Adult Numeracy Network

ANN Numeracy Discussion List:
“Numeracy and Paolo Freire ”

Digest of Messages from the Numeracy List - Topic - Paolo Freire (Numeracy@world.std.com)
Date: Mon, 16 Oct 1995 20:19:38 -0300
To: numeracy@world.std.com
From: adias@indiana.edu (Ana Lucia Braz Dias)
Subject: Paulo Freire

Hi. My name is Ana Dias and I am new to the list.

At the moment I am starting my dissertation study. It is going to be about using Paulo Freire's theoretical framework in the context of adult numeracy. The study is going to be done with participants of a literacy program in Brazil.

As early as in this introductory message, I would like to ask you if you know of anybody else - besides Marilyn Frankenstein - who has been applying Paulo Freire's ideas to math education.

Thank you!

Ana.

_________________

Date: Tue, 17 Oct 1995 13:48:20 +1000
To: numeracy@world.std.com
From: R.Zevenbergen@eda.gu.edu.au (Robyn Zevenbergen EDA)
Subject: Re: Paulo Freire

Dear Ana,
I am "observer" on this list. I work in teacher (mathematics) education so while I work with adults and numeracy, it is not in the sense of most communicators on the list.

I use Freire's work with my teachers - both at the undergraduate and post graduate level. My students are lead through the tenets of criticalmathematics over two semesters and I hope will exit from the course as much better teachers of a socially-just mathematics.

If you would like to talk more, please feel free to contact me. Good luck with your project,

Robyn
Robyn Zevenbergen _--_|\
Faculty of Education and the Arts / x
Griffith University - Gold Coast \_.--. /
PMB 50, Gold Coast Mail Centre, v
Bundall, Queensland, 4217, Australia
Ph: 61 75 94 8632
Fax: 61 75 94 8634
_________________

Date: Tue, 17 Oct 1995 15:32:02 -0400 (EDT)
From: Lynne Mikuliak
To: Ana Lucia Braz Dias
Cc: numeracy@world.std.com
Subject: Re: Paulo Freire

Ana,
Welcome to Numeracy. Your question about Freire made me realize that I have often heard of him and his ideas but have had no formal instruction in his theories. Over the years my supervisor has mentioned him in staff development sessions and shared some of the theories so it is possible that I DO incorporate some ideas without knowing their exact origin. Formats such as e-mail allow such broad communication that one may adopt an idea or strategy without knowing who originated it. I would be interested in the results of your study. Good luck with it!
Lynne Mikuliak

Community Women's Education Project - Phila. Pa.
_________________

Date: Tue, 17 Oct 95 17:32 MDT
To: numeracy@world.std.com
From: cfran@micron.net
Subject: Re: Paulo Freire

>Ana,
I am interested in how you are thinking about using Freire's ideas. I teach an adult critical thinking/math course for un-traditional learners and use a critical approach to the basic ideas and perspectives of mathematics. I see mathematics as the ultimate in instrumental reason (that is..reason in the service of reason as opposed to (for example..context based community problem solving)).

It seems to me that if we make explicit the alienating powers of the processes of abstraction and present the acquisition of this skill as a choice we are being morally responsible. I think it is also necessary, however, to provide a long term context for the development of this skill as well as opportunities and methods for the preservation of community as the "language of power" begins to do its work and transform the consciousness of the learner.

What sort of practical methods do you use for teaching math? I use a concrete ...representational...abstract...model as an undergirding for the entire process. Then I introduce grouping and classifying with concrete materials. After that we generally progress rapidly to developing addition/subtraction and multiplication/division algorithms from this perspective. At that point it is relatively easy to start using pictures and symbols to shorten the process.

The real problem, however, is proving the long term context for the development of these skills. It seems crazy to expect that a 6 week or 6 month course will address the continuing need to negotiate one's marginalization with the greater community.

Chris Francovich

_________________

Date: Tue, 17 Oct 95 23:42:49 -0400 (EDT)
From: tomc@web.apc.org (Tom Ciancone)
To: numeracy@world.std.com
Subject: Re: Paulo Freire
Cc: tomc@web.apc.org

Ana,

I work in literacy and ESL programs in Toronto. Although I have an understanding of Paolo Freire's methods and philosophy, I cannot say that I deliberately or consciously follow them in my numeracy work. I wish I did.

I want to tell you that many years ago I saw basic math materials in Spanish that were developed by VIMEDA (Vice-Ministerio de Educacion de los Adultos) under the former Sandanista government in Nicaragua. If you can find these materials, they are a fine example of Freirian methodology in an agricultural and rural milieu.

