Equality for all

Twitter is great for getting thought-provoking discussions now and again. For instance Tracy Zager retweeted about work in Year 4 at my school using the number balances:

This is what I'm talking about! http://t.co/mcN4jh46gv h/t @TracyZager @Simon_Gregg @helenjwc
— Christopher (@Trianglemancsd) May 21, 2014

Actually, there was an entertaining conversation that followed (with more branches besides).

When Christopher says, "This is what I'm talking about", he's referring to this post on the equals sign.

He discusses the problem Tabitha has with this sum:

As she says:

8 plus 4 is something, then plus 5?

As he says:

We train children to think that the equal sign means and now write the answer. Arithmetic worksheets reinforce this idea. Calculators do too. (What button do you press to perform a computation on a typical calculator? The equal sign!)

But doing algebra requires that we understand the equal sign to mean is the same as or has the same value as.

So, teachers, get out your balances! As Tracy says:

@Trianglemancsd @helenjwc Just read #tmwyk. Made to order! Have this balance for my kids. @Simon_Gregg inspiring me to pull it out again!
— Tracy Johnston Zager (@TracyZager) May 21, 2014

(There's a lot more to this task than just seeing the equals sign in a different light. For me, it also involves getting used to a model of equality, which gives sense to calculating with unknowns or makes them concrete in a particular way. A lot of calculation is involved, but the route is not specified. I'm wanting the children to have a "feel for" this kind of equation, which might be reduced by having an algorithm for finding an answer. Not that one algorithm would really do the trick here. I'm also edging towards algebra with those unknowns...)