a slide.

As much as I love playing games and a lot of them do have math inherently part of them, I just can’t help myself and I’m always asking my kids questions that pull out even more mathematics or just get them attending to the math so that when I’m not right there playing with them, they have basically learned how to notice the math in situations they may not have noticed before.

2. Develop routines

The consistency of routines builds the expectation of relying on patterns.  I remember all the books I read when my first child was born that talked about the power of developing a routine for your baby.  The same holds true throughout their lives.  These routines establish predictability.  When you trust that predictability, you can then use it to create order in your life.  The same is true in mathematics.  The Standards of Mathematical Practice also acknowledge the power of structure (Math Practice 7) and repeated reasoning (Math Practice 8).  Children need to be able to see the structure of mathematics and figure out how to use that structure to make sense of patterns they notice.  This is what I’ll be working on with my 5 year old who gets the pattern of the numbers (eight, nine, ten, eleven…) but isn’t applying it correctly to the counting sequence as it grows higher (Twenty-eight, Twenty-nine, Twenty-ten…).  They notice patterns, but often don’t understand how it applies.

The more we establish routines and patterns in our children’s lives the easier math becomes for them because math is All About That Pattern (not the Bass).

1. Be Less Helpful

I have asked my kids “How do you know?” for so long that I don’t even have to ask them anymore.  As soon as they figure out an answer they tell me their thinking process…they just know it’s an expectation.  Or, instead, they just think out loud to begin with.  Below is a video of my oldest (7.5 YO) that I took just the other day.  I was sitting in the dining room and he was in the kitchen preparing a treat we like to make.  I heard him count “6,12,24,30.” I asked him to repeat it and he said the exact same thing again.  I thought he was trying to count by 6s but doing it incorrectly, so I went into the kitchen and asked him to show me what he was thinking (Look at the picture below to see if you can figure it out, then watch the video).  Now, I was busy in the dining room working on stuff and I could have just said “No, Bud, it goes 6, 12, 18, 24.” But stopping to hear his thinking No.1 it was an awesome opportunity for me to see his cool thinking and No.2 I didn’t dismiss his thinking as wrong and correct him which inadvertently tells kids to stay on the “right track” and not think creatively with numbers.

With young children it is my belief (and research backs me up…Kamii, 1999; Clements & Sarama, 2004….just to name a few) that children should experience mathematics in a play-based way along with lots of visuals and discussion about what they notice mathematically in their world.

What are your thoughts?  Do you have a favorite way to Build Math Minds in young children???