Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
METHODOLOGY
The ultimate goal of the Adult Numeracy Practitioners Network Planning Project was
to change adult numeracy education within larger reform of the ABE system. To accomplish
this, two objectives had to be met. First, the project would create opportunities
for teachers, stakeholders, and specifically, adult learners, to participate in the
discussion of math knowledge and skills needed by adults in their roles as parents,
workers, and citizens. The second objective was to develop a framework for math
content standards and an initial plan for system reform around adult numeracy. This project
was designed and executed with those two objectives in mind.
DEMOGRAPHICS
ANPN has involved hundreds of learners, teachers, and other stakeholders during this
project. We gathered data from seven states across the nation, for a total of nearly
300 individuals participating in some phase of data collection. (See appendix.)
Adult Learners
Twenty-one Learner Focus Groups from seven states participated in this project, including
six each from Illinois and Virginia, two from Ohio, one from each of the New England
states of New Hampshire, Vermont, and Rhode Island, and four from Oregon. There
were 171 adult learners, all of whom were enrolled in adult education mathematics
classes, participating in the Learner Focus Groups. Over half of the learners were
female (59% females). Almost three-quarters (71%) of the learners came from urban
areas rather than rural. Since a key role for adults is that of parent, it was interesting
to note that 69% of adult learner focus group participants were parents. There were
more unemployed than employed adult learners (60% unemployed).
Efforts were made to gather information from regions across the country as well as
diverse groups of learners. Of those adult learner focus group members, half were
white. About a quarter were African American (26%). Hispanics represented 12% of
the adult learners. Seven percent were Asian and 3% were Native American. The ethnic background
of two percent of the adult learners was unreported.
Adult learner focus groups came from a variety of adult education classes. Almost
half (49%) were participating in GED classes, while just over a quarter (26%) were
Adult Basic Education class participants. The other 25% of the adult learners were
involved in other adult education programs such as English for Speakers of Other Languages,
workplace, and developmental college courses.
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And, although data was not collected
on the number of adult learners who came from correctional institutions, three adult
learner focus groups were held in correctional facilities.
Stakeholders
In January and February, five Stakeholder Focus Groups were held in various parts
of the country. The states of Illinois, Massachusetts, Ohio, Oregon, and Virginia
were represented. Most of the 61 stakeholders were in roles involved directly or
indirectly with adult education, training, or employment. Included were state and municipal
administrators/policy makers, college and university personnel, staff developers,
and publishers. Those employers who were involved in the focus groups represented
food services, and the automobile and printing industries.
Data was also collected over a period of time from a "Virtual" Study Group. This
group consisted of a mixture of teachers and stakeholders directly involved with
adult education. There were a total of 21 "Virtual" study group participants, including
researchers, graduate students, adult and mathematics educators from across the world,
who communicated via a closed electronic discussion network.
Teachers
Data for this project was collected from five Study Groups. Forty-one teachers came
from the four states of Illinois, Ohio, Oregon, and Virginia as well as a New England
Regional Math Group with representatives of all the New England states. These adult
education teachers came from a variety of settings: community colleges, correctional
facilities, school districts (Local Education Agencies), and community-based organizations.
Although it appears that adult education teachers represent the smallest group in
the data collection, The Massachusetts ABE Math Standards project was also considered
as a data point. This project involved 22 adult educators from Massachusetts. Through
the NUMERACY Electronic list and The Math Practitioner newsletter, the general membership
of ANPN were also invited to respond to the Study Group Questions.
PROJECT DESIGN
There were many layers of participation from the initial design of the project to
the final draft. The design included a Working Group, a Teacher Study Group for each
region, a Stakeholder Focus Group for each region, a Virtual Study Group, and at
least two Learner Focus Groups per region. Each of these groups pro-
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vided data for the project
with different groups having different levels of responsibility to the project.
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The Working Group consisted of representatives from each of the regions chosen to
participate in the project. The five regions/states -- New England, Illinois, Oregon,
Virginia, and Ohio -- were selected because they already had active Math Teams connected to ANPN. Members of these Math Teams were to be used as a basis for choosing the
Study Groups. Early in October 1995, the Working Group was asked to begin to think
about the make-up of their own Study Group members. Membership would include interested Math Team members and also a key regional stakeholder.
In late October the Working Group held its first of two meetings to begin to map out
the work ahead of them. The Group left the first meeting with a sense of the protocol
for collecting data. The Working Group, with feedback from their Study Group members, actively participated in the formulation of the focus group questions.
Focus Group Questions
Focus Group questions were developed using input from the Working Group and each Study
Group. The Focus Group Questions for the learners and stakeholders were very similar.
For stakeholders, we wanted to know how they themselves viewed and applied math
as well as what math skills they felt were needed by employees.
Each Learner Focus Group began with an ice breaker math autobiography activity where
each learner was asked to respond to the following questions: "Where did you learn
math?" "What was the BEST learning situation for you?" "Who was involved?" "What
was a frustrating situation?" "Who was involved?"
The Stakeholder Focus Groups were asked to think about a time when they were learning
math: "What were you doing?" "Where were you?" "How did you feel?" "What skills
were you using?"