Unfortunately, there no longer exists a publicly-supported adult education program in Nicaragua. It was one of the first casualties of the UNO government that that came to power in 1990.

Tom Ciancone
Toronto, Canada
_________________

Date: Wed, 18 Oct 1995 00:13:05 -0600 (MDT)
From: "M. Adele Megann"
To: numeracy@world.std.com
Cc: numeracy@world.std.com
Subject: Re: Paulo Freire

Ana,

What a good idea! I studied Freire years ago (applied to liturgy, if you can believe it) but have not thought of him in connection to math.

I emphasize in my teaching that math is a language, a cultural thing. One of the ways I do that is to look at the beginning of each year at various number systems, for example, Roman, Greek, tallying, Egyptian, base six. I know that's supposed to be very abstract, but my mentally handicapped students get it.

When we look at how our base-ten-place-value system emerged, I tell them it all starts in the fingers. We do a lot of counting on each other fingers (some are more valuable than others!). My punch line is to ask them what might numbers be like if people had three fingers on each hand. They usually look at their fingers, look up and someone says, "There would only be six digits." I shout in triumph. The lie that math is abstract is such a disservice to our students. Math is fingers.

Anyway, good luck. You've obviously struck a chord.

Adele Megann
Transitional Vocational Program
Mount Royal College
--------------------------/\__/\--------------------------------
Adele Megann & Linus_____; o o ; mamegann@freenet.calgary.ab.ca
Alberta, Canada _/`_____ =^= / Newfoundlander Abroad
---------------<_______>__m_m_>---------------------------------
________________
Date: Wed, 18 Oct 1995 11:21:21 -0500
To: numeracy@world.std.com
From: bsbell@utkux.utcc.utk.edu (Brenda Bell)
Subject: Re: Paulo Freire

Hi. My name is Brenda Bell and I work at the Center for Literacy Studies at the University of Tennessee. I've been a silent participant in this list, passing on to Tennessee practitioners some of the ideas and suggestions, and generally keeping up at a distance. I'm responding to the interest in the ideas of Paul Freire, and to Lynne M's comment that she has heard of his work. May I suggest a book which I think is a good introduction: We Make the Road by Walking: Conversations on Education and Social Change - Myles Horton and Paulo Freire. As one of the editors of this book, I've been told that it is one of the most accessible introductions to Freire's ideas and experiences. It was published by Temple University Press, 1990. See especially the chapter on Ideas, section "Is it possible just to teach biology?" - for a discussion of the political context of education.

Brenda Bell
CLS - UTK
600 Henley STreet, Suite 312
Knoxville, TN 37996
423-974-4109
bsbell@utkux.utk.edu
>
Brenda Bell
Center for Literacy Studies
_________________

Date: Thu, 19 Oct 1995 13:28:47 -0300
To:
From: adias@indiana.edu (Ana Lucia Braz Dias)
Subject: Re: Paulo Freire

Tom,
Thank you SO much for the reference you gave me. I will try very hard to get access to those materials, because, as you probably know, there is not a lot done in math education on these lines.

I am really glad the network could help me reach you, because I could not find this reference through computer data bases or any other sources.

Thank you!
Ana.

>Ana,
>
>I work in literacy and ESL programs in Toronto. Although I have an
>understanding of Paolo Freire's methods and philosophy, I cannot say that
>I deliberately or consciously follow them in my numeracy work. I wish I
>did.
>
>I want to tell you that many years ago I saw basic math materials in
>Spanish that were developed by VIMEDA (Vice-Ministerio de Educacion de
>los Adultos) under the former Sandanista government in Nicaragua. If you
>can find these materials, they are a fine example of Freirian methodology
>in an agricultural and rural milieu.
>
>Unfortunately, there no longer exists a publicly-supported adult
>education program in Nicaragua. It was one of the first casualties of the
>UNO government that that came to power in 1990.
>
>Tom Ciancone
>Toronto, Canada
_________________

To:
From: adias@indiana.edu (Ana Lucia Braz Dias)
Subject: Re: Paulo Freire

Adele wrote:

>The lie that math is
>abstract is such a disservice to our students.

It sure is. And it is a "service" to the elites that try to hold mathematical knowledge only for them. Check this quote by Apple (in the Journal for Research in Mathematics Education, 23(5)):

"Like all forms of knowing, mathematical knowing is of course partly aesthetic. Yet, in industrialized nations, it gains its high status because of its socioeconomic utility as a form of what I have called technical/administrative knowledge (...). The accumulation and control of technical/administrative knowledge by a limited group of people is essential in our science-based industries and for the production of material and weapons systems for the Department of Defense."

