[Numeracy 214] Re: manipulatives
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Wed Feb 24 13:15:53 EST 2010
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Indeed.
When I have a student getting the calculator out for 100 + 3 -- because she really does need it, because she really is not processing anything numerical -- I want to stop the world around us and find a way to teach her that these silly squiggles mean something *and* what 100 means.
Susan Jones
Academic Development Specialist
Academic Development Center
Parkland College
Champaign, IL 61821
sujones at parkland.edu
Webmastress,
http://www.resourceroom.net
http://bicyclecu.blogspot.com
>>> <awayman1 at kirksville.k12.mo.us> 02/23/10 1:24 AM >>>
Thank you for the ideas on manipulatives. I am interested also in
the Making Math Real Curriculum. I agree with you about using
concrete to abstract concepts. I would like some examples of the
intermediate levels (semi-concrete and semi-abstract). I also agree
that there are some things (such as multiplication facts) that need
to become automatic. I think that UNDERSTANDING (conceptualizing)
math ideas needs to be the basis for learning to manipulate numbers.
Rote memorization of processes does not give a solid foundation for
building "fluency" in numeracy.
---- Original Message ----
From: mcarro at lmi.net
To: numeracy at nifl.gov
Subject: [Numeracy 206] Re: manipulatives
Date: Mon, 22 Feb 2010 10:56:46 -0800
>Manipulative materials, I think have most value in the early
>grades.... when developing early concepts of place value, addition
>and
>subtraction, etc. I think the 'scanty understanding" of place value
>
>is at the root of many problems adults have with math. Most
>elementary math books, and certainly adult books, seem to devote mere
>
>paragraphs to the topic, although schools seem to be doing better at
>
>this more recently. Usually, I spend a considerable amount of time
>making sure students (even adults) understand this fundamental
>concept (place value) which is needed throughout the math curriculum.
>
>Decimals, exponential notation, powers of ten, etc. are concepts that
>
>build on place value. I use some base ten blocks, stories, and
>things
>like "straw bundles" , toooth picks, money, etc. to establish the
>hook
>for the basic concept. I spend considerable time demonstrating how
>the "decimal system" works, with 10 digits, 0-9 being the only
>symbols
>use to represent quantities. Once we have gone through the decimal
>system, I challenge the students to create values in the binary
>system, using only 2 digits, 0 and 1, and having them generate the
>values according to the same pattern. They usually are successful
>doing so, and I know they get the idea. When we get to "algebra", I
>
>review the basic concrete ideas (using concrete manipulative
>materials
>if necessary) to review what underlies the new learning, and then
>make
>the leap into the abstract. I do this each and every time we begin
>a
>topic where the prior knowledge required can be demonstrated with
>manipulative materials or real life examples.... the idea is to
>proceed from what is known/familiar to what is unknown/unfamiliar.
>When introducing equations in algebra, I start with the expamples of
>
>"real life" concepts , such as area,, perimeter, volume, etc. as
>examples of algebraic equations that serve as "formulas" that apply
>to
>certain types of problems. We can "solve" for any of the missing
>components of the equation. I also talk about "pi" by wrapping a
>string ( equal in length to the diameter) around many different size
>
>circles, such a plates, cups, etc.... noticing that on each occasion,
>
>it is "a little more than 3 times the diameter of the circle, no
>matter its size". I do a lot of "story telling" about the "geeky
>Greeks" and what they noticed about natural occurrences that still
>holds in math and upon which even today's computer scientists still
>build. ( Of course, it was more than the Greeks.... but it cuts to
>the chase without taking up too much diversionary time... the "geek"
>
>part is for an "emotional zap" and may not work with all groups / I
>follow it with: "I am proud to be a geek". You need to know your
>group).
>
>
>For those interested in the Making Math Real Curriculum, the
>curriculum uses manipulative materials extensively in the early
>stages
>of math, (moving from concrete, to semi-concrete, to semi-abstract
>to
>abstract) but by Pre-Algebra, holds that the concepts need to be
>well established and manipulated mentally. The bridge needs to be
>made from concrete to abstract, and some things to "automaticity"
>before algebra.
>
>
>Maureen Carro, MS, ET
>Academic Learning Solutions
>Alamo, CA
>mcarro at lmi.net
>
>
>
>On Feb 19, 2010, at 10:34 AM, Jacqueline Kiefer wrote:
>
>> Susan, I too am interested in what you learn from Making Math Real.
>>
>> I understand what you mean about manipulatives becoming one more
>> layer of confusion. When I used algebra tiles to explain algebra,
>I
>> BOMBED BIG TIME.
>> However, when I used them to explain integers, there were light
>> bulbs coming on all over the classroom. A deck of cards and a game
>
>> of Integer Showdown is also great.
>> Jackie
>>
>> From: numeracy-bounces at nifl.gov [mailto:numeracy-bounces at nifl.gov]
>
>> On Behalf Of Leslie Hunten
>> Sent: Friday, February 19, 2010 7:39 AM
>> To: The Math and Numeracy Discussion List
>> Subject: [Numeracy 198] Re: manipulatives
>>
>> Susan, please do share what you learn from Making Math Real!
>>
>> Leslie
>>
>>
>> On Thu, Feb 18, 2010 at 3:00 PM, Susan Jones <SUJones at parkland.edu>
>
>> wrote:
>> Nobody uses manipulatives here, which I think is a shame.
>>
>> Hard to make the bridge from concrete to abstract without the
>> concrete, though we sometimes can anyway.
>>
>> We do use some visuals -- but not much of that, either.
>>
>> I wish I could say that the folks working with the more basic than
>
>> pre-algebra did, but I'm 99 44/100% sure they don't either. We
>> explain and wish and wonder why students don't connect math to the
>
>> real world...
>>
>> That said, there's not a lot of evidence (either formal research or
>
>> anecdotal) to say manipulatives help... I've seen them be one more
>
>> layer of confusion, if the connection between the concrete to the
>> symbols isn't solidified. One reason I'm really looking forward to
>
>> the Making Math Real overview is that I have a feeling this does
>> that (or at least makes a good effort;)) and would give me the
>tools
>> to try.
>>
>>
>>
>> Susan Jones
>> Academic Development Specialist
>> Center for Academic Success
>> Parkland College
>> Champaign, IL 61821
>> 217-353-2056
>> sujones at parkland.edu
>> Webmastress,
>> http://www.resourceroom.net
>> http://bicyclecu.blogspot.com
>>
>>
>> >>> Jaye Luke <flipfloprun at gmail.com> 2/18/2010 11:52 AM >>>
>> I haven't taught a math class for adult learners...yet:) But I am
>
>> curious
>> 1- Are you using manipulatives?
>> 2- If you are using manipulatives are they specifically for math
>> (cuisenaire
>> rods) or more generalizable (tokens/tiles)?
>> 3- Do you think the manipulatives are beneficial and why?
>>
>>
>> Cheers
>> jaye
>>
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>>
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>
>
>
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