Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
COMPETENCE AND SELF-CONFIDENCE
You have to go back many decades ago when I was in grade school. That's where I first
think about math -- same thing, the times table. You were under the gun to be able
to verbalize. I can recall hitting the wall at 6 times something or other and that
was the end of it. I couldn't go farther. Fear was a motivation. In those days,
if you didn't produce, you flunked. So I learned methods of getting to the same
answers but not the standard subject methods. I never could figure out how, say
a, b, or c, had values to it in algebra, and that was sheer agony. I got into geometry. I was
in a private school, in a very small class. I knew where I was in the class, maybe
that was (my) self-image, but the problem was some of the fear of math, so the first
time I flunked it. Then I changed schools and never told anybody I'd taken geometry
before and I got an A the second time through it 'cause I had to take it to get
the math credit. And I like geometry but that's about where we stop. . . I was supposed
to take physics and did not and I avoided math. I've learned my own methods from dealing
with where I needed to do math.
Overview
In focus group after focus group, adult learners and stakeholders openly shared their
positive and negative experiences with math. They shared their best experiences
with math, and from whom they learned math. The also shared their worst math experiences. When given a choice -- a good experience or a bad experience -- the results were
striking. Many more learners, and a good number of stakeholders, described their
lack of confidence and competence in math. From the discussions, it became clear
that many adults fear math and especially lack confidence in their ability to handle the math
taught in classroom situations.
Key Findings
The loss of self-confidence in math, the lack of understanding of particular math
concepts, and fear of math inhibits power. Adult learners and stakeholders alike
often remembered experiences that discouraged them from enjoying math and appreciating
its potential. In focus group after focus group, adult learners reflected on particular
experiences when they had difficulty learning math: "In second grade I had trouble
with multiplication. The teacher just forced it down my throat and expected me to
memorize it and I just couldn't do it." "Math was okay until seventh grade when we started
fractions. I had no idea what was going on and the teacher would not explain it."
"In seventh grade I started to have trouble with geometry. I still have trouble
with the GED geometry. I don't know why we have to learn it. It's so confusing."
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Many adults do not feel confident, competent, or comfortable in math. "I don't like
math. We don't get along. I just don't like it. Adding and subtracting was okay,
but when you get to dividing, fractions, and algebra, it just gets hard." "All math
is frustrating." "I've always been really dumb in math."
Many adult learners are frustrated because they do not feel competent in math. Comments
like "Doing homework with the kids is most frustrating for me because my kids do
math better than me," or "Working with my daughter at home is really frustrating.
I won't let her use a calculator because I don't want her to get dumb like me," or "I
want my kids to be able to do math like I couldn't" reveal that sometimes this frustration
shows up when dealing with their children's math homework.
Adult learners and stakeholders alike, in some cases, fear math. As stated by one
stakeholder, I was taught to fear math. Or as stated by learners, I like math
but I m scared because I can t divide. Math makes me terrified and tense.
For some learners, frustration with math spread to frustration in other areas of school
as well. For example, one learner related, "I am not good in math. When I was
in school and we started on decimals and fractions, I could not catch on and my teacher wouldn't help so I got behind in class and could not keep up with everyone else
so I just gave up completely on all of school so that no one knew that I couldn't
do it and (I) quit school. I don't even like it anymore."
Is this lack of confidence in math because people are limited or lack the ability
to learn? Certainly not. The causes are more likely found in poor learning environments
and lack of recognition of different learning styles and needs. As one learner
stated, "I didn't understand math because the teachers wasn't explaining it right from
the base. They was getting to, they were starting the middle part of it and I didn't
understand the first part of it and I never could understand math." Or as another
learner noted, Mine was high school, too. It was close to what he was saying with
the problem with a teacher ... It would be at the point where maybe I wouldn t grasp
something and you try to ask questions, and it seemed that, if you were in the minority
that had trouble, it was always see me after class. It seemed you were being pushed
to the side a little bit. Maybe I didn t get enough where you drill with it and
it gets repetitive, but it was like the majority got it, so that was good enough,
so we went on to the next thing. So that was when I just fell behind.
Good learning environments -- within the family, at work, or in school -- produce
different attitudes toward math and can help to overcome fear and lack of belief
in one s ability. Confidence builds competence in math and competence builds confidence.
