I’m fascinated by how the simple is really the most complex. Just proving that the two assumptions
3 + 0 = 3
and
3 + x = 3
will force x to also be 0 is a serious and important proof. And harder to do than you think.
When we get even more basic and talk about equality and comparison, things get impossibly complex.
And that’s the fun in the challenge inspired by 2nd grade math teacher, Suzanne Weider. She wrote:
Another idea I have been looking into has to do with the equal sign: teaching it as a symbol that means “the same as” as opposed to the sign that comes before the answer.
Equality and comparison are everywhere.
Some people are obsessed with fairness. Almost all people have some sense of fairness. This means that things need to be roughly equal, if not the same, for all situations in life.
We go into every situation assessing what’s the same and what’s different. Which means a judgment call on equality.
The beauty of this is that you can tap into how our natural comparison connects with the comparison tools of mathematics. These are tools like the greater than, less than and equals signs. This can set your children up for some hard-core success in algebra, geometry, calculus, and Radon-Schure-Greenlee Mathematics. (I made that last one up, but I mean crazy everything math.)
Equality and comparison are so complex that a single article won’t hold all there is to write about it. So this is the first in a series.
The series will run roughly like this:
- Introduction to comparison (That’s this one.)
- Some Ways to Think of Equality
- Why People Aren’t Equal
- Other comparison tools
- The reflexive property
- The symmetric property
- Transitivity and substitution
- Playing with the equals sign
- Ranges and estimation
- Inequalities and ordering
I’m excited and overwhelmed. Ready for the ride, MathFourTicians? Hold on – it’s gonna get weird!
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