After the icebreaker, Focus Group participants were asked to respond to the following
four questions:
- Please describe a time that you made a decision using amounts, money, measurement,
graphs, or another kind of math. What was the decision? How did you make it? What
did you do? What skills did you use?
- (Learner Groups) What math skills to you need to be successful as a:
parent or family member?
worker?
community member?
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(Stakeholder Groups) What math skills do you (and/or your employees)
need to be successful as a:
parent or family member?
worker?
community member?
- Working in groups of three, please look at the following math topics, then pick the four most important and order them from most important to least important. You can add any other topics that you think are important that are missing. You can also t
ake out any topics that you don t think are important. You should agree on the top four in your group. Be ready to explain why you picked these four topics and why you ordered them the way you did. The topics were: Problem-Solving, Communicati
on,
Reasoning, Estimation, Decimals, Fractions, Percent, Algebra, Measurement, Whole Number Computation, Patterns and Relationships, Statistics and Probability, and Geometry and Spatial
Sense.
- What recommendations do you have for improving basic skills/workforce development/family literacy/workplace education (etc.) math instruction and programs?
In January 1996, the seemingly overwhelming task of convening focus groups began.
Focus groups were run by Study Group members. The protocol required that two individuals
share the task of running each focus group -- one individual to ask the questions
and guide the discussion and the other to take notes. The protocol also specified
that each focus group be tape recorded. Later, all the discussions were transcribed
and forwarded to the product coordinator. All quotes by focus group members were
to be verbatim. (See appendix.)
Analyzing the Results
In each region, as learner focus groups were completed, the Study Group met to conduct
an initial analysis of their data. Topics were noted and discussed by the group,
then coded after consensus was reached.
By early March all learner focus groups had met, the data initially analyzed by the
Study Groups and forwarded to the product coordinator. Also, each region had conducted
one Stakeholder Focus Group and forwarded the data.
The two project co-directors and the product coordinator then met to compile all five
regions' data. Thematic topics sometimes varied from region to region, especially
those in more rural areas as compared to more urban areas. The data was combined
and recoded in order to look at the data as a whole rather than regionally. Using the
coding from the Study Groups as well as our own, we
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found several overall thematic
areas. The five areas were Empowerment, Math Content and Skills, Using Math, Ways
of Learning and Teaching, and System Reform. Each of these five areas were then further coded.
(See appendix.)
The data, after being initially coded, was then entered into one large data pool.
Because we wanted to ensure that whole thoughts were captured, we used a simple
coding method to identify region and focus group number at the end of each data item.
At the beginning of each data item, we coded for major themes. Because a quote often included
themes from more than one area, all data bits were cross-referenced. For example,
a comment made by a learner may have included bits of information focusing on Empowerment, Ways of Learning/Teaching, as well as on the Content area of Algebra. The
quote, therefore, would be found under three areas: Empowerment, Ways of Learning/Teaching,
and Content.
In late April 1996, the Working Group again met. At this meeting they were divided
into groups and given all the data for a particular theme. Since there were five
major themes, but many sub-topics under each theme, we decided to use the four key
math topics that were chosen by focus groups as being most important. (See focus group question
3). These four topics were Communication, Problem-Solving, Whole Numbers and Estimation.
(For complete results of the prioritization, see the Appendix.) Each group chose one topic to further analyze the data from learners, stakeholders, and teachers.
After looking at the focus group data, they were then tasked to review other sources
-- The Massachusetts ABE Math Standards, SCANS, Equipped for the Future -- and come to consensus about what was being said about the topic. Their task was to arrive
at five key points that reflected all the data sources. Each of the five key points
had to be substantiated by specific documentation from the data. (See appendix for
direction sheets.)
Later, each of the regional Study Groups had an opportunity to participate in the
same process but with the five content math skills groupings: Algebra/Patterns and
Relationships, Fractions/Decimals/Percents, Measurement/Time, Probability/Statistics/
Graphing, and Geometry/Spatial Sense.
The feedback from the Working Group and the Study Group was then collapsed into three
process themes and four content themes which serve as a framework for standards.
The three process themes are Communication, Connections/Relevance, and Problem-Solving/Reasoning/Decision-Making. The four content themes are Number and Number Sense, Algebra:
Patterns and Functions, Geometry: Spatial Sense and Measurement, and Data. Number
includes whole number operations, estimation, money, and fractions/decimals/percents. Algebra: Patterns and Functions is a combination of algebra and patterns and
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relationships.
Geometry: Spatial Sense and Measurement includes measurement, geometry, and spatial
sense. Data involves probability, statistics, and graphing.
In addition to the three process and four content themes, a good deal of the data
categorized as mathematical empowerment provided us with a set of affective issues
which continually emerged. These issues include learner self-confidence, attitudes
about mathematics, and beliefs about what one can or cannot accomplish in mathematics.
After much discussion about the title of this section, we finally came to a consensus
that when adults talk about the affective aspect of math, they are referring to their
self-confidence in doing math and their sense of competency around tasks involving math.
Therefore, the section on adults' feelings and attitudes about math has been titled "Competence and Self-confidence."
Copies of all the primary documents (verbatim transcriptions of the focus groups,
notes of study group meetings, and coding) are on file at World Education.
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