The article goes further into this subject.

Ana.

_________________

Date: Thu, 19 Oct 1995 13:29:02 -0300
To:
From: adias@indiana.edu (Ana Lucia Braz Dias)
Subject: Re: Paulo Freire

Subject: Re: Paulo Freire

Chris wrote:
>>Ana,
>I am interested in how you are thinking about using Freire's ideas.(...)
>It seems to me that if we make explicit the alienating powers of the
>processes of abstraction and present the acquisition of this skill as a
>choice we are being morally responsible.(...)
>
>What sort of practical methods do you use for teaching math? (...) It seems crazy to expect that a 6 week or 6
>month course will address the continuing need to negotiate one's
>marginalization with the greater community.
>
>Chris Francovich
>
>
>

I totally agree with your approach (making explicit alienating powers and presenting acquisition of math skills as a choice). Now, how do I do it? Right now I still don't do it. So let me explain what I am doing and plan to do:

I was in Brazil this summer, and got involved with a non-formal literacy program that is based on volunteer work and is happening in many communities throught the country. This program uses Freire's ideas to teach reading and writing. However, volunteer teachers told me that they have been having difficulty translating Freire's ideas to math education. They just don't have resources where to get ideas from, and end up teaching in a way they are not satisfied with. Knowing I am a doctoral student in math education, they asked me if I could help them improve their teaching. I told them about Marilyn Frankenstein's work, and they said they had no idea somebody was doing such a work (applying Freire to math education), and that was just the kind of help they needed. So we decided to collaborate in a "participatory action research" to try to improve their practice. And this is going to be my dissertation study.

What these teachers have been doing at the moment is actually very good, but since they are so committed with Freire's ideas, which I also am, they (and I) thought it was not enough.

What they do is: they encourage students to verbalize to the group in class their own ways of solving a particular problem or computation. They emphasize to students that their way of solving problems and computing is (or should be) as legitimate as academic methods. They progress to registering these non-academic processes (remember they are also learning how to write). Finally, the teacher presents the academic method or algorithm as one more way to do that computation, but emphasizes that students should choose which one they want to use. It is a way to dismistify academic mathematics, but at the same time, teachers don't deny this knowledge to the students.

Teachers have been considering this approach unsatisfactory for a number of reasons, but specially for not been necessarily linked to a context relevant to students socio-political "liberation", as are their reading and writing classes. This is also why they liked Marilyn Frankenstein's work: because she always presents math linked to political situations. However, Frankenstein's work is not the final answer, specially because each situation provides a different context, and we cannot just "follow her recipe" and do the same in Brazil. Teachers there will have to adapt and create their own solutions, maybe inspired by her work and that of others. This is why I wanted to know about more people who have been "translating" Freire into math teaching and learning.

As for the time constraints, I agree that it is going to be difficult to develop critical awareness and empower students in 6 months, but we will try to do the best with the time we have, and fight for the opportunity to continue the work (I am sure this is what you have been doing too).

Thank you, and sorry for the lengthy message.

Ana.

_________________

Date: Thu, 19 Oct 1995 13:29:08 -0300
To:
From: adias@indiana.edu (Ana Lucia Braz Dias)
Subject: reply to Robyn Zevenbergen

>Dear Ana,
>I am "observer" on this list. I work in teacher (mathematics) education
> so while I work with adults and numeracy, it is not in the sense of most
>communicators on the list.
>
>I use Freire's work with my teachers - both at the undergraduate and post
>graduate level. My students are lead through the tenets of
>criticalmathematics over two semesters and I hope will exit from the
> course as much better teachers of a socially-just mathematics.
>
>If you would like to talk more, please feel free to contact me.

Dear Robyn,
I would very much like to know more about your work. How do you think we could do that? Can you give me a short description of the course? Or do you have materials I could read?

I don't want to be inconvenient, though, because I know you are probably very busy. But I would appreciate your help very much. It sounds that like what you have been doing is in complete accordance with what I will try to do.

Thank you!

Ana.

_________________

Date: Fri, 20 Oct 95 07:59 MDT
To: numeracy@world.std.com
From: cfran@micron.net
Subject: Re: Paulo Freire

> Ana wrote:
>>>>
>
> .... volunteer teachers told me that they have been having difficulty translating Freire's ideas to math education.
>
> What they do is: they encourage students to verbalize to the group
>in class their own ways of solving a particular problem or computation.
>They emphasize to students that their way of solving problems and computing
>is (or should be) as legitimate as academic methods. They progress to
>registering these non-academic processes (remember they are also learning
>how to write). Finally, the teacher presents the academic method or
>algorithm as one more way to do that computation, but emphasizes that
>students should choose which one they want to use. It is a way to
>dismistify academic mathematics, but at the same time, teachers don't deny
>this knowledge to the students.

