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Math Mondays: Seeing Stars (and Circles, and Squares)

Is your child a space explorer? Even if “astronaut” isn’t one of her top “what do you want to be when you grow up?” choices, the answer is yes!

Spatial thinking is thinking about space and how our bodies move through it. It is about recognizing and categorizing shapes and objects, relating objects to each other in space, and transforming objects — rotating, flipping, scaling, composing, or decomposing them. It is also about space in two dimensions — understanding of spatial symbolic systems on paper, like maps, graphs, and diagrams.

Not that your child grasps these high-minded concepts. He’s just thinking, “Can I drive this fire truck between the couch and the coffee table? Will it fit or will it get stuck?”

Can we learn spatial skills? Yes! The good news is that we can learn and develop our spatial skills. In other words, it’s not that we are simply born with it, we can learn it and become better thinkers as we grow up! Want evidence? Check out this recent study from Northwestern University.

You can get started by recognizing and categorizing simple geometric shapes. This is a fun game you can play with your kids and learn together!

We’ll start with our good old triangle, square, circle, and rectangle — and we also invite our fancier friends the trapezoid, hexagon, and rhombus. Learning about these shapes is not a matter of memorizing their names; it’s about recognizing them in different sizes, orientations, and proportions. It’s also about analyzing unique features like the number of sides each has and/or the number of corners.

Children’s common mistakes:

Children can be fooled by appearances. Although they can easily “see” that a small triangle and a large triangle are both triangles (see image 1), they tend to believe that an atypical triangle (like the obtuse triangle on the left in Image 2) is less like a triangle than is a 4-sided figure like the one on the right (Satlow & Newcombe, 1998).
Image 1:


Image 2:

Children can easily recognize shapes in their pro-typical orientations (see Image 3), but they have difficulty in recognizing shapes in a random orientation (see Image 4).


Image 3:



Image 4:


How we can help children develop their spatial skills:

  • Engage in various activities that involve spatial thinking. Those activities might be solving puzzles, building towers with blocks, drawing and coloring shapes, or challenging them to find all the circles in the kitchen (think beyond pots and plates!).
  • Use spatial vocabulary in everyday language and while playing. For example, use words such as “rotate,” “flip,” and “move” when solving puzzles or when playing with blocks or Legos.
  • When you talk about transformations (rotate/flip/move etc.), demonstrate these actions with your hands.
  • Point out shapes in picture books or while you’re out with your kids, and ask your child to look at them closely. What shape is a face, or a window, or a STOP sign, or an airplane wing, or a fallen leaf on the lawn?


Cross, C.T., Woods, T.A., & Schweingruber, H. (Eds.). (2009). Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity. Washington, DC: National Academy Press.

Uttal, D. H., Meadow, N. G., Tipton, E., Hand, L. L., Warren, C., & Newcombe, N. S. (2013). The Malleability of spatial skills: A meta-analysis of training studies. Psychological Bulletin.