[Numeracy 599] Re: Teaching math and numeracy skills to adults learning English
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Thu Oct 28 19:04:47 EDT 2010
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Why doesn't this work for 18 X 35? I must be doing something wrong. I
come up with 665. But when I reverse the numbers to 35 X 18, I get 630
which is the correct answer. Does it not work in all cases?
Laura E. Sherwood
Literacy Coordinator
Adult Education
College of Lake County
Grayslake, IL 60030
847-543-2327
lsherwood at clcillinois.edu
"Their story, yours, mine - it's what we all carry with us on this trip
we take, and we owe it to each other to respect our stories and learn
from them." William Carlos Williams
From: numeracy-bounces at lincs.ed.gov
[mailto:numeracy-bounces at lincs.ed.gov] On Behalf Of Chip Burkitt
Sent: Wednesday, October 20, 2010 8:34 PM
To: numeracy at lincs.ed.gov
Subject: [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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