Volume 4, Issue B ::: September 2000

# Developing Adults' Numerate
Thinking:

Getting Out From Under the Workbooks

## The author makes a case for substantive change in how and what we teach in mathematics

**by Mary Jane Schmitt**

*
The standard-bearer of basic math instruction in adult basic education (ABE) and
preparation for the tests of General Educational Development (GED) has long been the consumable student workbook.
It is not hard to understand why. Workbooks are relatively inexpensive. They are
logically incremental and modular, usually with one or two pages devoted to a
narrow topic. They place minimal demand on teachers by posing no open-ended
questions or investigations; rather, each problem has one and only one right
answer, which can be readily checked by the student in the back of the book. For
the most part, the mathematics content focuses on standard computational rules
(algorithms) with whole numbers, fractions, decimals, percentages, and prealgebra.
Adults learn paper and pencil computational processes and symbol
manipulation on routine repetitive problems. These problems are then followed by
"real-life applications" or word problems whose reason for being seems to be
that they provide more opportunities to practice the algorithm. As a result,
success in the adult education math class is defined as the ability to follow
successfully a sequence of rule-based instructions that can be matched to
one-step or two-step word problems.*

Some may think this affords a benign and reasonable way for adults returning to school to learn math at their own pace, to keep track of where they are, and to feel a sense accomplishment from plowing through pages of a workbook. I disagree. Used as the primary resource, workbooks are anything but benign: they promote not a second chance but a second-rate education for students wanting to learn math. It is second rate because the mathematical demands of the world inhabited by adults are not sufficiently emphasized. Nor do the workbooks take into account the diverse characteristics of learners and how their rich understandings and usable skills develop. And finally, they put forth a restricted view of the learning process itself. Most workbooks implicitly promote a myth that rule-based math is most important, that adults all learn the same way, and that learning happens by transmission. It is a simplistic and erroneous view of the way in which mathematical thinking develops. To improve adult math education in ABE, these three myths need to be seriously challenged.

**Challenging the Math Status Quo**

A growing of body of work emphatically challenges the ABE/GED math status quo. A group of seven recently published and/or released policy and research documents has the potential of moving us beyond the basics toward a more realistic, flexible, and adult-centered mathematics curriculum. Taken together, these seven serve as a rich resource for updating the mathematical content of adult basic education. None of these documents abandons the "basics" but they do redirect the emphasis on what the basics are. And while their underlying messages are similar, each document contributes uniquely to a new mission for ABE/GED mathematics instruction.

Some of the documents put an emphasis on "adult" in the
"lived-in world." The * SCANS Report *
(1991) and * Equipped for the Future Content Standards: What Adults Need to
Know and Be Able to Do for the 21st Century* (2000) are grounded in data
gathered from the workplace and from adults in their roles as workers, parents, and community members.
They emphasize mathematics as a tool for decision-making and problem-solving. In
these documents, mathematics is the subtext that weaves through the larger
picture of adults (as * Equipped for the Future * would put it) gaining access to
information, expressing ideas, acting independently, and bridging to the future.
Curricula developed within these frameworks tend to present problem situations
to which people are expected to bring their
full set of skills. In these curricula, isolated mathematics topics are
not emphasized. It is never math for math's sake, but math to aid in the
accomplishment of a larger task.

Another group of documents is based on theories, research, and
practice centered around children's mathematical thinking. The National
Council of Teachers of Mathematics' * Principles and Standards for
School Mathematics* (2000) and
its predecessor, * Curriculum and Evaluation Standards for School Mathematics *
(1989), put an emphasis on understanding over rule-based learning
in support of the development of problem-solving and decision-making
skills. This emphasis is supported by a body of research that draws heavily upon the Piagetian tradition that
knowledge requires a process of active construction and the Vygotskian emphasis
on sociocultural aspects of learning. These ideas found their way into some adult education math classes when, in
1994, a group of Massachusetts ABE, GED, English for speakers of other languages (ESOL), and workplace education teachers
studied the K-12 publication and wrote an adapted version entitled * The Massachusetts ABE Math
Standards*. They implemented them in various adult basic
education settings (Leonelli & Schwendeman, 1994). Their report provided the
basis for the curriculum frameworks adopted by the Massachusetts adult basic
education community. Embracing the vision of the NCTM *Standards*, some Massachusetts
teachers began to insert new topics and strategies into their classrooms,
emphasizing communication, problem-solving, reasoning, and connections to other
disciplines.

