Algebraic Intuition

[Alex]

When I used to teach algebra for an equation like:

2x + 5 = 11

I found many kids confused about the rules for what you can do to manipulate the equation.  For example, why can’t you just divide 2x and 11 first to get:

x + 5 = 5.5

Or if you want to subtract 5 first, do you subtract it from every term like this:

(x-5) + (5-5) = 11-5

It can be a little difficult explaining why those steps are incorrect using written notation, but students quickly gain an intuition of these rules through visual examples.  We recently added a set of “Algebraic Intuition” games to the curriculum section of Tile Farm classroom for middle school and high school to give students a deeper algebraic intuition by solving simple visual equations using mental math.  Here is an example:

https://classroom.tilefarm.com/activityPreview/h/curriculum/10

[ApplePi]

Even after all these years of teaching Algebra II, I still see my students tripping over the same kinds of mistakes. They get so wrapped up in memorizing steps that they miss the bigger picture of what’s really happening. It seems to have gotten worse over the years.  Yes, procedures have their place, but it’s absolutely essential to help them develop a sense of intuition first.  I’ll give this a try.

[Author]

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