Chris writes:

The problem that I have with teaching math comes way before the process of learning algorithms. First I think that the "real world" (as engaged by poor and "uneducated" people (including American students)) presents us with few authentic opportunities for using formal or informal algorithms. When we ask a student to solve a problem in their own way I think it sets the student up for failure at worst and a tolerance for "odious" comparisons at best. The "academic method" is more than a method. It is a process by which the subject is disembedded from the object (individual and community). Most students know what the agenda is. They are being socialized to a system that exerts inexorable pressure on them and their socialization is a way to cope with it. Those that adapt the quickest and most accurately win the prize.

Solving life problems is rarely a mathematical adventure. My point is that the process of abstracting common sense principles of number and amount, position, and group to the formal "set aside" system of mathematics is in itself a transformative leap into a new sort of consciousness. I am thinking of Piaget and Vygotsky both in their treatment of scientific thinking. Work with the so called primitive illustrates that schooling conditions us to believe that our propositional structures are reason itself. A question here is whether or not learning how to read is in the same ball park. I think that it probably is.

I guess my position implies a bifurcated system of teaching. On the one hand we eat our food, laugh, and tell stories. On the other hand we get very serious and learn to trade in abstractions and talk at levels of abstraction that make us dizzy. Some people seem to have an affinity for this. Others find it always strange and unreal. Perhaps formalizing the transition from one kind of discourse to the next is what is needed. Whatever the method I think all concerned should know what the change in modes means. The teacher..the community..try to help all concerned find a place in the structure that exists. I think that mixing logic, categorization structures, etc. with the food and story telling is hard on my heart and digestion.

Chris Francovich

______________

Date: Fri, 20 Oct 95 08:11 MDT
To: numeracy@world.std.com
From: cfran@micron.net
Subject: not abstract!
Sender: numeracy-approval@world.std.com

I have gleaned from fragments (I am new to the list) that it is held that mathematics is not abstract. I can't understand or believe this (perhaps I would believe it if I understood it). Could someone explain? How do we define abstract? Is not language abstract? If language is abstract then the question is how abstract? I hold mathematical thinking to be at the very height of what is defined as abstract. Is it thought that what is aesthetic is abstract and vice versa? Is abstraction aesthetics? What do we mean by aesthetics? Some kind of rareified diversion that the rich and powerful engage in? This seems simplistic to me.

Chris Francovich
Alternative Educational Services
_________________

Date: Fri, 20 Oct 95 14:33:35 EST
From: "Mark Schwartz"
To: numeracy@world.std.com
Subject: Freire, math-ing, and abstraction

I absolutely love this discussion!!! About a zillion years ago when I was in graduate school, we "discovered" Freire's concepts and they were - and still are - very refreshing.

I particularly appreciate Ana's story.

If you are willing to accept the following argument, or even partially consider it, then I contend that our everyday experiences are so rich with math-ing and so resonant with the entire concrete-abstract continuum, that students of all ages can have more and more math "eureka" experiences if the math community helps them examine things.

Consider that some domains of mathematics (maybe all, maybe most?) are nothing more than the external capturing of those internal, natural, automatic "calculations" and "math-ing" we do in order to move around our environment and do things. This sounds simplistic, but reflect on it. For example, is a baseball center-fielder doing "calculus" when tracking a flyball? Are you "math-ing" when you are judging the width of a stream to jump? Does one do "math-ing" when mimicking a sound to sing or whistle? If I estimate that this bunch of bananas has "more" bananas than that bunch, am I math-ing?

Where, in the real world, are we on the concrete-abstract spectrum when we run up a flight of stairs two at a time?

Are formulae of any kind simple summaries of relationships (y = ax + b)? Is the relationship abstract/concrete? Is the formula abstract/concrete?

I think we need to pay attention to what we do, how we do it, when we do it, and how it's related to the internal environment as much as the external environment. I realize that finding exemplars of theories (Freire's and others) isn't always easy, but I think that finding them is a function also of the tools we're using. It isn't always "out there" or abstract.

