A Framework for Adult Numeracy Standards:


The Mathematical Skills and Abilities Adults Need

To Be Equipped for the Future



The terms "mathematical literacy" and "numeracy" are used interchangeably in this document. Both terms should be viewed as loosely referring to the aggregate of skills, knowledge, beliefs, patterns of thinking, and related communicative and problem-solving processes individuals need to effectively interpret and handle real-world quantitative situations, problems, and tasks. (Proceedings of the Conference on Adult Mathematical Literacy, March, 1994)

INTRODUCTION



In October 1995, the National Institute for Literacy (NIFL) funded eight planning grants for system reform and improvement as part of the Equipped for the Future (EFF) project. World Education, Inc., in cooperation with five state literacy resource centers, accepted the grant on behalf of the Adult Numeracy Practitioners Network (ANPN). The purpose of the ANPN Planning Grant is to begin the work of developing Adult Numeracy Standards for adult basic education. We are augmenting previous work done in this area (e.g., NCTM, SCANS, Massachusetts ABE Math Standards) by interviewing adult learners, teachers and other stakeholders.

This project, while furthering the work of other projects, was exciting in that the voices of the adult learner as well as stakeholders were added to the mix. Based on all the voices along with the work done previously in the area of adult numeracy, the following seven themes emerged and serve as the foundation for adult numeracy standards:


Along with the seven themes noted above, adult learner and stakeholder voices also gave us greater insight into affective issues. A section on Competence and Self-confidence was added to ensure that adults' voices were heard and their feelings considered as this document is read.
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We not only asked adults what they need to know and be able to do to be productive citizens, workers, and parents, but also we encouraged the adults we spoke with to share their opinions on how math instruction should be changed. Adult learners shared how math instruction should be changed in the classroom while stakeholders tended to look at system reform issues. From the uniformity of voices of adults across the country, Recommendations for System Reform have been drafted and are reflected in the final chapter of this document.

What We Need Is an Honest List!

In March, 1994, over 100 adult educators, mathematics educators and other stakeholders in the field of adult education and training came together for three days to discuss the topic of adult numeracy. One of the major suggestions of the Conference on Adult Mathematical Literacy was that an important next step would be to develop an honest list of the skills and knowledge that adults really need to be mathematically literate. The participants called for a serious rethinking of the content and relevance of the adult basic education mathematics classes as they are currently taught. Through analysis of the mathematical demands on adults in today s society, educators can refocus the adult numeracy curriculum in a meaningful way.

A Massachusetts cohort of adult education teachers, inspired by the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics, had already begun this task in earnest. However, because the cohort reflected the input of teachers only, many participants at the conference felt that more research was needed. That research should include consideration of data from the Secretary's Commission on Achieving Necessary Skills (SCANS) Report, other recent documents, employer and community needs assessment, and especially the opinions of adult learners.

In this report, our grassroots organization formed at the conference, the Adult Numeracy Practitioners Network (ANPN) will bring together essential documents and the many voices of adult learners, teachers, and employer and community stakeholders. Through the Equipped for the Future Initiative, an ANPN working group was encouraged by the National Institute for Literacy to carefully listen to the data by analyzing the transcribed tapes of twenty-one learner focus groups, five stakeholder focus groups, and five teacher study groups. In addition, the ANPN working group examined pertinent documents such as Equipped for the Future, the SCANS Report, the 1994 Conference Proceedings, the NCTM Standards, and The Massachusetts ABE Math Standards (See Table 1).

The ANPN working group was struck by the fact that all the voices -- from SCANS to The Massachusetts ABE Math Standards to the focus group partici-

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pants -- resonate, all be it with diverse perspectives. It is this resonance that must and will guide our honest list .
Table 1 Putting Together the Honest List


Responding to SCANS Research

The SCANS Report for America 2000, What Work Requires of Schools lists the following foundation skills :

  1. Basic Skills: reading, writing, mathematics (arithmetical computation and mathematical reasoning), listening, and speaking;
  2. Thinking Skills: creative thinking, making decisions, solving problems, seeing things in the mind s eye, knowing how to learn, and reasoning; and
  3. Personal Qualities: individual responsibility, self-esteem, sociability, self- management, and integrity.


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The basic skills are the irreducible minimum for anyone who wants to get even a low-skill job . . . the thinking skills, by contrast, permit workers to analyze, synthesize and evaluate complexity. (SCANS, p. 17)

SCANS holds that even these foundation skills are not enough. They must be integrated with other kinds of competencies to make them fully operational. Competencies such as managing or using resources, interpersonal skills, information, systems, and technology are needed by everyone from the entry level or unskilled worker to managers and executives.

