Decimals before fractions? [TDI 1]

The Khan Academy knowledge map got me thinking about this recently, but the basic question at the heart of this Institute has been on my mind for a very long time.

Does it make sense to study decimals before fractions?

The Khan Academy knowledge map. Decimals lie beneath addition and subtraction in the hierarchy. Fractions are not in this part of the map; they are far off to the lower left.

We do not have to answer that question right away. Indeed I do not think that there is a simple answer. I will argue in the coming weeks that the preponderance of theoretical and empirical evidence points to no.

You are not obligated to agree with me.

As I worked on formulating an argument the other night, I tried to make my question more concrete. Here is what I came up with (via Twitter):

Someone needs to explain something to me…+

— Christopher (@Trianglemancsd) September 27, 2013

+ if decimals depend only on whole number place value, addition and subtraction, then what exactly is a “tenth”? http://t.co/Ght3VE2FpH

— Christopher (@Trianglemancsd) September 27, 2013

You can talk all you want about “tens” and “tenths” but if we don’t have a common language of fractions, you’re talking nonsense.

— Christopher (@Trianglemancsd) September 27, 2013

And if you want to claim that a “tenth” is the thing you need ten of to make a whole, then I will need to know what a “hundredth” is.

— Christopher (@Trianglemancsd) September 27, 2013

But seriously, what is your explanation for why one tenth is the best fraction to study first?

— Christopher (@Trianglemancsd) September 27, 2013

Now, Twitter is a medium that makes nuance difficult.

So let’s strive to find nuance, subtlety and complexity in this conversation.

That last question is an important one for me. Traditionally, U.S. curriculum has had students working with decimals before they work seriously with fractions. Khan Academy isn’t going against the curricular flow in this area. What this means is that one-tenth is the first fraction students study. Is this justified?

The arguments in favor of studying decimals before fractions include these:

Place value. Decimals are the logical extension of the whole-number place value system. Just as you go from 1 to 10 to 100 by moving one place to the left, you also go from 100 to 10 to 1 by moving one place to the right. When you move left, the value of the place is multiplied by a factor of 10; when you move right, the value of the place is divided by a factor of 10. Decimals just continue that process.

Money. Children come to school with experiences involving money. They know what one dollar is; they know that 10 dimes make up a dollar; they have seen $1.25 and can talk about what that means. As a result, decimals are part of children’s everyday experience in a way that (say) sevenths are not.

Measurement. Metric measurements (and many but not all Imperial measurements) are expressed in units and tenths of units. Children are familiar with the meaning of “12.2 fluid ounces” or “3.2 meters”. So it makes sense to operate on tenths and hundredths even before formalizing the underlying mathematics of fractions.

How say you? Are these powerful arguments for you? Have I missed any arguments in favor of studying decimals before fractions? Do you have evidence to bring to bear on the question of whether it makes sense to study decimals first? Can you provide curricular examples to support (or refute) my claim that U.S. curriculum typically presents decimals before fractions? Can you provide an international perspective for us?

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