Nice hearing from you ... mark
_______________

Date: Sun, 22 Oct 95 14:35:59 EDT
From: RYAN CLAIRE M
To: @netserv.hvcc.edu:numeracy-approval@world.std.com
Subject: Re: Paulo Freire

I shamefully admit that I am familiar with neither Freire or Frankenstein's works, but I was very interested in the techniques that were being used in Brazil, in terms of adapting these works to practical math classrooms. This semester, I have promoted this kind of approachwith my "pre-algebra" class for college bound adults. What I am seeing is that it gives the students greater ownership of their math skills. They can use any meaningful method. We find it interesting to see how many different approaches students have taken to solve the same problem. With this they lose some of their math anxiety and when rid of that, they dramatically increase their potential for mastering basic math and anything beyond that they may encounter.
Claire
ryancla@hvcc.edu
_________________

Date: Wed, 25 Oct 1995 21:09:53 -0400
From: KTamarkin@aol.com
To: numeracy@world.std.com
Subject: Re: Paulo Freire

In response to the ongoing discussion about Paolo Freire, I was fortunate to see him at the give a talk at the Harvard Graduate School of Education last year. My teenage daughter went with me mainly because she "had never seen you so excited about seeing someone." I wasn't the only one. We waited for over two hours on a long line hoping we could get into the lecture hall. You would think we were waiting to see a rock and roll star. We barely got in; hundreds were turned away.

Even though his English was a bit unsteady and he often spoke in Portugese with an interpreter translating for him, it was impossible to not be struck with his enormous warmth, caring, and humor. I hope that I am not grossly oversimplifying when I say that to me, Freire's core educational message is for us to strive to empower the individuals of society's most oppressed groups and in so doing also to empower those groups as well. I think that the discussion I have been reading in this group and the maltt (Massachusetts Adult Literacy Technology Team) team list regarding project based learning is very much in the spirit of Paolo Freire.

Kenny Tamarkin

_______________

Date: Mon, 30 Oct 1995 23:08:38 -0500
From: SouthWoods@aol.com
Subject: Re: Paulo Freire - Is math ab...

Subject: Re: Paulo Freire

I agree with your observation about prospective elementary school teachers. I teach math methods at a local university and my eperience has been that at least 25% of my students are math illiterate when they enter my class. My class helps . . . but . . . There are problably less than 20% of the all the students I have taught who really understood mathematics and its related concepts. I scares me to see what we are sending out there to teach the next generation and I believe we will see their future students in adult ed. It is such a vicious cycle.

Something will have to be done soon. Maybe math experts on the El Ed level. Just adding my two cents. Eileen Simons

_________________

Date: Tue, 31 Oct 95 07:29:47 EST From: "Mark Schwartz" To: numeracy@world.std.com
Subject: a quickie

Friere, if nothing else, forces us to think about things not so much as abstract/concrete but rather "what the hell is really going on here?

Look at the subtraction algorithm. We say
13
- 7
and then we say, in essence, we can't subtract a larger number from a smaller number, therefore, the way to solve this problem is to "borrow" the 1 from the tens unit, add 10 to the 3, and then we can subtract 7 from 13.

Now, really stop and think about this hard. We haven't really done anything at all!! The problem is still the same. We may have scratched out the 1 and then written a little one above and to the left of the 3, and some how all of this kabala-like activity has provided an insightful and understandable "solution".

Think about it. You should not be surprised if students don't get it. After all, most of us didn't ... but we subtract. Do we really want them to "get it" or do we just want children to do it? I propose that this is about as concrete as you can get.

By the way, there is an explanation and a very nifty algorithm for converting the reducio absurdum algorithm to, in essence, an addition problem.

I gotta' go but I'll post the "answer" after you've played with it a while.

_________________

Date: Mon, 30 Oct 1995 13:41:22 -0700 (MST)
From: "M. Adele Megann" To: numeracy@world.std.com
Cc: numeracy@world.std.com
Subject: Re: Paulo Freire - Is math abstract

Subject: Re: Paulo Freire

When I think about the abstract/concrete question, I like to look at division.

Look at how we teach division to children. First they get the basic facts. Examples are carefully selected so that the answers always come out evenly (6/2 = 3). This is their first impression of division.

We slowly build in complexity -- more digits, remainders, (7/2 = 3 with 1 remaining), fractional remainders (7/2 = 3 and 1/2), and decimal quotients (7/2 = 3.5). Etc.

Each level is introduced with examples. 3 pairs of socks with one leftover, that kind of thing. Then student do pages of exercises to practise the algorithm. There are a few word problems at the bottom of the page. Students aren't foolish! They realized that those word problems are solved using the method they have been practising. Each word problem is written so that it is solved best by that method.

Later on, they get a mixture of word problems. If they happen to remember that "the ones about rows of chairs in the gym" require a remainder, and "the ones with money" require decimal quotients, they are okay. Otherwise, they are completely lost.

Educators then fret that students don't "really understand," the concepts and they come up with strategies for approaching word problems (as if words were the problem), along the lines of "read it really slowly." Whether students master the strategies or not, it's not a big deal because word problems make up a small enough proportion of tests that students pass anyway.