The learner quoted above who could never understand math when talking about his current
ABE experience stated, "Now I understand it perfectly. I used to hate math; now
I love it." Or as another learner related, "Here, when I ask them ... I feel
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that
builds up your confidence level and self-esteem ... they always try to help. It makes
me work harder than ever. " Or as another learner states, "I hated math but the football
coach made it interesting to me. So I had to learn to deal with it. The coach made learning math fun." Or within the family: "It (math) was my best subject. My grandfather
helped me a great deal when I needed help. He was very helpful to me because he
was a carpenter. " And "my mother was the one who would help me the most with math. I would work at it by myself until I would get frustrated ... so I would ask her
to help me and she would sit down and explain things to me. "
Sometimes confidence in math comes after gaining self-esteem as an adult. One stakeholder
explained, "Now that I am older, I feel much more confident in the math I need to
do. I wouldn t voluntarily go back and take a higher math course, (but) math doesn t frighten me. I have more confidence in myself ... This was nothing I was taught.
It is something I picked up." Math skills are also acquired on the job. For example,
when learners were asked to describe a good math learning situation, they responded, "The people that helped me was my boss at work;" "The best learning was when I am
at work using my tape measure;" and "I worked in a Chevrolet parts department and
learned more math on my job than in school."
Those learners that feel comfortable with math have confidence in their ability and
respect for the domain of math. "I bought a house last year. The price of the house
sounds pretty inexpensive, but when you add up the interest on it, the points they
charge you, the closing fees, the maintenance. It's like on a 30-year loan, you end
up paying three times as much as the house is worth. You gotta compute simple interest,
compounded interest, all that sort of stuff. First I took what I made a month.
I took an average, then I deducted all my expenses, then I had a budget saying what I
could afford to pay a month. Simple math. Only you divide that if you have a roommate
or whatever. Just basic planning and basic math skills, averages. When they first
tell you, 'Just put down 5% or 10%, then pay this much a month, you take it like that
and you don't know what it really costs you. You gotta figure everything else.
That's what math does, it makes you organize, makes you think in a certain manner."
Confidence in math increases power, voice, and the ability to act. For example, "I went
into the store. The lady had an item that was supposed to be discounted, I think
like 50 or 60% off ... And she brought it up and it didn t sound right to me, and
I was in a hurry that day and I really didn t have time to figure it out on my own. So
after I got home, I figured it out. I went back to my math book and looked at the
amount that was supposed to be discounted and it was wrong. And so I kept my sales
receipt and I took it back and I got six dollars back. She was wrong. "
The more adults learn, the more confident they become, and the more enjoyable the
experience of learning becomes. "The more you learn, the more fun it is." Stakeholders
explained how knowing how to do math improves confidence. "In 1946, in high school, I was taking geometry and the teacher made it so clear that I actually understood-
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what I was doing and thought that I was really good in math!" "It's funny, most
of the stuff I thought of (about learning math) didn't have to do with school ...
I learned a lot of my math as a kid from my dad and it was one of the few things that he did
with me so it was important for that reason. I have clear memories of the two of
us looking at a word problem together and my dad always drawing pictures of whatever
was going on in the problem. And my growing up with a sense that I could figure anything
like that out. All I had to do was draw a picture of it. I have a memory when I
was in the sixth grade, when I was getting kind of bored with math, my dad saying,
'Oh, well, do you want to learn algebra?' So I have clear memories of him basically teaching
me how to write sentences in math and leaving holes in the middle of them and plugging
letters in. So I had this great confidence in my ability to do it, partly because
I had a dad who assumed I would be good at it and who kind of instilled me with that."
Implications for Teaching and Learning
Teachers need to become comfortable presenting math concepts using a variety of strategies
and approaches. This suggests that teachers need staff development where they can
share with each other successful teaching strategies. Teachers need to become comfortable using manipulatives, calculators, computers, whatever it takes for learners
to grasp math concepts. A stakeholder suggested, "I have five children in their
twenties, but they missed out on math somehow. I don't know where math education
has gone to but I think we need to go back and educate the teachers." Another stakeholder
shared her own personal experience with becoming comfortable with other approaches:
"I thought of last year. I was teaching reform calculus for the very first time.
