[Numeracy 210] Re: manipulatives

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Maureen Carro mcarro at lmi.net
Tue Feb 23 00:16:45 EST 2010


True enough!


Maureen Carro, MS, ET
Academic Learning Solutions
Alamo, CA
mcarro at lmi.net



On Feb 22, 2010, at 1:04 PM, Carolyn Dickinson wrote:


> Maureen,

>

> In the interest of creating less antagonism between the "Western"

> world and the "Muslim" world, you might also mention that a very

> large part of algebra (including its name) came from the Arabic world.

>

> Carolyn

>

> On Mon, Feb 22, 2010 at 11:56 AM, Maureen Carro <mcarro at lmi.net>

> wrote:

> 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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