Then what happens? Let me tell you. Those students study to be teachers. My math education course during my elementary degree was like group therapy. People were regularly near-tears, and we had a few hysterics. The prof spent most of the year trying to explain place value. People almost walked out when she introduced a cute execise on base-4. Only two people could do it. (Me one.)

I can hardly believe that these teachers (fine educators in most ways) won't pass along their panic to their young students. And so it goes.

How does this relate to Paulo Freire? I continue . . .

Date: Mon, 30 Oct 1995 13:54:13 -0700 (MST)
From: "M. Adele Megann"
To: numeracy@world.std.com
Cc: numeracy@world.std.com
Subject: Re: Paulo Freire - No, math is not abstract

I'm breaking this up because I'm being so long-winded. Sorry, but I've been thinking about this for years, and this is my first opportunity to talk about it.

So, you ask, what does this have to do with Paulo Freire? I think it goes back to the big myth about the abstraction of math. We teach students that math is an abstract discourse, mostly beyond their understanding (my students are mentally handicapped) but that maybe if they work really hard, they can learn enough to APPLY math to the real world.

The truth is the real world came first. Which brings me to point one of my theory: NOBODY ADDS NUMBERS IN THE REAL WORLD. People add stuff. We add numbers as practise for adding stuff. Here's my second point: NUMBERS DON'T EXIST. They are theoretical constructs that facilitate the business of adding stuff.

Now, I have nothing against numbers. I like lots of things that don't exist. I do number puzzles for entertainment. You wouldn't believe the nasty comments I have sustained over that. How about a new oppressed group -- people who like math? By the way, I was also harrassed in that education class -- for enjoying and understanding math. By the end of the class, I barely said a word, and I covered my paper so no one could see that I had finished assignments. The atmosphere was unbearable.

Let me go back to division. A math book can tell you how to divide numbers, but it can't tell you how to divide stuff. If it's your stuff to divide, you have to decide. So I ask my students: How do YOU want to do this?

If you have 7 socks, do you have 3 and a half pair of socks, or 3 pairs of socks?

If you are dividing money amongst yourselves, are you going to go make change to it can work out to the penny, or will a rough division suffice?

If you are in a factory where you need x units of stuff in each box, will you keep the leftovers for next time? What if they are perishable? Send the extras home with the workers as a sign of good will? And what about the famous question - divide two cookies between three children. How can you answer this without knowing whether the cookie is hard or soft? Is there access to a knife? Are the children the same age? Did one of them just scrape her knee? Is a cookie a rare event, or can inequities today be addressed tomorrow?

The algorithms are still important and need to be learned. I think students will be more motivated to learn them if they identify an approach a problem, and a teacher says, "okay, this is HOW you can do it that way."

The texts have a big concern that students not be introduced "prematurely" to algorithms. ("They don't know remainders yet, so chose examples that come out evenly.") Students, therefore, can not chose the examples themselves because they might come up with something too "hard" so them. If they come up with the question, how can it be too hard? They don't have to do the algorithm, the teacher can. After all, the factory owner doesn't divide - he tells the account to do it.

When my students pose a problem that involves a procedure that they haven't learned yet, I say: "here is what it looks like. I'm going to teach you that in more detail in a couple of weeks." Or maybe they can do it on the calculator for now. Then they get a better sense of "Math - the big picture," and they have something to look forward to. During my degree, I was told not to do this, because this will "scare" children. This teaches them, of course, that math is scary.

This is how I think the myth of the abstraction of math is a disservice to students: they are told that math comes BEFORE the real world, therefore, they will have to figure out math before they can have any understanding of, access to, or power in, the real world. The real world comes first, and if any of the stuff in it is theirs, they decide what to do with it, then apply numbers to their actions. Of course, if none of the stuff is theirs, then they can't do anything to it.

I think the ideas of Paulo Freire has a lot to add to this discussion. Good luck to those to are working on this.

Date: Thu, 2 Nov 1995 18:02:31 -0500 (EST)
From: Lynne Mikuliak
To: "M. Adele Megann"
Cc: numeracy@world.std.com
Subject: Re: Paulo Freire - No, math is not abstract

Adele and all,
This is a great "thread" and you've brought up some questions I've been thinking about.

I firmly believe that math DOES relate to life in a very concrete way that, when they begin to see how much they already know, empowers our students. Math is change at the store, interest rates on loans, buying on time, figuring the "best buy", and deciding if a "percent off" sale is a good one. When I teach these topics I use real life examples.I also ask in the journals how students might relate what we learned that day to real life. I get some great answers. One of the best, and it relates to Adele's "cookie" example, is a student saying, "I have to divide one love between three kids."

