First, this is not a blog about how to tell if you have a mathematically talented child. There are many great resources out there by people more educated on and experienced in that topic. (I’ve found the Hoagies’ Gifted Education Page , and the book “Developing Math Talent” by Assouline and Lupkowski-Shoplik very helpful.)

If you think you have a mathematically gifted preschooler, then you might have discovered that it’s hard to find a program for gifted children that caters to this age group. These are just a few tips I’ve found myself sharing with other moms of three- to five-year olds that you might also find useful.

Building Sets

LEGOs, Tinker Toys, Lincoln Logs, K’nex, Magna-Tiles, tangrams, blocks of all shapes and sizes. All of these and similar toys are great for stimulating different areas of mathematical thinking at different stages of childhood.

First, you can play all kinds of sorting games. Group the red pieces over here. Group the square pieces over there. Oh no, what do we do with the red squares? We can put them in the middle! All the rest go on the outside.

Voila! Introduction to set theory.

Then there is visual-spatial reasoning.

Have you ever observed a preschooler building a structure? She’s often down on her hands and knees looking at it from this way and that way, trying to figure out where to put the next piece. Seems like a pretty good way to encourage the ability to envision objects from different angles.

And a message to parents of gifted and talented girls from a former girl: We love, Love, LOVE these kinds of toys!

Mathematical Logic

This can sound so daunting at first. “How do you expect me to teach mathematical logic to a 4-year old?” The answer is that you probably already do it every day without realizing it. Does this sound familiar:

Dad: “Your mom and I don’t play with the crayons, so either you or your brother drew on the wall.” 

Child: “Not me!”

Dad: “So who was it then?”

Child: “He did it!”

Wait, wasn’t that just [(P or Q) and (not P)] implies Q?

Or how about this one:

Mom: “If you want me to take you to the park, you need to sit down and finish your lunch.”

Child is still running around.

Mom: “Okay, I guess we’re not going to the park.”

So now we have [(P implies Q) and (not Q)] implies (not P).

Or worse yet:

Dad: “We’re cutting out junk food in our family. We all need to eat healthier.”

Child spies Dad sneaking some barbecue potato chips.

Child: “Hey, you said we couldn’t eat that!”

Dad: “Uh, I’m not really your dad, so I’m not in the family?”


See, logic is really the underpinnings of childhood discipline. Hmm, let’s leave that one for a different blog.


I’m sure we’ve all said something like this to our kids: “You can have half the cookie now and save half for later.” And then you wordlessly break the cookie in half in view of your child.

If you cook or bake, let your kids observe and narrate as you go:

“We need a quarter teaspoon of salt. Would you please pass me the quarter-teaspoon?”

“Which one is it?”

“The one that says one and then a slanted line and then a four.”

“Why does it say that?  Why did you call it a quarter? That’s a coin.”

There’s nothing like parenting gifted children to keep you on your toes!

If your child’s fine motor skills are pretty good, then get a plastic knife and let them cut up soft ingredients.

Say, “Cut it in half, and then cut the halves in half so you get quarters.” It doesn’t matter if they cut accurately, just that they comprehend that we get fractions from dividing up a whole.

Keep a set of measuring cups in the bath toy rotation, preferably ones with the amounts (e.g., 1/2) written in big numerals. If you have room, keep several sets so that you can take one cup of water and pour it into three different 1/3 cups.

“Look at that! The first cup is empty now and the other three cups are all full.”

Lose the Lecture

As you have similar kinds of enriched dialogue with your little Fermats, keep in mind that at this age there is no need to make a big production out of any of these lessons. Little ones generally don’t have the patience for a mini-lecture, nor do they seem to really embrace new information delivered that way.

Mathematically gifted and talented youngsters will welcome these experiences as part of rhythm of their lives. It just takes a little more conscious effort on our part as parents to disguise the learning as play.

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