How Vertical Alignment Makes Algebra Easier to Learn

Stop using the 'is equal to' symbol, = , to mean 'the answer is'

Podcast is AI generated, and will make mistakes. Interactive transcript available in the podcast post.

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Ever seen a student write something like this?

\(10x+3=43-3=\frac{40}{10}=4\)

We all know why they do it.

In primary school they learn to ‘do sums,’ like this:

\(3+2=\)

The way to ‘answer’ that is to write this:

\(3+2=5\)

This carries through a lot of the arithmetic in primary school.

Then they come to us in secondary school and we reinforce it.

We even reinforce it when we ask students to ‘expand the brackets:

\(10(5x+3)\)

And we tell them to write this:

\(10(5x+3)=50x+30\)

And we reinforce it when we ask them to simplify by collecting like terms:

\(3(x)+2(y)+7(x)=10(x)+2(y)\)

The problem is not that any of what we’re showing them is wrong. The problem is that it is unclear. And because it is unclear we end up with kids writing things like this:

\(10x+3=43-3=\frac{40}{10}=4\)

Which is clearly wrong.

But they won’t accept that it’s wrong, because they ‘got the right answer.’

‘It’s four, sir, so I got it right. Stop telling me I got it wrong.’

The good news is that this is not only very easy to rectify, but that the solution connects to future learning very neatly, and it also makes learning what to do and how for each of these instances even easier. It’s basically a massive win win win.

The problem is that we use a statement, the words: ‘is equal to,’ when what we really want to say is ‘the value of this arithmetic expression is…’ or ‘when we expand the bracket we get…’ or ‘this expression simplifies to…’

The solution is to say these things using vertical alignment instead.

When we use horizontal alignment to evaluate or simplify we lose the ability to use it to state a relationship between quantities; to state equality. As already said, it’s not that it’s wrong to use the equals sign, it’s that it’s unclear.

Unlike horizontal alignment with the equals sign, I have yet to find any context where using vertical alignment confuses our meaning.

Below we’ll look at several examples of what I mean.