Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
RELEVANCE/CONNECTIONS
I remember teachers asking me if a drop of water is falling, at what point will it
pick up the highest speed, the beginning or the end? . . . Like who cares?! This
is the stuff they put in there just to mess you up.
. . . they just started this when I was in 8th grade, but we had a business class
where you'd go in there, and they'd give you a stock book and, you know, they'd give
you so much money and you got to invest in these companies and the guy that came
in there actually used the real paper and he'd tell you how much money you made, how much
money you lost. You were your own broker and that was real neat. You know you invested,
you put so much money in like Nike, for instance, and then McDonalds. You know,
you go across the board and he tells you what you made and what you want to invest it
in and what you lost. Whoever made the most money, they get something like a free
pizza, whatever. And it was using real numbers . . .
Overview
In school, when math was made relevant, the concepts were better remembered. All
too often, though, the school experiences involving math have not been positive or
interesting. They tended to be like those described by the first adult learner.
On the other hand, when adults talk about math in every day life, they tend to perk
up. When adults use math at work, at home, or in the community, they often present
a brighter picture about using math. This is because the math has relevance to them.
They are able to apply the math and see connections. Adults need to see connections
in math -- connections within the domain of math itself, connections to other disciplines,
and connections to real life and work situations.
Key Findings
Math takes on greater meaning and understanding when it is directly applied in the
workplace or in real-life situations. Adult learners provided specific examples
of how they learned math best. "You know when I was young I used to empty out coke
bottles at home and take them in to get candy bars. That's how we learned to make change."
"The best learning was when I am at work using my tape measure." "I worked in
a Chevrolet parts department and learned more math on my job than in school."
Many of the adult learners participating in the focus group discussions felt that
their best math situation was when they learned math at work. This suggests that
the math they learned on the job was directly applicable for them. "The best situation
I've been
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in was when I got a construction job about a year and a half ago -- being good
with numbers and stuff, it made it that much more easier on me doing the job as far
as measuring, weighing. Everything just seemed to flow naturally. I felt comfortable."
Adults see little relevance or connections between math and their everyday living
and working conditions. Adults often ask, What is it used for? about math topics
that they, thus far, have seen little relevance or connections to in their everyday
living and working situations. ". . .And I started off using basically pennies for math,
adding and subtracting which was real helpful. I liked math all the way up till
about high school and then algebra and geometry. I kind of lost it right there.
The way I seen it responding to the same question, What is it used for? You don't use it
unless you're teaching it or unless you're going into some kind of manufacturing
type deal where you're actually making diagrams and stuff like that, but otherwise
it is of no use. . . I use math every day, fractions and so on and so forth, but just don't
use algebra or geometry." The adult learner quoted above shares the same sense of
frustration as this stakeholder: "I remember my father standing over me at the dining
room table attempting to drill into my head the algebra x, y and x + y. I couldn't understand
how anyone could understand it and why anyone would want to."
Adults feel they are more successful when they are able to link any new learning to
something they already know. This adult learner has a clear sense of how to make
math learning more meaningful: "I learn better if I start off with something I already
know, if you go back to the basic formula and link it to an easier way. Because the
more I learn the easier it gets. I can go all the way through from basic multiplication
and division all the way to algebra; if you would just refer back to the other form
of math. Link it to something you already know and you'll get it; you'll remember
it. I mean, you can sit down and read a book. Within 15 minutes, you've lost 80%
of what you've just read, but if you link it to something else, I mean, it is that
much easier to remember."
Textbook math, and particularly word problems, seem to have little relevance to what
adults perceive as math in everyday life. The phrase "who cares" often seems to
be used by adult learners when asked about word problems. "When it comes to math,
you've got to remember the word frustrating. . . It gets so frustrating and it is not that
I don't like it, it is like I don't care how many cookies Sally made. And I don't
care how many were oatmeal and I don't care how many were chocolate chip and I could
care less who ate them. You know, I'll never in my life forget that problem as long as
I live. Who cares?! You cook 'em, you eat 'em." ". . . Start with the bad: the
most frustrating part in math are the word problems in my class because you do them
endlessly. They are senseless. You do not use them later on in life. They confuse you
for days.
Adults' real math skills often don't show when they do meaningless word problems.
Adults often actually use math successfully in their daily lives, yet fail to see
any con
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nections to word problems presented in the class. An adult learner explained
this lack of connection: ". . . Math was good for me. I always liked it. English was hard.
I wanted to be a draftsman. I went to school at PCC. I chose building things.
I succeeded, I got into that work, hurt my back. I used math for building. After
my back I lost it [the math]. I feel good now -- I think some of what I knew are really
coming back. Reading is hard for me -- word problems. Working with math is one
thing. Reading with math is a whole other."
Implications for Teaching/Learning
Teach math in the context of real-life and workplace situations. "For all adults,
mathematics learning should be connected to real life situations. (The Massachusetts
ABE Math Standards, p. 32) When math is taught in context, adults understand that
there is a practical application for that skill. "The thing that I regret when I didn't
learn math was how to use a calculator. You know, problems with subtraction; how
to use it in life. I can add but when it comes to things like when I want to cash
my check or write checks, I've got to be able to subtract, etc.", explained an adult learner.
Several stakeholders echoed the same sentiment about relevance and connections.
"Whatever skills are needed, there needs to be relevance to life and application
across activities." ". . . One of our hiring practices is to run through a simulated
production. You need to develop interesting programs, have a cash register in the
classroom, do medical calculations, simulate real life in the classroom. Textbooks
get boring. Come visit our plant. Make it as real as possible." "Mathematics should
be taught as an experience in context, not as a lecture. To this end mathematics
needs to be taught using REAL problems, not textbook reality."
