Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
GEOMETRY: SPATIAL SENSE AND MEASUREMENT
I need math when I redid my house, measuring dry wall. That was a problem but we
did it. How much did I need? How much to go buy? ... I cut dry wall to remodel
my kitchen. When we put it up it didn't fit. It's uneven but most people can't
tell.
Overview
As told by the learner quoted above and noted in The Massachusetts ABE Math Standards,
"adult learners who attend basic mathematics classes at any level share a wealth
of pragmatic experience surrounding geometric and spatial concepts. They've probably
built a bookcase, laid out a garden, applied wallpaper or tiled a floor, all the while
discovering informally the rules which formally govern the study of geometry itself.
For many adult students, geometry is one math topic that immediately makes sense
to them and gives them confidence in their ability to learn." (p. 51) It is also true,
however, that many adults associate geometry, like algebra, with failure. "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." And "the hardest
part for me is geometry."
Measurement, a foundation skill for geometry, is also an essential life skill, one
that adults use in many different but familiar contexts: "on-the-job, for home improvement
projects, in the daily task of food preparation." ( Massachusetts ABE Math Standards, p. 53) Or as one learner states, "Measuring. You can put it under workplace,
family. You're always measuring something. You can be at home or stuff where you're
measuring out ingredients, whatever, like cooking.
Key Findings
Measurement is not an end in itself. It is a tool used in many contexts: home, work
and community. We measure many different attributes of physical objects and time
in many different ways in many different situations and contexts. As learners state,
Measuring, well, cough medicine, anything like that. Temperature, yeah. You re not
using it, but it s on the thermometer, so that s a form of math. 98.6 is normal,
right? So that s math. And When I worked in a factory, we made fan belts ... We
had to measure them if they re too long or too short. We had to use a cutting machine to
adjust, if too long or too short. What I had to do if they were too long, I had
to cut em or sew em together ... measured by two sticks to check if they were right.
Measured in meters I think it was. And During the windstorm our fence got blown down.
We had to go back out, measure everything, and, you know, put it up. How far apart
everything would be and then figure out how much fencing we needed.
48
Measurement is essential to our sense of ourselves and our orientation to the world.
For example, as one teacher states, I work with 80% welfare mothers, 20% low income
... They work with people in nursing homes ... Some don t have that concept, measurement. They have to do measurement. How tall someone is. How much they weigh. 5'10"
can be like 4'10" to them. Kind of things we take for granted about how we see our
world. We try to bring them to something that s real in their lives so that they
will tie into it and try to generate some trust in that.
Because measurement is used so often and in so many contexts, many learners have great
confidence in their measurement skills. For example, We sell fry food and chicken
and fish. The fish, we sell a lot of fish, fried fish. For example, the fish is
$3.99 a pound. And the people say, I want $15. I don t have to go to machine and
check how many pounds is $15. We think and we fry a lot of fish and we separate
and exactly for the customer $15. I do that every day. And, I am night manager
in a restaurant, so I have to order every night. I have to do a balance for everything. Everything
by the pounds, like sugar. See how many pounds I have and how many pounds I need
to order.
For ESOL learners, teaching measurement is very important as a cross-cultural component
of mathematics and second language learning, since many of these learners have used
the metric measurement system much more than the U.S. system. For example, as one
learner states, In addition, it s very difficult for us to use the American system.
I think about mathematic, and American system about labor, pounds, miles, yards,
because in European you have metric system. I heard United States try to change
to this sys |
