Children Are Natural Mathematicians

In my last BLOG, I wrote about mathematizing our young children’s worlds. No sooner had I written and submitted my BLOG for posting, that my grandnephew came over to visit. Isaac is 3 years old and very shy, but when he decides to talk, he doesn’t stop. This little guy loves to build and create things. He also loves to count anything and everything. When we are together, almost unintentionally, the teacher in me comes out and I almost always give him things to count, bring out number games or books. I always ask questions, use lots adverbs and adjectives and mathematical language to highlight things he may not readily recognize in his environment. However, during his last visit, I really took pause to just watch and listen to what he was doing and saying. As I watched and listened I really was quite stunned with how he engaged with his cars, puzzles, blocks, books, and of course us, the adults in the room. I was pleasantly surprised by his choice of words when talking, much of which was self talk. Enchanted by his play with cars on his town and road carpet, I began to take anecdotal notes – just as I had many years ago when I was walking classrooms looking for evidence of student engagement in mathematics. Below are just a few of my observations.


  • began placing cars and trucks on the road, first randomly then progressing to a linear organized fashion and counted them
  • randomly picked up blocks, stating the letter or number, and placed them on or near the mat
  • placed his pound and play tower in the middle of the mat and used it as a parking garage
  • moved cars around the track stopping at random places and creating stories
  • counting as he placed cars into the colored shoots (parking structure), some of which were too big so he had to place them directly on the ramp – manipulating them and moving cars around so that they fit (see orange & green car in photo)
  • taking cars out of structure one at a time, placing them on the mat by size – moving and reorganizing multiple times
  • taking wooden blocks with numbers on them and placing cars on them
  • a wooden block was labeled with 3 and he placed three cars next to it

As I reflect on my observation, I noticed Isaac was noticeably engaged in mathematics.

  • He was attending to attributes (size, color, type of vehicle).
  • He was counting (he always began with 1 and when asked how many, he in many cases was able to say give the quantity without having to begin with one – last word response).
  • He demonstrated one-to-one correspondence when counting, each car held a count.
  • He identified numbers.
  • He organized his cars by size (length and height) in a linear pattern.
  • He used mathematical reasoning and problem solved.

30 years ago, I would have only noticed a little boy playing with his cars. Fast-forward 30 years, I see a little boy interacting with mathematics through play. As I mentioned in my previous blog, as adults we unconsciously mathematize our environments every day. After watching my grandnephew, it’s evident children do, too. As you work with your little ones, I encourage you to observe them playing and identify the mathematics they may be engaging in – without even knowing.

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