"THE WORDS ARE THE PROBLEM" is a very funny idea, but sometimes reading comprehension IS a problem. I often have very good math students who don't seem to need my class, then I check their reading "scores" and understand why they're with us. My first math research was on attempting to create a "word problem formula". It gave SOME students a SENSE of control but there is no "magic" answer.

Why do word problem phobic students freak even when the page heading says: FRACTION ADDITION WORD PPOBLEMS ??? I think the're SO scared that they don't "see" that they are being told what to do on that page. It happened again today.

I've found it very helpful to get students to share their ways of doing problems with others. They often have very creative solutions. I only sometimes have to say it's a good plan but won't always work. EX: In "borrowing" some students like to go all the way to the largest column and cross out everything in advance. This is fine if they NEED to, it can goof them up if they don't.

I encourage personal solutions, Lizette can't remember all the times tables such as 8x7, but she does know that 8x5 is 40, so she adds 8 two more times. She's used this method for so long that she's become quite fast at it. If it works for her I'm not going to argue. I let all the students choose their own methods only point out that there may be faster ways they can try when they want to.

All of this is great when it stays on the teacher/student/real life level. It becomes a problem when the students have to pass archaic, often stupid tests in order to get into the next program or college. That is the balance beam we walk as we bridge the gap between practical math knowledge that excites and empowers and "that which I NEED to know for the test".

Some elementary teachers can pass on their math fear to students. Funny how most elementary teachers are women, huh? Yet, one of the most gifted math teachers in Phila. was the late Sue Stetzer who excited both students and teachers through her love of math. Let's hope her joy in the subject long outlives her. And let's hear from some more people on how they use Friere's ideas in their classes!

Lynne Mikuliak- Phila. Pa.

___________

Date: Mon, 06 Nov 1995 10:02:44 -0600 (CST)
From: "Fancher E. Wolfe"
Subject: RE: Paulo Freire - No, math is not abstract
To: numeracy@world.std.com

I am concerned about word problems. What would students reactions be to word problems if all of the word problems were applications to real world problems? After all our goal is to have students use mathematics to understand and perhaps solve ill-structured problems. By ill-structured problems I mean problems the way we find them in the world.

Fancher E. Wolfe
Chair, Department of Mathematics/Statistics
Metropolitan State University
730 Hennepin Avenue
Minneapolis, MN 55403-1897
612-341-7256
Fax 612-373-2751
_______________

Date: Wed, 08 Nov 1995 08:50:44 EST
From: TGNV79B@prodigy.com ( NANCY L MARKUS)
To: numeracy@world.std.com
Subject: Paulo Freire
Sender: numeracy-approval@world.std.com

Hi my name is Nancy Markus and I have taught adult ed for seven years. I am now working for the Ohio Literacy Resource Center as a graduate student in math ed. and am working with our state math planning committee. I am a member of ANPN (adult numeracy practitioners network), and have been enjoying this conversation.

While I agree that math should be concrete, I'm afraid that at a very early age the divergence of school and real math becomes so wide as to be almost impossible to reconcile. Those of us (proabably 10-20%) who did well in math in school often become teachers, teaching those who didn't. I am dismayed at how often I hear teachers saying "why can't they learn it the way I did?" Even more discouraging are those teachers who seem to have lost the idea that math should be and is concrete. At one workshop I was involved with, a highly respected GED math teacher was unable to show her results using blocks to a problem. She could get the answer by using algorithms, and was sure she was correct, but struggled to show it to using the blocks. Her answer continued to be that see how the numbers work.

Until we as teachers can begin to see math as concrete, it's going to be tough to communicate to our students.

_____________

Date: Sun, 12 Nov 1995 16:43:46 -0700 (MST)
From: "M. Adele Megann"
To: Lynne Mikuliak
Subject: Re: Paulo Freire - No, math is not abstract

Thanks for your reply, Lynne. Come on, others, let's hear your ideas, too!

The question about the standardized tests is a tricky. Authorities tend to lump themselves together. (One teacher doesn't question another, the principal doesn't question the social worker, etc.) When we have private disagreements, we are loathe to present a "divided front" to our students. We are even told that this is the more professional way to behave. Thus, we are reluctant to indicate that we think the GED or SAT or whatever (I administer the Standford Diagnostic Reading and Mathematics Tests) is anything other than a "good thing."