Other documents also connect "adult"
with "developing mathematical thinking." SCANS and * Equipped for the
Future * are grounded in considerations of the skills embedded in adult
roles; the NCTM documents are situated in
research into how children's mathematical thinking develops. Both
movements offer important guidance for ABE math education, but neither alone is
sufficient. We need to take into account what we know about

the mathematical demands on adults as well as what we know about
the development of mathematical thinking. One document that draws from
both is the practitioner-developed * A Framework for Adult Numeracy
Standards: The Mathematical Skills and
Abilities Adults Need To Be Equipped for the Future * (Curry, Schmitt, & Waldron, 1996). Its message is focused directly on ABE and
GED programs across the nation about the "honest list" of what adults need
to know in math in their roles as workers, parents, and community members. It
organizes that list into categories that reflect the mathematics education
community.

**What About the GED?**

That is all well and good, but what about the GED? After all,
passing the GED is a major goal of students and thus drives much of mathematics
curricula. Adult educators should note that the new GED * 2002-Test Series * is
strongly influenced
by the NCTM *Standards*.
The content of the upcoming test will be aligned, and appropriately so, with the
emphasis on algebra and patterns, data analysis and statistics, geometry and
measurement, as well as number sense. The inclusion of a
scientific calculator as a tool on part of the test symbolically releases ABE
from the "drill and kill" of workbooks to
more of an emphasis on the importance of estimation and problem-solving.
We can look at the new GED as an opportunity for ABE/GED programs to rethink the
mathematics curriculum in a way
that is not inconsistent with any of the aforementioned documents.

Finally, I will include a document that adds a new wrinkle to the discussion and suggests that the focus for adults
should not be on "school math" but on "numeracy."
A recent working paper conceptualizing the assessment of numeracy skills in the
adult population is part of the international * Adult Literacy and Lifeskills
Survey Numeracy Framework Working Draft * (Gal, van Groenestijn, Manly, Schmitt,
& Tout, 1999). The paper says that numeracy is the bridge between
mathematics and the real world. In considering the mathematical demands that
adults are faced with and the skills needed to meet those demands effectively,
the authors have arrived at a definition for adult "numerate behavior."
Numerate behavior, they posit, is observed when people manage a situation or
solve a problem in a real context; it involves responding to information about
mathematical ideas that may be represented in a range
of ways; it requires the activation of
a range of enabling knowledge, behaviors, and processes" (p. 11).

Numeracy, in this framework, has to do not only with quantity and number but also with dimension and shape, patterns and relationships, data and chance, and the mathematics of change. People identify, interpret, act upon, and communicate about this mathematical information in various ways. The authors - of whom I am one - have attempted to turn this multifaceted definition into test items to be used in a household survey to assess the distribution of skills in the adult populations of participating countries. This treatment of numeracy has the potential to redirect the ABE/GED emphasis from school math to a subject more closely connected to authentic, real-world mathematical demands.

In these seven documents, is there one message or many messages?
What kind of coordinated guidance can these documents, taken together, offer
adult basic education mathematics instruction? None of them has the full
message. Each provides an essential component to help
us improve service delivery radically. Taken together, the message that comes
through can be summarized as follows:

**1.** Adult
basic education and GED mathematics instruction should be less concerned with
school mathematics and more concerned with the mathematical demands of the
lived-in world: the demands that adults meet in their roles as workers, family
members,
and community members. Therefore we need to view
this new term * numeracy* not
as a synonym for mathematics but as a new discipline defined as the * bridge that
links mathematics and the real world*.

**2.** Adult basic education and
GED mathematics instruction need
to draw upon * what is known about
the development of children's mathematical thinking * and extend that research
to address the development of adults' numerate thinking and practice.

Putting these two messages together, I propose their summary
into a major mission statement for adult
basic education: * the development of adult numerate thinking*.

