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Knowing Math and Passing the GED
Sally Spencer
Care Center, Holyoke
I have been the math teacher at the
Care Center, a school for pregnant and parenting teenage mothers
in Holyoke, for a little over a year. This by no means makes me
an authority on evaluation in the adult mathematics classroom. But
as a member of the ABE Math Team, I’ve had the opportunity
to think about it a lot lately. I’d like to share some ideas
and some questions.
In November, the ABE Math Team received a grant from the National
Institute for Literacy through Holyoke Community College. The purpose
of this grant is to review and adapt the National Council of Teachers
of Mathematics’ Curriculum and Evaluation Standards for
School Mathematics (the Standards) for the adult education community.
To accomplish this, the ABE Math Team has sub-divided into workgroups
focusing on either the ESL, the ABE, the GED classroom or workplace
education. It is through participating in the ABE Math Team that
I have been focusing my attention on the “Evaluation Standards”
at the GED level.
The Standards were written as a response to the publication
in 1983 of A Nation at Risk which made it clear that the
mathematics education which the nation’s students were receiving
at that time was inadequate. Over three years, mathematics educators
from across the nation wrote, tested, revised and, in 1989, finally
adopted the Curriculum and Evaluation Standards for School Mathematics.
The Standards reflect a new vision of what it means to “do”
and “know” math. In its introduction, the Standards lists
its societal goals as: mathematically literate workers; a citizenry
of lifelong learners; opportunity for all learners; and an informed
electorate. For the individual student, that means it is no longer
enough to be arithmetically proficient. Instead, the Standards
hope to ensure that students will: learn to value mathematics; become
confident in their own abilities; become mathematical problem solvers;
and be able to communicate and reason mathematically. To that end,
the Standards have repriori-tized the emphasis on various
topics in math instruction, and stress new methods of teaching and
evaluation. The curriculum is separated into three sections: grades
K-4, 5-8 and 9-12; evaluation is the final fourth part.
So how can this national mathematical movement be incorporated
in the ABE classroom? How does that impact assessment? What does
this mean for the adult learner?
| “The vision of mathematics education in the standards
places new demands on instruction and forces us to reassess
the manner and methods by which we chart our student’s
progress. In an instructional environment that demands deeper
understanding of mathematics, testing instruments that call
for only the identification of single correct responses no
longer suffice. Instead, our instruments must reflect the
scope and intent of our instructional program to have students
solve problems, reason and communicate. Furthermore, the instruments
must enable the teacher to understand student’s perceptions
of mathematical ideas and processes and their ability to function
in a mathematical context. At the same time, they must be
sensitive enough to help teachers identify individual areas
of difficulty in order to improve instruction.” (NCTM
Standards). |
Some of the issues which I have been able to identify which make
evaluation in the GED classroom distinct from the traditional K-12
setting are:
- grading is not an issue in the adult classroom;
- intake evaluation is an essential component for admission to
the GED classroom;
- many adult students bring to the classroom a fairly traditional,
narrow and rigid preconception of what it means to “know”
math, and a long history and a strong sense of their own abilities
(or disabilities) within the context of that definition; and,
most importantly,
- the ultimate evaluation for the GED student is successful completion
of the state administered GED exam.
How do these differences affect the evaluation standards? I confess,
I am one of the converted. I believe strongly in the vision of the
math class as advocated by the NCTM. As part of my work with the
ABE Math Team, I have adapted from page 191 of the Standards the
following NCTM evaluation guidelines for the GED classroom:
| Increased Attention
Assessing what students know and how
they think about mathematics
Having assessment be an integral part of teaching correct
answers
Focusing on a broad range of
mathematical tasks and taking and a holistic view of mathematics
Developing problem situations that require the applications
of a number of mathematical ideas
Using multiple assessment techniques, including written,
oral and demonstration formats in individual and in group
Using calculators, computers and
manipulatives in some assessment
Using the standardized GED test as
only one of many indicators of progress
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Decreased Attention
Assessing what students do not know
Having assessment be simply counting
Focusing on a large number of specific isolated skills
Using exercises or word problem requiring only one or two
skills
Using only individualized written exercises and tests, because
group work is cheating
Excluding calculators, computers, and manipulatives from
all assessment
processes processes
Using the standardized GED test as the only indicator of
success |
Admittedly, while these are worthwhile goals to promote students’
growth as informed citizens and empowered mathematicians, it is
equally essential that teachers do not ignore their GED student’s
priorities. Passing the GED test, which still tests for “single
correct responses”, is the primary goal of the GED student.
The goals of developing a problem solving attitude, being able to
communicate in mathematical terms, being able to reason mathematically
and being able to see mathematical connections to their everyday
life can seem, at best, secondary to the students and, at worst,
irrelevant to them.
I believe it is important to allow time in the GED mathematics class
to discuss these additional goals so that the students have a chance
to voice their expectations and identify and incorporate these new
ideas of what it means to “know” math, while at the same
time acknowledging that passing the GED test is a long-term objective.
I am planning to continue to explore ways to resolve this dichotomy.
My next question in this quest is: what kinds of assessment instruments,
both formal and informal, can I find or develop to help bridge the
gap between promoting, reasoning, communicating and making connections
and “getting-the-right-answer” on the GED test?
Editor’s note: Please write to Sally c/o Adventures in
Assessment your thoughts, ideas, or assessment instruments that
explore this dichotomy in teaching math in a GED setting. If you
have some experience with math assessment not at the GED level,
we welcome hearing from you as well.
Originally published in Adventures in Assessment,
Volume 4 (April 1993),
SABES/World Education, Boston, MA, Copyright 2003.
Funding support for the publication of this document
on the Web provided in part by the Ohio State Literacy Resource
Center as part of the LINCS
Assessment Special Collection.
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