I like to tell my students that standardized tests have "good things" about them, while, to certain extent, disassociating myself from the tests. I explain the purpose of the tests, and how they are only effective if administered consistently. (That's how I explain why they can't use calculators.) I tell them that the results are simply "a score on a test," not something inate to them. They seem to understand this, which is good, because my adults students test out at around the Grade 4 level.

Then I tell them that as helpful as these tests are, they do use some pretty arcane language. Therefore, I will use that language, so that they will recognize it when they see it. I will also use our language, so that they will know what I am talking about.

Which means I talk like this: "Let's rewrite this in expanded notation, which is the same as the long form." "Put these expressions in standard form, that is the plain old number." "Which is the denominator, the one on the bottom?" By the end of the term, I have driven myself fairly crazy, listening to all that jargon, and saying everything twice. I was told during my training not to use the jargon, but I think that part of our role as teachers is to mediate the system to our students -- not rationalize it or ignore it, but simply help them navigate it.

I'm not sure how effective this is. My students grade equivalents creep up on average (probably a third a grade a year), but sometimes stay the same or go down. If someone has other ideas, I would like to hear them.

____________

Date: Mon, 13 Nov 1995 10:42:00 -0600 (CST)
From: "Fancher E. Wolfe"
Subject: RE: Paulo Freire - No, math is not abstract
To: numeracy@world.std.com

i like to view all tests as formative evaluations. Instruments to give the student direction for further work. tests should be viewed as friends to help learning.

Technical vocabulary is not all jargon. It makes use of specific terms or words for a conceptual structure that is often quit large. Part of learning a discipline is to internalize the concepts of the dicipline. this is a richer deeper understanding that rote learning of definitions. If one is to progress to the level of reading the literature of the dicipline as a path to new learning one must understand the specific constructs of the dicipline.

Fancher E. Wolfe
Chair, Department of Mathematics/Statistics
Metropolitan State University
730 Hennepin Avenue
Minneapolis, MN 55403-1897
612-341-7256
Fax 612-373-2751
_________________

Date: Mon, 13 Nov 1995 11:23:55 -0800 (PST)
To: numeracy@world.std.com
From: MMELLISSINOS@sunstroke.sdsu.edu (MELISSA MELLISSINOS)
Subject: Standardized Tests

This is in respone to Adele Megann and Fancher Wolfe.

I agree with Fancher Wolfe's view of assessment as formative (to provide feedback for instruction) and unfortunately standardized tests do not serve that purpose, even when they say they do. Standardized tests are typically multiple choice and normed on some population. The scores are relative to the norming population rather than to the mathematical content. But even if that were not the case, standardized tests do not tell you what students know and can do because you only have information about whether the responses were correct or incorrect. And for this, and many other reasons (e.g., changing views of mathematics and mathematics learning), the mathematics education community is working to develop more "authentic" assessments for a more "authentic" mathematics curriculum.

It is unfortunate that Adele Megann has to teach to a standardized test. This can further confirm a belief that testing drives the curriculum. If we want to help students to develop reasoning and other higher order thinking skills, then the assessments must reflect that value. There is a lot going in to change K-12 assessments, but I am afraid that the adult math education community is going to remain chained to the status quo unless we pressure the "powers that be" to develop assessments that provide information about what students know, or develop them ourselves. Although we have a lot of resources through NCTM (National Council of Teachers of Mathematics, the New Math reform of the 1960's showed us that simply having wonderful ideas and materials is not enough. We have to make good use of that information in a public way.

Can I suggest a recent book that offers some informed perspectives on standardized testing and authentic assessment? It is called "Reform in School Mathematics and Authentic Assessment" edited by Thomas A. Romberg (SUNY Press, ISBN 0-7914-2162-7 for the paperback). Tom Romberg has been writing about authentic mathematics since at least the 1980's. He also chaired the development of the NCTM Standards. Also, for those of you who are not NCTM members, NCTM just published Assessment Standards for School Mathematics.

Adele Megann and others: Can you tell me what the purpose is for administering the standardized tests in your program? Who interprets the results and how are they interpreted? How are the results used? How do you feel about the present use of assessment? If you could make any changes in present assessment practices, what would you change? Research suggests that the timed multiple choice test format favors males. Have you found this to be true?

Melissa M.

-----------------------------------------------------------------
Melissa Mellissinos also at:
CRMSE/SDSU UC San Diego
6475 Alvarado Road Suite 206 Mathematics and Science Education
San Diego, CA 92120 Department of Mathematics
mmelliss@crmse.sdsu.edu La Jolla, CA 92037

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ANN Numeracy Discussion List: “Numeracy and Paolo Freire ”

ANN Numeracy Discussion List:
“Numeracy and Paolo Freire ”