I started teaching from the TIAN materials (fractions, decimals and percents book) and they're wonderful.  One of my students said the visual number line and the "half of a half" concept for understanding one-fourth of a number has given her a new understanding of fractions.  She's very bright in reading and writing but has always struggled with math.  Others have also "religiously" used that number line to understand the concept of breaking down a whole number into fractions.  I taught from the data and graph and algebra book last year.   I heard similar comments:  "They never taught us this way when I was in school"!!

Mari John
Kansas

-----Original Message-----
From: specialtopics-bounces at nifl.gov [mailto:specialtopics-bounces at nifl.gov] On Behalf Of specialtopics-request at nifl.gov
Sent: Tuesday, September 18, 2007 11:00 AM
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Subject: SpecialTopics Digest, Vol 14, Issue 30

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Today's Topics:

   1. [SpecialTopics 664] Re: Components of Numeracy/Manipulatives
      (Lynda Ginsburg)
   2. [SpecialTopics 665]  Components of Numeracy (David J. Rosen)
   3. [SpecialTopics 666] Re: Numeracy-Children vs. Adult
      (Lynda Ginsburg)
   4. [SpecialTopics 667] Re: International Discussion Ends     and
      Numeracy  Discussion Begins (Mary Jane Schmitt)


----------------------------------------------------------------------

Message: 1
Date: Mon, 17 Sep 2007 20:33:26 -0400 (EDT)
From: "Lynda Ginsburg" <ginsburg at rci.rutgers.edu>
Subject: [SpecialTopics 664] Re: Components of Numeracy/Manipulatives
To: specialtopics at nifl.gov
Message-ID:
        <1155.68.84.41.133.1190075606.squirrel at webmail.rci.rutgers.edu>
Content-Type: text/plain;charset=iso-8859-1

Hi all,

I have used measuring tools, particularly rulers and tape measures, as
"concrete manipulatives" to help learners "see" fractions and decimals
(cm. rulers or tapes). The topic is ostensibly measurement, which
virtually every adult has found useful and worthwhile, and the need for
fractions or decimals is quite apparent. Equivalent fractions make sense
on a ruler, as do adding and subtracting fractions.

It has also been fun to have groups of learners design their ideal house
or apartment, draw it on graph paper to scale, and then make scale models
with cardboard. Lots of proportional reasoning, measurement, etc. People
have even built small cardboard furniture and brought in toy cars for the
driveway or street. Problem-based learning, collaboration, need to
communicate mathematically, and lots of math issues arise.


Lynda

Mary Wooten wrote:

> Manipulatives--

>

> I'm so glad someone is interested in manipulatives.  We actively use

> manipulatives in all our ABE/GED math classes to illustrate concrete and

> abstract concepts, concretely for students.  It is a way of illustrating

> a concept.  We have a wonderful response from students, in general.

>

> We use them both with small groups and individually.

>

> The key to acceptance with adults is modeling use of them and having

> them out and available in the classroom as a rule of thumb, not an

> exception.  We like the rolling plastic drawers to store them in so we

> can pull them around the room.

>

> We have obtained most of our manipulatives through the Summit Learning

> Company.  We have quite a few but ones we use most often are:

> Multiplication Wraps- great for abstracting times tables, Clock to show

> elapsed time,  large cardboard Thermometer - for positive and negative

> numbers; fraction tiles, dice, Pizza game- great for fractions with a

> group, decimal/fraction/ percent dominoes.

>

> Teachers do need to be trained on these and encouraged to use them.

>

>

>

>

>

>

>

> Mary S. Wooten  M.Ed.

>

> GED Coordinator

>

> Adult Basic Education

>

> Santa Fe Community College

>

> Santa Fe, NM 87508

>

> Phone  (505) 428-1329

>

>

>

> -----Original Message-----

> From: specialtopics-bounces at nifl.gov

> [mailto:specialtopics-bounces at nifl.gov] On Behalf Of Kathie Daviau

> Sent: Sunday, September 16, 2007 4:49 PM

> To: specialtopics at nifl.gov

> Subject: [SpecialTopics 652] Re: Components of Numeracy

>

>

>

> I am interested in the use of manipulatives in the adult ed math

> classroom.  How are manipulatives used?  How do you introduce

> manipulatives to adults?  Do you use manipulatives in an individualized

> setting?  What are your favorite manipulatives?

