No Pencils in Math?

What if math education used no writing for the first few years? What if all sorting, arithmetic, geometry and algebra problems were done with movement and objects? Chocolate-bar fractions and M&M probability. Area and perimeter using square tiles and real rulers. Graphing using footsteps and string. "Solving equations" using a scale and bags of goodies.


I wonder how much of people's math difficulties and fears stem from premature writing, and too few hands-on activities. "Manipulatives" is a current buzz-word, but if they're only tossed in as an extra now and then, are they enough? When I tutor math students and they're struggling with a particular concept, I always try to show them in a hands-on manner what is going on. But why should I wait until they're struggling? Why can't math be kinesthetic all along?


My kids are (almost) 6 and 4 1/2 and they've both been doing kindergarten this year. I have done no worksheets about numbers and counting, but we talk about numbers all the time. We spent all Fall doing math activities concentrating on classifying, directions, and quantities. Numbers were something I brought up every now and then. Now my kids bring up numbers themselves and are continually telling me things like, "Mom, 2 and 3 make 5!" My older child has tried writing equations on her own because she's becoming enamored with writing in general. But I wonder if I wouldn't be better off saving the writing for later.


I think I would have more fun teaching and I know the kids would have more fun learning, if math were taught this way. And maybe, as a small side benefit, our next generation would not be so math illiterate.

Math Everywhere

Math can be found anywhere. I had my three kids with me the other day at the local high school, and in a common area, the floor was covered with many square tiles. Around an area of small squares were another few rows of larger tiles. I asked the kids to count how many squares there were, and they balked! “There’s too many!”

First I showed them how there were not only a lot of small squares, but how if you put four of those together, you get a larger square. And nine makes another size, followed by sixteen and then twenty-five. If my kids were older I probably would have told them that these are all “square numbers” demonstrated by the fact that they form a square. 

Then I counted one row of small tiles and squared that number to show Naomi how we could “count” how many tiles there were without numbering them one by one. She was fascinated! There happened to be over one thousand!

She was so taken with this method of counting large numbers quickly that when we went outside, she also wanted me to calculate the number of tiles on the patio. She excitedly told her brother that there were 200!

Finally, there were some benches on the patio that were full of holes and I showed Naomi and Josiah how we could estimate that there were 2,600 holes on each bench, or over 11,000 between the four benches. I used estimation, mental math, and multiplication.

I know these concepts are beyond my 5 and 4-year olds, but I remember my dad exposing me to difficult math concepts when I was young. I would then come across the same ideas in school later and find them easy to understand, in part because my dad had already given me a foundation. I figure it’s really never too early to show kids how math works, and let them see it in their own world.