We had completely switched over to reform calculus, Harvard Reform Calculus which involves
a lot of manipulatives, a lot of graphing, calculator work, a lot of computer work,
emphasis entirely on understanding and not on manipulation. I came up through a
very traditional background which most of us all did -- the rote, go home, be able to do
50 problems and all that stuff. All of a sudden, I was faced with teaching these
students all these concepts without showing them the manipulations but actually get
them to understand the concepts not just how to do it. I sat back with other instructors.
We met on a very regular basis to share our woes. And we said, 'Don't know why
we ever -- now it makes sense.' We just sort of did it by manipulation before. We
now understood. So I learned probably as much calculus as my calculus students did. Now
that's a terrible confession. And it was amazing the complex concepts that my students
could understand before I had even shown them the algebraic manipulations to do something. We didn't show them the manipulations until afterwards and it was just phenomenal
and so I learned a lot of math, they learned a lot of math. I learned a lot about
how to teach math."
In recent years, more research has been done in the area of math learning. This research
has revealed that individuals learn math differently. Some are comfortable with
learning step by step procedures while other learners tend to jump to the big picture
60 and work forward and backward to solve problems. Teachers need to let go of the
need to make all learners solve problems the same way that they were taught in school.
An adult learner shared how this step by step method does not work for him: "It
(math) was hard because they wanted you to write everything down, every step you took.
I did a lot of it in my head. I couldn't write how I'd done it 'cause I'd done
it in my head. I had the right answer but I couldn't write down this is the step,
this is the step, because I'd done it in my head. They'd try to show me the steps but it didn't
always look like how I had done it."
Success needs to be built into the adult education classroom. Adult learners need
to have success early on and often when they begin a math class. This success enables
them to develop confidence in their ability to do math, which in turn paves the way
for further positive math learning experiences. All individuals benefit from positive
feedback, but it is particularly important that adults who have experienced failure
in math class previously now find success in the adult education classroom. As one
adult learner put it, "It (math class) can be just as interesting as a social studies
class, and the positive feedback is the best thing. When my teacher told me when
I was doing something, that I really was a good thinker, I felt so good! That sounds
really dorky, but it's the truth." When asked what recommendations should be made in math
instruction, stakeholders offered these comments: "We need to build confidence in
our students;" "People lose confidence in math because they don't realize that they
are already doing lots of math and that can be built upon;" and "The other thing is, that
I really noticed, more than any other subject area, when students feel competent
in math, their self-esteem really grows and their confidence in themselves as learners
really grows."
A stakeholder voiced her concern, not about the adult education classroom, but the
K - 12 system. Because she felt that her daughter might not get supported to be
successful in math, she had to take on this responsibility as a parent. "The other
thinking that was important for me as a kid and that I've tried to do as a parent -- not so
much math skills -- the belief that my kids will be good at this and can be good
at this. That it is logical, simple, always do-able. That's probably the other
piece out of this as a parent. Especially for my daughter because I assume a little less that
school will give her that message -- but the belief that she's good at it (math)."
Another stakeholder reflected on her past experience in math: "I have sadness that
no one ever said to me, 'You're really good in math.' I was good in math."
Math content skills need to be presented in the context of real-life situations.
When learners can immediately apply what they have learned, the learning crystallizes
and the learners gain confidence and competence in their math ability. When asked
about his experience learning math, one adult learner responded, "I picked up some stuff
from me helping my father. I used to know, like all the money. We owned a restaurant
back home and every day he gives me the money and at the end of the month, I used
to add it up, let him know what we got. That helped me a lot." A suggestion from
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a
stakeholder was to change the perception that math is difficult: "We need to start
over and completely redesign the way math is taught. There should be more application.
The current application attempts to teach application with too much theory and in too
convoluted a way. The perception is that math is too hard and that perception must
be changed."
Connecting to real-life situations and understanding the why behind math processes
improves math ability. A stakeholder, even though she enjoyed math as a child, shared
this revelation, "But I always felt good about math. I always enjoyed math. It
was in college then, in teacher preparation work, that I picked up a lot of why I was doing
it and the background and it would click and then it made more sense at that point
than previously when I was just repeating a process."
