So my older son and I are discussing his suggestion of how to build a sandbox in my backyard for his kids to play in.

He’s describing kind of a ground level frame of 4×4 beams in the shape of a square, with a layer of a black plastic moisture barrier beneath, and then a slightly smaller offset frame of 4×4 beams laid into the ground.

I’m having trouble visualizing what he’s describing. So he goes to the dusty back window of his van and starts drawing a partial diagram of the sandbox he’s got in mind. Now I see what he’s talking about – there’s a picture there that I can examine.

Then I asked him, “Could you picture in your mind what you were describing, before you drew the diagram?” He said, “Sure. You couldn’t though, could you?”

“Nope,” I admitted. And I realized why he could visualize his diagram and why I couldn’t.

   He was starting with the picture in his head, then using words to describe what he saw. 

I was starting with his words, then trying to create a picture in my mind. The process in my head was the reverse of the process in his head.

So why could he so easily picture in his mind how a sandbox could be built?


He’s had a lot of experience working with beams and studs and frames. He spent two summers in college doing construction and remodeling with some very experienced remodelers, plus he spent 2-3 years in high school and 3+ years in college working in the technical side of the school theater departments – building sets, putting up doors and door ways, constructing stairways, framing stud walls with sheetrock layers and plywood.

Experience. Based on that experience, it was easy for him to picture in his mind’s eye the kind of sandbox he thought would work.

That was experience that I didn’t have. He’s probably forgotten more about construction than I will ever know.

There is at least one area where I have enough experience to picture in my mind’s eye what’s going on: in algebraic factoring of quadratic expressions.

What prompted this blog was that I was creating some algebra problems for my SAI students to factor. In SAI, we use pieces to show elementary age students what quadratic factoring is. Many times it’s easier for me to picture the pieces for 2x2+ 7x + 6 than it is to write out those symbols.

So why is it easy for me to picture those algebra pieces but not the 4×4 beams? Experience. I’ve got a lot more experience with algebra pieces than I do with wood beams.

I can picture what I want in my head, then use words and symbols to describe what I’m already seeing.

That’s the advantage of SAI: we give your child the experience of working with math in ways that train them to see in their mind’s eye what they can then describe with words and symbols.