> Thanks,

> Kathie

> Billings, Montana

>

>

> -----Original Message-----

> From: specialtopics-bounces at nifl.gov on behalf of David J. Rosen

> Sent: Sun 9/16/2007 5:44 AM

> To: specialtopics at nifl.gov

> Subject: [SpecialTopics 649]  Components of Numeracy

>

> Colleagues,

>

> Some of you have emailed me that you have been eagerly awaiting the

> discussion on the components of numeracy study.

>

> To get full benefit from the discussion this week you will need to

> prepare.  It won't take long.  You'll find links to the readings at:

>

> http://www.nifl.gov/lincs/discussions/specialtopics/07numeracy.html

>

> or the short Web address:

>

> http://tinyurl.com/yvo6hf

>

>

> So far I have not received any questions from subscribers.  Please

> read the preparation documents and then e-malil your questions to me

> or to the list today.

>

> Thanks,

>

> David J. Rosen

> Special Topics Discussion Moderator

> djrosen at comcast.net

>

>

>

>

>

> -------------------------------

> National Institute for Literacy

> Special Topics mailing list

> SpecialTopics at nifl.gov

> To unsubscribe or change your subscription settings, please go to

> http://www.nifl.gov/mailman/listinfo/SpecialTopics

> Email delivered to ginsburg at rci.rutgers.edu



--
Lynda Ginsburg
Senior Research Associate, MetroMath
Rutgers University
tel: 732-445-1409


------------------------------

Message: 2
Date: Mon, 17 Sep 2007 22:12:42 -0400
From: "David J. Rosen" <djrosen at comcast.net>
Subject: [SpecialTopics 665]  Components of Numeracy
To: specialtopics at nifl.gov
Message-ID: <9EF504A9-BB0A-4873-A4D9-74B1EBE8D3FB at comcast.net>
Content-Type: text/plain; charset=WINDOWS-1252; delsp=yes;
        format=flowed

Colleagues,

I do hope our guest authors might address the three questions I posed
yesterday, and here are  three more:

4. One difference, that you point out in the study on page 15,
between how children and adults learn numeracy is ?The inclusion of
societal contexts in adult-focused frameworks stands in marked
contrast to the exclusion of such contexts in school-based
frameworks.?  Are there other differences?

5. I have been looking at some numeracy teaching/teacher training
videos, for example:

http://mlots.org (?Ratio and Proportion?)
http://www.teachersnetwork.org/media/index.cfm (?Real Math?)

Most of the videos I have found are focused on children; very few are
focused on adults; but the approaches are similar: getting teachers
comfortable in the language and use of numeracy thinking, organizing
classrooms so students are actively engaged in discovery of numeracy
concepts, and helping learners make those concepts and related skills
their own. What do you see as the similarities between how children
and adults ideally should learn numeracy?

6. On pages 16-17 of the study you describe a continuum of
contextualization and give examples of two very different word
problem learning activities, the opposite ends of the spectrum. The
first is a decontextualized opportunity to practice some recently-
taught skills ? an activity that is ?realistic?, not ?real?. The
second grows from a real-life context where students do not have
clues, other that the context of the problem itself, for what
numeracy is needed. I wonder if you have other examples along the
continuum that you could share.

David J. Rosen
Special Topics Discussion Moderator
djrosen at comcast.net




------------------------------

Message: 3
Date: Tue, 18 Sep 2007 00:19:38 -0400 (EDT)
From: "Lynda Ginsburg" <ginsburg at rci.rutgers.edu>
Subject: [SpecialTopics 666] Re: Numeracy-Children vs. Adult
To: specialtopics at nifl.gov
Message-ID:
        <1381.68.84.41.133.1190089178.squirrel at webmail.rci.rutgers.edu>
Content-Type: text/plain;charset=iso-8859-1

Hi David et al,

I wanted to comment on some of the issues you raised about the differences
between children's and adults' experiences learning math/numeracy. To me,
one of the primary differences is the whole idea of learning math vs.
learning numeracy.

In school, children are generally learning math so that they can go on to
and be successful in higher levels of math. Children are full time
students; that's pretty much what they do. While there is an assumption
that the math children learn will be available for other, everyday
purposes, meeting those purposes (usually expected to be in the future) is
not generally the goal of school.  Thus, our statement about the exclusion
of societal contexts in school math. I know that's a gross generalization,
but I think it's often true. Just think about "word problems" that have
sometimes been promoted as "real world applications." Word problems are
virtually always contrived, pretty formulaic, and function as
computational examples with words, and usually aren't very
realistic/meaningful to the learner (When was the last time a teenager
really needed to figure out when the two trains would meet? For that
matter, when was the last time you needed to figure that out?). Most of us
noticed pretty quickly that the word problems following the pages on
multiplying fractions could all be solved by multiplying the fractions
between the words.

