[Numeracy 592] Re: Teaching math and numeracy skills to adults learning English

  When I taught basic math at Century College here in Minnesota, I 
taught how to multiply multi-digit numbers. I used the algorithm I 
learned as a child: write down partial products in staggered columns and 
carry extra digits to the next column for adding. Most students were 
already familiar with this method, although strings of zeroes in the 
multiplicands tended to confuse them. However, one student from Russia 
came to me after class and asked if he could use his the method he 
learned in Russia. He showed it to me. (I wish I had written it down 
because I can't remember it.) It took only a few moments reflection to 
realize that his method would work just as well, so I gave him the go 
ahead. The method was very different, but the outcome would always be 
correct.

For students who struggle with the "standard" method of doing 
multiplication, I sometimes explain an alternate method that involves 
halving one multiplicand while doubling the other. After getting down to 
1 on the first multiplicand, then you eliminate all the pairs (halved, 
doubled) where the halved number is even. Summing the remaining doubled 
numbers gives the correct answer. It basically uses binary arithmetic to 
get partial products and then sum them.

For example:

     37     x        82
18              164
      9                328
4                656
      2               1312
      1               2624

82 + 328 + 2624 = 3034

Of course, for some problems this method can be cumbersome, and it 
always pays to put the smaller number first. However, many students find 
it easier to implement.

Chip Burkitt

On 10/20/2010 9:51 AM, Seltenright, Ginny wrote:

>

> I think that there's a misunderstanding due to the title of the 

> booklet referred to here, /"The Answer Is Still the Same...It Doesn't  

> Matter How You Got It!"' /

>

> It does matter how you get there, what doesn't matter is that the 

> student uses a different process than what the teacher perhaps is 

> showing or another student is using.   I went through the TIAN 

> training in Arizona which emphasizes student exploration and the idea 

> that there are many ways to get to the answer and then having students 

> show how and why their answer works (or perhaps doesn't work) and 

> making sure it works every time too.  It isn't about just getting an 

> answer and it being ok- which is possibly how the title may be 

> understood now that I am reading this discussion.  I agree with you 

> Susan, in that we need to be sure the student is making a connection 

> to the problem, the process, and what means to them.  This is the idea 

> behind the TIAN approach and Mary Jane's training involves training 

> teachers to think this way also.

>

> Ginny

>

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