"Many adults already do complex math on their jobs and in their everyday life. it
is important for math teachers to use this as a basis for developing new ideas or
extending old ones to different places." Carrying this teacher suggestion one step
further, teachers need to become more knowledgeable about the world of work in order to offer
relevant math curricula.
Use learner-centered approaches to teaching to ensure that learners see the relevance
of what they are learning. Math learning for adults should be relevant to their
own personal goals, whether it be to attain a GED certificate, a job, or whatever.
"I think a lot of times people use the excuse 'Well, I don't need to know this.' But
maybe just pointing out to them why they need to know it, then it becomes more valuable
to them to know it." (learner)
Adult learners need to have a voice in what is taught in the classroom. A teacher
suggested, "The student has to 'buy into' the math item/concepts in order for her/him
to internalize them." The teacher may think something is important for the adults
to learn, but unless the learner sees the relevance to his own life, s/he finds little
value in the
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topic. This stakeholder further explained: ". . . To get a hook in
them [the student] and bring them along. Because I think once they see the relevancy
and understand what they can do, they will pursue it on their own. It becomes a mind
set for them to proceed to the higher levels of mathematics if they desire to. But
right now it is difficult. They have such low skills and they have been functioning,
at least in their estimation, fine in society. You know, if they don't have a checkbook,
'Why do I need to do it? I'll never have one.' They pay cash for their needs, everything
is done on a cash basis. So, in most cases, until they have a need to proceed to the next level or see that there is something beyond the level where they are already
at, they come with limited experiences in many cases." Whether teachers "hook" the
students or get them to "buy into" the math, adults will find the relevance when
the material is relevant to their needs and goals.
Use an interdisciplinary approach to teaching. Math should be an integral part of
other content areas. "Integrate math instruction with other literacy development
-- use reading and writing in teaching math and show that math content/skill (e.g.
reasoning, problem-solving) are vital to making sense of the world -- in other disciplines
and in the workplace and as citizens and parents." (teacher)
Link new math learning to previous learning. Linkages should be made with other math
concepts and skills as well as with other prior knowledge. A stakeholder suggested,
"We need to connect prior knowledge of the learner with formal instruction in math."
Not only should the new learning be connected to prior learning, but there should
also be a connection between knowing how to perform a skill and being interested
in performing that skill. "Shouldn't the whole thing, if you say you're not interested
in something, wouldn't it be easier to try a different style to get you interested in
that kind of stuff, from the teacher's perspective, to find out why you're bored
with it. You know, then go about a different teacher style that would make it easier
for you to learn, because once you start learning stuff, you get interested in it because,
I mean, the only reason you're not interested in it is because you don't know how
to do it. I mean, if you don't know how to do it, speak up and then there will be
someone there to help you. I mean, find a different way to make some difference and then
you won't have that problem, math especially, you've got to link it to something
else." (learner)
Teach concepts before rules. For example, teach the concept of area of a rectangle
as a counting of square units. The grouping of those units into rows and multiplying
units per row times number of rows is a shortcut that can be summarized in a formula, but formulas are easily forgotten with no connection to models, examples, experience,
etc., offered one teacher.
Help adults see the relevance of learning by seeing the "big picture". In SCANS'
terms, this would be considered the "Systems" competency, the ability to understand
how all the small pieces work in relation to the total system. When adults are shown
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how math skills are interconnected with one another, they begin to see relationships and
the relevance of what they are learning. This stakeholder explained how she learned
quicker by having the big picture: ". . . When we ran a business, I did most of
the accounting. I had no accounting background whatsoever, but when it is your own money,
you learn real fast. We were running a business and I was the office manager. But
he [husband] taught me how to do that by giving me the big picture. In a very short
time, I learned the concepts. You didn't have to go back and take an accounting class
because when you are dealing with it in real time with real things that have real
consequences, you learn pretty fast." And this stakeholder expressed his concern
about seeing the whole puzzle: "One of the concerns I've noticed . . .[is the] need to learn,
of seeing the whole puzzle before we put it together. [There] will always be a dilemma
taking a person from the known to the unknown. How can you show them the unknown in its entirety before you get there? What we are doing with people now is we are
telling designers before you design something, come and meet with the binders, meet
with the press person, meet with the pre-press person, as a team, so that you understand what the limitations and possibilities are. As far as math class, this is the dilemma
that we see in our industry -- taking people from the known to the unknown and giving
them a picture of what it's going to be when they get there."
Support teachers in making their classrooms more relevant and connected. Before the
curriculum can be changed and any of the above strategies implemented, teachers need
to be retrained. A stakeholder offered this recommendation: "We need to teach teachers to teach math concepts and connections rather than rules and to convince their
students of the importance of these. Some of the rules are not that important in
life, but their development is and transfers to solving problems on the job and in
life."
Connecting to the Four Purposes
Learner 1, "You use math almost every day of your life, everything you do practically."
Learner 2, "You don't think about it that often; it's just there.
Learner 1, "You just do it."
The conversation between two adult learners above illustrates how math skills play
a critical role in literacy. Whether it be to access information, to have a voice,
to act independently, or to prepare for the future, adults connect math to their
every day lives -- whether it be at work, at home, or in the community.
When adults see the relevance of math, they are able to use it to their benefit.
They are able to understand the wealth of information surrounding them and know what
pieces of information they need to access in order to solve problems. When adults
are able to make connections to everyday life and work situations, they are better equipped
to express their opinions and make informed decisions as this adult learner explained:
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" As a business man in a community, I use math everyday to run my business. Without it, my business would come to a standstill. I use it from controlling my inventory,
receivables, payables, and accounting. It is probably the most important aspect
to understand to run my business. Without having any math skills, it would probably
be impossible to run my business."
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