On the other hand, we have been thinking of "numeracy" as being integrally
connected with real world activity, continuously crossing the
school/everyday life chasm. Adult learners have one foot in the classroom
and the other in the outside world. They bring that world into the
classroom with their experiences, and they should be able to bring their
classroom-based learning out to their real lives. Tasks and problems in
real life are messy, call for judgements, estimations, and assumptions.
Math becomes a tool, not an end in itself.

Without getting into the whole "math wars" thing, the K-12 math reform
movement has tried to shift the emphasis of school math learning from a
focus on acquiring and mastering decontextualized computation skills to a
focus on developing conceptual understanding. To me, this is a shift
towards my vision of numeracy.

Getting back to your question about the teacher training videos that show
children exploring, talking about math concepts, struggling with making
meaning of the math -- I agree these are similar to what I would like to
see in adult ed classes. The few existing videos of adult ed math
instruction are also in this vein (from the TIAN/EMPower projects, from
NCAL's PDK, others?) Generally all these videos are from reform classes,
often from National Science Foundation curriculum projects. I think these
video tapes have been created from the need for teachers (K-12 & adult ed)
to be able to see what a different kind of instruction might look like,
especially since most teachers didn't experience this kind of schooling
themselves. [I know that this was the rationale behind "Captured Wisdom"
which focused on using technology in the classroom].

That said, I am sure there are also some videos out there promoting rote
learning of math facts, but we all already know what that looks like.

Sorry to be rambling,
Lynda


David J. Rosen wrote:

> Colleagues,

>

> I do hope our guest authors might address the three questions I posed

> yesterday, and here are  three more:

>

> 4. One difference, that you point out in the study on page 15,

> between how children and adults learn numeracy is ?The inclusion of

> societal contexts in adult-focused frameworks stands in marked

> contrast to the exclusion of such contexts in school-based

> frameworks.?  Are there other differences?

>

> 5. I have been looking at some numeracy teaching/teacher training

> videos, for example:

>

> http://mlots.org (?Ratio and Proportion?)

> http://www.teachersnetwork.org/media/index.cfm (?Real Math?)

>

> Most of the videos I have found are focused on children; very few are

> focused on adults; but the approaches are similar: getting teachers

> comfortable in the language and use of numeracy thinking, organizing

> classrooms so students are actively engaged in discovery of numeracy

> concepts, and helping learners make those concepts and related skills

> their own. What do you see as the similarities between how children

> and adults ideally should learn numeracy?

>

> 6. On pages 16-17 of the study you describe a continuum of

> contextualization and give examples of two very different word

> problem learning activities, the opposite ends of the spectrum. The

> first is a decontextualized opportunity to practice some recently-

> taught skills ? an activity that is ?realistic?, not ?real?. The

> second grows from a real-life context where students do not have

> clues, other that the context of the problem itself, for what

> numeracy is needed. I wonder if you have other examples along the

> continuum that you could share.

>

> David J. Rosen

> Special Topics Discussion Moderator

> djrosen at comcast.net

>

>

> -------------------------------

> National Institute for Literacy

> Special Topics mailing list

> SpecialTopics at nifl.gov

> To unsubscribe or change your subscription settings, please go to

> http://www.nifl.gov/mailman/listinfo/SpecialTopics

> Email delivered to ginsburg at rci.rutgers.edu

>



--
Lynda Ginsburg
Senior Research Associate, MetroMath
Rutgers University
tel: 732-445-1409


------------------------------

Message: 4
Date: Tue, 18 Sep 2007 08:38:23 -0400
From: Mary Jane Schmitt <mary_jane_schmitt at terc.edu>
Subject: [SpecialTopics 667] Re: International Discussion Ends  and
        Numeracy        Discussion Begins
To: specialtopics at nifl.gov
Message-ID:
        <OFABA13AAA.8B1914E3-ON8525735A.003D7D31-8525735A.00456EAD at terc.edu>
Content-Type: text/plain; charset="utf-8"

Hi Louise

Yes, current versions of spell-check reject the word numeracy, even though
its usage is becoming more common. When we used it in our papers, we
generally meant adult numeracy. Early childhood numeracy* is different
because numeracy does depend upon context - and age can be thought of as a
contextual  and a cognitive factor. The math appropriate for a 3-year old
to learn, understand, and be able to do is different for an adult. On the
other hand, all age groups are included when being numerate is defined as
having `the ability and inclination to use mathematics effectively in our
lives--at home, at work, and in the community' (New Zealand Ministry of
Education, 2001).

