3.7x10= 3.70

A

apple2357

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Any thoughts on how to pull part and deal with the underlying cause ?

3.7x10 = 3.70

Presumably, it has arisen because of remembering a rule to do with 'add a zero' when multiplying by 10. So I am wondering should that even be taught? And are we doing something wrong when teaching young children rules like this?
If you could go back and teach this child who made this mistake, how would you begin so this misconception didn't happen?
 
apple2357 said:
Any thoughts on how to pull part and deal with the underlying cause ?

3.7x10 = 3.70

Presumably, it has arisen because of remembering a rule to do with 'add a zero' when multiplying by 10. So I am wondering should that even be taught? And are we doing something wrong when teaching young children rules like this?
If you could go back and teach this child who made this mistake, how would you begin so this misconception didn't happen?
Click to expand...
In my opinion:

There is no misconception involved here - only missed last step of "placing the decimal point correctly at correct position".

So I would teach:

3.7 * 10 → 370. → 37.0
 
apple2357 said:
Any thoughts on how to pull part and deal with the underlying cause ?

3.7x10 = 3.70

Presumably, it has arisen because of remembering a rule to do with 'add a zero' when multiplying by 10. So I am wondering should that even be taught? And are we doing something wrong when teaching young children rules like this?
If you could go back and teach this child who made this mistake, how would you begin so this misconception didn't happen?
Click to expand...
But 3.7 * 10 = 37.

To explain it

[MATH]3.7 = 3 + \dfrac{7}{10} \implies\\ 3.7 * 10 = \left (3 + \dfrac{7}{10} \right ) * 10 = 3 * 10 + \dfrac{7}{\cancel{10}} * \cancel {10}= 30 + 7 = 37. [/MATH]
 
Subhotosh Khan said:
In my opinion:

There is no misconception involved here - only missed last step of "placing the decimal point correctly at correct position".

So I would teach:

3.7 * 10 → 370. → 37.0
Click to expand...

I think there is, i can't be certain but i think it arises because the child is remembering a rule ( add zero at the end) and extending it from integers to decimal numbers?

So you would teach by thinking about place value? the tenths become units, the units become tens? I remember as a child i was told to move the decimal point...
 
Move the decimal point one position to the right is a rote rule, not an explanation.
 
Subhotosh Khan said:
But what does it mean "conceptually"? How can I make groups of π and collect those into √2 piles?
Click to expand...
This highlights the danger of defining multiplication as repeated addition, yes sure it makes sense for a particular case but not generally. Some argue that it should be done properly (?) at the outset otherwise all you end up doing is making lots of special cases for kids to remember.
 
I teach it like this. When you multiply by 10, move the decimal one place to the right ( I put a little loop showing that I moved the decimal). If the loop has no digit above it, then I put in a 0.

When you multiply by 100, move the decimal two place to the right ( I put little loops showing that I moved the decimal). If any loop does not have a digit above it, then I put in a 0.

When you multiply by 1000, move the decimal three place to the right ( I put little loops showing that I moved the decimal). If any loop does not have a digit above it, then I put in a 0.

....

When you divide by 10, move the decimal one place to the left ( I put a little loop showing that I moved the decimal). If the loop has no digit above it, then I put in a 0.

When you divide by 100, move the decimal two place to the left ( I put little loops showing that I moved the decimal). If any loop does not have a digit above it, then I put in a 0.

When you divide by 1000, move the decimal three place to the left ( I put little loops showing that I moved the decimal). If any loop does not have a digit above it, then I put in a 0.

...


You can point out that if you have a number without a decimal (An integer), then you can put the 0's at the end with no concern. You put as many zeros as 10, 100, 1000, ... has


Have the student do many problems multiply and dividing by powers of 10 until they say I had enough of this I see the rule. Then they can use the rule!
 
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apple2357 said:
This highlights the danger of defining multiplication as repeated addition, yes sure it makes sense for a particular case but not generally. Some argue that it should be done properly (?) at the outset otherwise all you end up doing is making lots of special cases for kids to remember.
Click to expand...
In my opinion, you have to teach students that multiplication is repeated addition. That is how they can learn the multiplication table (6*4=24, so 6*5 = 24 + another 6). They can tell you how seats there are in a movie theater (assuming equal size rows). This is important! Later on, they can be told that sqrt(5)*sqrt(7) = sqrt(35) or that (1/2)(5/8)= 5/40.
 
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