The seven adult numeracy themes in our Framework reflect this "more than the basics" slant. Relevance/Connections, Problem-Solving/Reasoning/ Decision-Making, and Communication combine with the four content areas of Number and Number Sense, Data, Geometry: Spatial Sense and Measurement, and Algebra: Patterns and Functions to deliver an up-to-date, SCANS-friendly definition of mathematical literacy.

Building upon The Massachusetts ABE Math Standards

The Massachusetts ABE Math Standards posited Problem-Solving, Communication, Reasoning, and Connections as the four over-arching standards for mathematical literacy. Through ANPN s further research, these four standards, often referred to as process standards, were consolidated into three adult numeracy themes: Relevance/Connections, Problem-Solving/ Reasoning/Decision-Making, and Communication. Responses showed that it was difficult for individuals to differentiate between problem-solving and reasoning, both key skills in decision-making. Our data also revealed that the issue of relevance frequently occurred.

The remaining seven MA ABE Standards have been integrated into four adult numeracy content themes. Number and Number Sense includes two MA ABE standards, Estimation and Number, Operations, and Computation. Data is similar to the MA ABE standard called Statistics and Probability. Geometry: Spatial Sense and Measurement incorporates two MA ABE standards, Geometry and Spatial Sense and Measurement. Two MA ABE standards -- Patterns, Relationships, and Functions and Algebra -- correspond to the adult numeracy theme, Algebra: Patterns and Functions. This reorganized structure is a reflection of the words of adult learners, teachers and stakeholders as they told us about the math that they need and use.

The final standard of The Massachusetts ABE Math Standards is Evaluation and Assessment. The Framework for Adult Numeracy Standards, while not choosing to include a separate theme to address these topics, addresses assessment under System Reform. Many focus group participants saw evaluation and assessment

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as issues that need to be approached through system reform efforts.

Connecting to Equipped for the Future s Four Key Purposes

The Equipped for the Future (EFF) project focused on goal 6 of the National Education Goals which stated: By the year 2000, every adult American will be literate and will possess the knowledge and skills necessary to compete in a global economy and exercise the right and responsibilities of citizenship. When asked what they needed to compete in a global economy and exercise the rights and responsibilities of citizenship, adult learners responded with four key purposes:


The Framework for Adult Numeracy Standards supports these four key purposes through the seven adult numeracy themes. Literacy for Access and Orientation includes access to the broader world of ideas and opportunities that surround them and they know literacy -- including the ability to work with numbers as well as read and write for themselves -- is the price of the ticket. (Equipped for the Future, p.11) The four content themes: Number and Number Sense; Data; Geometry: Spatial Sense and Measurement; and Algebra: Patterns and Functions provide access to the world of mathematical thought. Literacy as Voice refers to adults ability to communicate to others what they think and feel. The Communication theme addresses this issue and is considered a key process that is integrated in all other math areas. Literacy for Independent Action reflects adults desires to be able to act independently and make informed decisions. All focus group participants in the Adult Numeracy project could clearly describe how decisions were made involving math. The process theme Problem-Solving/Reasoning/ Decision-Making is an outcome of their comments. The fourth key purpose -- Literacy as a Bridge to the Future -- explains why adults participate in adult education programs. They realize that education is a key to future success, not only for themselves but for their children. Over and over again, the adult learners in our project shared that a key reason for wanting to learn math was to help their children be successful. In essence, they saw the importance of our third process theme, Relevance/Connections.

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The ANPN Planning Project for System Reform sought to discover what math adults needed to accomplish the EFF key purposes in the roles as parent, worker, and citizen. Focus group participants were specifically asked what math they need to know and be able to do in order to be successful in their roles as parent, worker, and citizen. The feedback from these questions is integrated throughout the Framework for Adult Numeracy Standards. Table 2, on the following page, compares ANPN s Numeracy Themes with The Massachusetts ABE Math Standards, Equipped for the Future, and SCANS.


How Much Closer to the Honest List Are We?

This document is not a set of standards, but a framework for developing standards. Sometimes one has to step back before really going forward. The ANPN is being true to the data collected. Through this project, ANPN has spent an enormous amount of time listening to learners, teachers, employers and other stakeholders in a systematic, structured manner. This has given us a rich base from which to derive the honest list , the next step.
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Table 2 Comparing the Documents

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.

Project Design

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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:
  1. 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?

  2. (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?

  3. 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.

  4. 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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