As far as far as the relationship among mathematics, literacy, and
numeracy, some  use a Venn diagram to illustrate numeracy as the
intersection of mathematics and literacy - that might be a better analogy
than a bridge between math and literacy. In fact, we see the term
"mathematical literacy" to be synonymous with numeracy.

* An aside, as we meant to focus on adult numeracy during this discussion:
 There is a rich body of research on early numeracy development, even in
infants. I am fascinated by studies that have shown 6-month olds to be
aware of subtraction errors (as evidenced by extended gaze), or the idea
that babies can subitize, (recognize small quantities without counting) .
Australia and New Zealand have early numeracy educational initiatives that
are very interesting. I think Dave Tout and I stand corrected on the K-12
designation for "school math before reaching adulthood."  Even though many
of the documents we referred to focused on K-12, we could have included
pre-K.

Take care,
Mary Jane


Mary Jane Schmitt
TERC
2067 Massachusetts Avenue
Cambridge, MA  02140
mary_jane_schmitt at terc.edu
www.adultnumeracy at terc.edu




Louise Wiener <lwiener at llfinc.org>
Sent by: specialtopics-bounces at nifl.gov
09/17/07 10:02 PM
Please respond to
specialtopics at nifl.gov


To
<specialtopics at nifl.gov>
cc

Subject
[SpecialTopics 663] Re: International Discussion Ends and       Numeracy
Discussion Begins






Dear David,

I found the Tout and Schmitt chapter particularly invigorating and
challenging and hope Dr. Schmitt might comment on two thoughts for
starters.

I was surprised at the frequent reference to K-12 with almost no reference
to pre-K.  I first became familiar with the term numeracy in the context
of Head Start standards. Is there research on numeracy in the early
childhood field ? or has the name alone been adopted?

I was struck, too, by the reference to numeracy as the bridge between
mathematics and the real world. I see it  equally as the bridge between
mathematics and literacy because  it captures (builds on?) the language
and concepts of math as contrasted with the pure computation of math.

You will note that at least my spell-check rejects ?numeracy? as a valid
word.  Perhaps we should start by lobbying there!

Thank you, Louise
--
Louise W. Wiener, Chairman of the Board
    Learning and Leadership in Families
    2701 12th Street NE
    Washington, DC 20018

    Mobile Phone: 301-213-6516
    Office Phone: 202-243-7783
    Website: www.LLFinc.org
    Email: lwiener at LLFinc.org

    United Way / CFC # 8981


  On 9/15/07 8:10 AM, "David J. Rosen" <djrosen at comcast.net> wrote:

Special Topics Colleagues,

I want to thank our guests for the topic:  What International Literacy
Programs Offer Programs in the U.S. : Brenda Bell, Pamela Civins, Dr. John
Comings, Barbara Garner, Dr. Erik Jacobson, Juliet Merrifield, and Dr.
Ujwala Samant. I know we have only scratched the surfaces of several
issues here in this one short week, but the discussion has been
tantalizing.  I also want to thank Oxfam for making the book Developing
Adult Literacy: Approaches to planning, implementing and delivering
literacy initiatives by Juliet Merrifield Juliet McCaffrey, and Juliet
Millican available by download free for this discussion. It will be
available in hard copy on September 30, 2007.

This marks the end of the international literacy discussion, for now at
least.

On Monday we will begin a new discussion on The Components of Numeracy
 with Mary Jane Schmitt, Myrna Manly and Dr. Lynda Ginsburg, an occasional
paper published by the National Center for the Study of Adult Learning
and Literacy.

For more information, and a short list of readings to prepare for the
discussion please go to:

http://www.nifl.gov/lincs/discussions/specialtopics/07numeracy.html

or the short Web address:

http://tinyurl.com/yvo6hf

Please e-mail your questions for our numeracy guest experts
to specialtopics at nifl.gov

Your colleagues who may wish to join this discussion can subscribe
by going to:

http://www.nifl.gov/mailman/listinfo/specialtopics

After they complete a simple registration form (30 seconds) they
will receive an email asking them to confirm that they wish to
subscribe. They should Immediately reply to the email to complete their
subscription. After the discussion ends they can unsubscribe from the same
Web address, or stay on for the next discussion.

David J. Rosen
Special Topics Discussion Moderator
djrosen at comcast.net





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