[Numeracy 256] Looking for patterns
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Tue Mar 30 17:40:55 EDT 2010
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I, too, have a problem remembering if the answer is 54 or 56. But I know for 7 x 8 it must be 56 as 54 adds up to 9 and so it is the answer to a 9's basic fact.
I tell the story of the little boy who didn't study as he should have, so he copied down all the math facts as he knew he would be in trouble if he didn't at least look busy.
9 x 1 =
9 x 2 =
9 x 3 =
9 x 4 =
9 x 5 =
9 x 6 =
9 x 7 =
9 x 8 =
9 x 9 =
Well, he knew that one times any number would be that number so he answered the first one correctly. And then because he knew he needed to look busy, he decided to number his paper.
9 x 1 = 9
9 x 2 = 1
9 x 3 = 2
9 x 4 = 3
9 x 5 = 4
9 x 6 = 5
9 x 7 = 6
9 x 8 = 7
9 x 9 = 8
He looked around and noticed everyone was still busy so he figured he better still be writing. So he numbered his paper going up.
9 x 1 = 9
9 x 2 = 18
9 x 3 = 27
9 x 4 = 36
9 x 5 = 45
9 x 6 = 54
9 x 7 = 63
9 x 8 = 72
9 x 9 = 81
And boy, was the little boy surprised when he received a 100 percent on his paper. The adult students usually enjoy the story. And then I ask them to look at all the answers. I ask them to add the sum of the digits of each answer and they are pleasantly surprised when the sum is always nine.
1 + 8 = 9
2 + 7 = 9
3 + 6 = 9 and so on.
For those that have been challenged by math, it helps to have them feel good about something related to math.
I agree that it is important to learn the basic facts. It helps with your speed in doing many of the functions dealing with fractions and factoring. But I also understand that some of the adult students have difficulty memorizing at this point. I feel it is most important that students understand the many processes when dealing with numbers and if a calculator will facilitate their utilizing math, I encourage the use. But I also warn students that you should be able to do the problem with paper and pencil because you never know when the light may be too dim for your solar operated calculator to work! :)
Cheryl Hagerty
Marion Technical College ABLE program and Community Faculty teaching dev. ed math on campus and at the local correctional institutions
-----Original Message-----
From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov] On Behalf Of Patricia Donovan
Sent: Tuesday, March 30, 2010 3:06 PM
To: numeracy at nifl.gov
Subject: [Numeracy 249] Re: Knowing your facts / stereotype threat/developing number sense
Hi Laurie and All,
Knowing one's facts is one thing; having number sense is quite another. Even when using the calculator, a person needs to have a strong command of number sense to ensure unreasonable answers get checked. If a student cannot hold on to number facts like 7x8 = 56 (and not 54 -- a frequently offered alternative answer) that will affect only their precise calculations; however if they do not understand that 70 x 8 will result in a three digit answer, while 7 x 8 will not, they are in deep trouble with our without the calculator.
Tricia Donovan
Tricia Donovan
SABES CRC
World Education
44 Farnsworth St.
Boston, MA 02210
617-482-9485
Fax 617-482-0617
>>> "Lauri Schoneck" <SchonecL at seminolestate.edu> 03/30/10 2:02 PM >>>
I will have to agree to disagree with Kerry... I believe math facts are
not the ABC's of math, but rather another code in the seemingly unending
plethora of codes that work together to help us understand all kinds of
math. Proof that you can have math understanding and not have your math
facts is in the TABE applied math section. Time and time again,
students score FAR better on the applied math portion (with a
calculator) than they do on the calculation section (without a
calculator). There are a few simple rules to keep in mind when setting
up problems on a calculator, and students who are not math fact savvy
are not also necessarily math concept inept. More students understand
the concepts and could work the problem if it weren't for multiplying
and dividing sitting in their way.
With that said, my 7 year old *will know his times tables and division
tables*, I will see to it that he does. I use those facts everyday!!
But...adult learners learn differently than children. And when I see a
32 year old single-mother of 4 struggling to make it past her math GED
test b/c her rote memory of the times tables eludes her, I get so
frustrated with "the system". This same 32 year old has passed every
GED subtest, and a promotion is riding on her passing her GED test...it
begs the question...if she understands the concepts (and she does), why
hold her back b/c she lacks the rote memory skills to have rapid recall
of her math facts?
This single mom is but one of the hundreds, if not thousands of stories
around the country. I would **definitely** hold children responsible
for learning their math facts (dycalculia aside), but adults may be past
the point of learning them with fluency or reliability.
I certainly welcome others' opinions on this subject. Especially if
there is anyone out there who is consulting or writing tests such as the
TABE or GED... I'd personally like to see more calculator use available
on these tests.
:-), Lauri (PS: Being that I'm a math teacher, I'd rather not be held
accountable for my writing/language skills... ;-))))
Lauri M. Schoneck, M.Ed
Professor, ABE/GED
Seminole State College of Florida
Sanford, FL
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