## Tilting the number line

Is pure left-to-right the best number line?

The team found that the eye movements could be used to predict the size of the next number before it was spoken. If a volunteer looked left and downwards, he would typically chose a number that was smaller than the previous number, and if he looked up and to the right, he chose a number that was larger . . . What’s more, the extent to which he looked in a particular direction correlated with the extent to which the number was larger or smaller than the last.
— New Scientist, Mind over matter? How your body does your thinking

Given that 10% of people see sequences as their own personal spacial arrangement, and even normal people appear to have some internal number line (see the quote above) how should that influence our teaching?

This is the standard representation of the number line:

However, according to studies like the one above, and also studies of synesthesia, it is quite common to include an up-down component:

[From Galton’s Visualized Numerals.]

While I’ve never heard it used before, I theorize it might be best when teaching students to intuitively handle the number line to present a tilted format:

### 12 Responses

1. While I agree that it might be good for basic numbers, when we get to graphing with an x- and y-axis, a tilted format may seem more awkward?

• Yes. It would be a tradeoff.

I have 18 year old students who can’t do -2 + 3 to save their life. This is for them.

• @calcdave I’ve left a prezi response:) http://prezi.com/mnn4lyogyvww/

• Ha! I like it.

My fiancee is a synesthete (is that a word?), so I get the point of this post. Sadly, there often seems to be a trade-off in math between the objective formalism of manipulating symbols in “pure” math and the subjective intuition in more “applied” situations. So, I’m totally in favor of this for Jason’s situation and for most things, but maybe at some point when they get better at manipulating numbers, we move them towards the more “traditional” form?

• but maybe at some point when they get better at manipulating numbers, we move them towards the more “traditional” form?

We’d have to, yes. But the above study (and some others) make me wonder if people have it internalized as the tilted form more than we realize, so really, there’s not much harm in making it explicit since that’s how people mentally have it anyway.

Mind you, this is all theory, I haven’t experimented with this in class yet.

• Funny; seems to me that our x-y axis graphs already have the number line in this format.

http://screencast.com/t/ZjgxMmZjMWUt

• (Or, okay, not exactly, but clearly there’s a very strong connection between the two that could be used to bridge the gap.)

2. I like this idea. I’ve got a tacky Lakeshore numberline up right now, but one of my end of the year projects is to have the kids make a new one – each one gets one of the numbers and they decorate it on a half sheet of paper. For next year, I think angling it will be a worthwhile experiment.

3. One of the old math teachers at my school insisted that a vertical number line was the way to go. She said it was more intuitive to think about positive numbers as up and negative as down when her students were adding and subtracting them.

It’s sort of like Mr K’s use of a human number line where positive is forward and negative is back.

Ultimately, the lesson is give them options and let them use what works for them. If nothing works, let them create something on their own.

4. I have used a vertical number line plus stories to help my young students get comfortable with negatives (here), but I think I like the slanty one even better. I can imagine a house at the origin on the side of a hill, and all sorts of story problems we could make about the adventures of the people living there…

5. I like it! I may use this number line in future videos for kids. Shall I call it the “Dyer Number Line”?