**And so . . .**

This brings me back to my opening
volley. The ideas represented in these seven documents and * the development of
adult numerate thinking * are systemically under-represented in our instructional
materials. They are missing as well in our methods, assessments, teacher
development, research agenda, and program and national policies. It is going to
take much more than replacing the word math with the word numeracy. It is
heartening
that the newly proposed National Reporting System (Pelavin Research, 2000)
includes a list of numeracy skills, but disappointing that the list looks more
like the table of contents of a traditional workbook than any
of the seven documents. As the workbooks do, the April 2000 draft
of the NRS holds adult education accountable for a very limited set
of numeracy skills. Adults who come to our programs deserve and need much more.
It is my hope that the ABE delivery system can heed
their own documents and put the principles into practice. Otherwise the math
curriculum in ABE will remain as uninspiring
as the table of contents of the nearest workbook.

**References**

American Council on Education (forthcoming). * GED 2002- Test
Series*. Washington, DC: GEDTS.

Curry,
D., Schmitt, M.J., & Waldron, S. (1996). * A Framework for Adult Numeracy
Standards: The Mathematical Skills and Abilities Adults Need To Be Equipped for
the Future*. Boston, MA: World Education.

Gal, I., van Groenestijn, M., Manly, M., Schmitt, M.J., & Tout, D. (1999).
* Adult
Literacy and Lifeskills Survey Numeracy Framework Working Draft*. Ottawa:
Statistics Canada.

Leonelli,
E. & Schwendeman, R. (eds.) (1994) * The ABE Math Standards Project, Vol 1:
The Massachusetts Adult Basic Education Math Standards. * Holyoke, MA: Holyoke
Community College/SABES Regional Center.

National Council of Teachers of Mathematics (1989).
* Curriculum and Evaluation Standards
for School Mathematics*. Reston, VA: NCTM.

National
Council of Teachers of Mathematics (2000). * Principles and Standards for School
Mathematics*. Reston, VA: NCTM.

National
Institute for Literacy (2000). * Equipped for the Future Content Standards: What
Adults Need to Know for the 21st Century*. Washington, DC: NIFL.

Pelavin Research Center (2000). * National Reporting System for Adult Education
Guidelines. * Washington, DC: American Institute for Research.

Secretary's
Commission on Achieving Necessary Skills (1991). * What Work Requires of Schools:
The Report of Secretary's Commission on Achieving Necessary Skills*.
Washington, DC: US Government Printing Office

**About the Author**

*Mary Jane Schmitt * is a National Center for the Study of Adult Learning and Literacy
(NCSALL) fellow at the Harvard University Graduate School of Education. She is a
member of the Adult Literacy and Lifeskills Survey's Numeracy Team and
co-director
of the (Extending Mathematical Power (EMPower)
Project at TERC, Cambridge, MA.

**Further
Reading**

*The
seven documents discussed in this article can be found at these web sites.*

·
*A Framework for Adult Numeracy Standards: The Mathematical Skills and
Abilities Adults Need To Be Equipped for the Future* (Adult Numeracy
Practitioners Network, 1996): http://www.std.com/anpn/framewkTOC.html

·
*ALL Numeracy Framework Working Draft *(National Center for Educational
Statistics and Statistics Canada, 1999): http://nces.ed.gov/ilss/

skills_domains.asp#numeracy

·
*Equipped for the Future Content Standards: What Adults Need to Know for the
21st Century *(National Institute for Literacy, 2000): http://www.nifl.gov/nifl/eff.html

·
*GED 2002- Test Series *(American Council on Education, forthcoming):
http://www.bhef.com/calec/ged/test2002-A.html#test5

·
*Massachusetts Adult Basic Education Math Standards *(SABES, Holyoke
Community College, 1994): http://www2.wgbh.org/MBCWEIS/

LTC/CLC/abemathhomepage.html

·
*Principles and Standards for School Mathematics *(National Council of
Teachers of Mathematics, 2000): http://standards-e.nctm.org

·
*What Work Requires of Schools: The Report of the Secretary's Commission on
Achieving Necessary Skills *(Secretary's Commission on Achieving Necessary
Skills, 1991):
http://www.ttrc.doleta.gov/SCANS