Adults use math in their daily lives but often do not connect their real world math
to the math in the classroom. When asked whether they use math, adults who are not
confident in math will often say that they don't use math yet they earn wages, spend
money, buy gas for their cars, and so on. Connecting math to their real-life situations
helps adults understand that they do use math. A stakeholder suggested, ". . . Building
on the familiarity that they (adults) do have. I think that one thing, we estimate, we talk about adults' wealth of experience, but that experience has given adults
math intuition -- the way that they've dealt with it -- so we can find strategies
to go with their own intuitive way that they've walked through things. It is very
natural for them. I think you'll find this with some of the women students, that they've
developed some strategies that they can build off, solve their problems." Other stakeholders
added, "People lose confidence in math because they don't realize that they are already doing lots of math and that can be built upon." "Most people don't perceive
themselves as being math literate. We get through the classes, we get a 'B' in algebra,
maybe we get an 'A' in trig, but when we get out, we perceive people who are math
whizzes are engineers, or physicists, people who are in math fields. Most people
in this country do not perceive themselves as being math literate and so we shy away
from it."
There needs to be a level of trust in the adult education classroom. The adult education
teacher needs to build an environment that is comfortable for adults and one in which
adults can be open. Adults need to feel comfortable sharing their frustrations and lack of math skills. One adult learner shared how he felt a need to "expose"
his lack of times table knowledge to his teacher, "Well, math is hard for me, but
I can learn it. The hardest part for me is the geometry and the division. But,
if I knew my times tables right off the top of my head, I could get all of it. I don't know
all my times tables right off the top of my head. I could work the problem out but
my time tables slow me down. When I go into the classroom I'm going to have to explain
to the teacher on the outside of the door that I'm not good in math and she'll have
to explain it to me over and over again. I will get it eventually, but it will take
time. Once I've got it I feel good about myself when I get it because math is the
hardest thing for me." A stakeholder explained
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what she values in an instructor: "With
my staff, what I think is successful -- what is just as important as the academic
background a person brings with them to the classroom, the knowledge that they have
-- is the ability to interact with students on a personal basis. Being able to sit down
and talk to them as human beings, let alone just as students that sit in front of
you and I have to teach them this material. Most of the students that I have had
or I have talked to whether in the alternative high school or adult have had negative experiences
in educational programs. As a result, that is why they quit. Coming in, they say,
'Well, people care about me here'. That just raises their self-esteem ... gets them on target again ..."
Connecting to the Four Purposes
For adults to be literate enough to accomplish their goals, they need to understand
and use math. When adults do not have a handle on math, they have difficulty coping
-- whether it be in their role as parent, worker, or community member.
The following adult learner lost his job because he was not able to read scales to
access information: "I worked for Nabisco. As a mixer you had to know the correct
scale and formulas. I kept messing up. I lost my job. It doesn't look too good
on the record. If you don't know math you can't suceed."
This adult learner expressed his feelings about how it is difficult to have a voice
because he lacks confidence in his math ability: "I guess I'm not too comfortable
because I lack a lot of knowledge (in math)."
These adult learners were not successful in making decisions for work. "Dairy Queen
wouldn't hire me because I couldn't make change in my head. I couldn't give the
answers in an oral quiz to making change questions." "In the bank when I had to
10-key, do some things with checks. . . couldn't put it in the machine. If I messed up checks,
I couldn't work. I quit the job." "One time I was at work and this guy came up
to my register, and I rang all this stuff up. And when my register opened, he gave
me like $20 or something. And he's like 'Oh, wait a minute, I have the change.' And
I'm like looking at him and I'm like, Oh my God, I have to figure the whole thing
out and it took me about five minutes. The register doesn't do it for you. Dealing
with money and stuff is important. Sometimes when they give me extra change and stuff, I
just ignore it and then say, Oh, I'm sorry. "
Math skills, knowledge and abilities are gatekeepers. To bridge to the future: to
get a job or a better job, to go on to college or to create a brighter future for
their children, adults need to understand math. "My daughter asks me about that
(percentages) so I'm teaching her a little about that. They're always asking why I don't know
more about the algebra and geometry and stuff. So I told 'em about what happened
in the past. She can see how automation is coming with the computers and all -- and
she knows if
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you don't know it, you'll fall through the cracks, be on the street." And
this adult learner now understands that math is critical to moving ahead. When asked
what was a frustrating math experience, he replied, "Math in general. In school
we had to know it all at once. We had to go on or else. Some like me never went on."
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