Review of the Literature in Adult Numeracy: Research and Conceptual Issues

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American Institutes for Research®

A Review of the Literature in Adult Numeracy: Research and Conceptual Issues

Prepared By:
The American Institutes for Research®

1000 Thomas Jefferson Street, N.W.

Washington, D.C. 20007
Prepared For:
Office of Vocational and Adult Education
Division of Adult Education and Literacy
U.S. Department of Education
Washington, D.C.

Project Staff:

Principal Investigator:

Larry Condelli, AIR

Co-Project Director:

Kathy Safford-Ramus,

Saint Peter’s College,

Jersey City, New Jersey

Co-Project Director:

Renee Sherman, AIR

Diana Coben, King’s College,


Iddo Gal, University of Haifa,

Haifa, Israel

Anestine Hector-Mason, AIR

March 27, 2006

American Institutes for Research

1000 Thomas Jefferson Street, NW | Washington, DC 20007-3835
Table of Contents

1. Introduction 1

Organization of the Review 2

2. Issues in Conceptualizing Adult Numeracy 5

Definitions of Numeracy 5

Formative Phase 6

Mathematical Phase 7

Integrative Phase 7

Theories on Learning and Knowing Mathematics 11

Behaviorism 11

Constructivist Theories of Learning 11

Socio-Cultural Perspectives on Mathematics 13

Numeracy and Cognition: Experience and Situations 14

Affective Factors, Anxiety, and Learning Styles 16

Learning Styles 18

Brain Research: “A New Science of Learning” 19

Summary 20

3. Adult Numeracy and Mathematics Instructional Approaches and Interventions 22

Professional Society Instructional Standards 22

National Council of Teachers of Mathematics Standards 22

Crossroads 23

Other Frameworks 24

Research Evaluating Instructional Approaches 24

Methodology for Identifying Research 25

Quality of Research 26

Effective Instruction for Adult Learners: Research Findings 26

Use of Technology in Instruction 27

Computer Use in ABE Instruction 28

Computer Use in Correctional Education 29

Computer Use in GED Instruction 30

Computer Use in Developmental Mathematics Instruction 31

Research Evaluating Instruction Based on Constructivist Theories 32

Cooperative Learning 32

Discovery Learning 33

ABE Instructional Interventions 34

Summary 35

4. Assessment Issues in Adult Numeracy 36

The Purposes of Assessments in Adult Numeracy Education and Related Research 36

Purposes of Assessment 36

Related Research 37

Overview of Widely Used Instruments for ABE Numeracy Assessment 39



A Critical Look 41

Defining the Meaning of Assessment and How It Can Be Improved 43

Considerations for Developing Improved Assessments for Adult Numeracy 45

What Should Be Assessed in Adult Numeracy Instruction? 46

Conclusions 48

5. Professional Development in Adult Numeracy 50

Issues in Professional Development 50

Need For Professional Development in Numeracy 51

Overlapping Relationship Between Literacy and Numeracy 53

Research in Professional Development and Adult Numeracy 54

International Efforts 57

Summary 58

6. Summary and Implications for Future Research 60

Definitions and Theories of Adult Numeracy 60

Instructional Approaches and Interventions for Adult Numeracy 60

Implications for Further Research 62

Further Research on Instruction 62

Research on Mathematics Instruction for Children 63

Development of Improved Assessment 64

Research to Improve Professional Development 66

Conclusion: Moving Forward 67

References Cited 68

References Consulted 85

Appendix A – Definitions of Numeracy 1

Appendix B – Professional Society Standards 1

Appendix C – List of Web Sites and Journals Searched 1

Appendix D – Summary of Mathematics and Numeracy Intervention
Studies Reviewed 1

1. Introduction

The increasing need for numeracy skills in all aspects of adult life—family, employment, community—has made numeracy a requisite skill for success in today’s society. In the context of Adult Basic Education (ABE), more emphasis is needed on providing quality numeracy instruction to adults to help them achieve the mathematical knowledge and skills that will enable them to adjust to this growing societal demand. The Office of Vocational and Adult Education (OVAE) recognized the need for learners to improve their numeracy skills when it identified mathematics as a core academic area for the development of rigorous content standards. As adult learners are encouraged to move beyond the General Educational Development (GED) and into postsecondary education, the development of numeracy skills will become more critical. However, as educational assessments have shown, 35 percent of all U.S. students are scoring “below basic” on the National Assessment of Educational Progress (NAEP) (NCES, 2002, Math Assessment), with even higher proportions of Hispanic, African American, and low-income students scoring “below basic.”

This problem is of significant concern to adult educators because an increasing number of 18- to 25-year-olds are enrolling in adult education programs: the very same students who lack numeracy skills. The concern about the numerous skill deficiencies in today’s adult learners is exacerbated by the fact that adult education programs are not adequately prepared to provide numeracy education to a diverse student population that bring different needs, interests, skills, and behavior and attitudes toward numeracy.

Although numeracy instruction plays a significant role in adult education in many countries—notably Australia, the Netherlands, and, more recently, the United Kingdom—the United States has experienced limited attention to numeracy instruction and little research on how local adult education programs teach mathematics or numeracy. There are many reasons for this lack of focus: little agreement on what constitutes numeracy; poor professional development in numeracy; limited understanding of how adults with diverse characteristics, needs, and backgrounds obtain numeracy skills; and the lack of alignment among content standards, curricula and instruction, and assessments. Schmitt (2002) points out that GED preparation has been the driving force in mathematics instruction in most adult education programs. Workbooks focusing on standard computational rules, fractions, whole numbers, decimals, percentages, and prealgebra drive instruction. Exercises tend to emphasize repetitive problems, word problems, and problems with real-life applications.

The Adult Numeracy Initiative is the first major effort of the U.S. Department of Education to improve the research and practice of adult numeracy. This project has several goals:

  • Develop a thorough understanding of the current state of the field of adult numeracy.

  • Identify the gaps in knowledge about common strategies for teaching adult numeracy and how these strategies differ across different types of learners.

  • Identify the type of professional development and teacher certification that should be required for teachers of adult mathematics.

  • Identify the type of assessment instruments that might be appropriate for measuring adult quantitative skill acquisition.

The project will achieve these goals through two phases of activity. The first phase, consisting of a literature review, an environmental scan, a technical working group convened to identify critical issues, and commissioned papers to address some of these issues, will distill the limited body of knowledge about current research and practice on adult numeracy instruction, assessment, and professional development. The information from this first phase will inform the second part of the project, which entails the design of curriculum and professional development materials and activities and the design of a research-based intervention or demonstration program that can be tested with a rigorous methodology.

These activities of the Adult Numeracy Initiative seek to answer the following research questions posed by OVAE for the project:

  1. How does adult numeracy develop and how does it differ from the development of quantitative literacy in children?

  2. What are the social variables that affect quantitative skill acquisition in adults? How should programs address these social variables to enhance skill acquisition?

  3. What instructional practices exist in mathematics education for adult learners that are worthy of replication?

  4. What outcomes are most important to address in the evaluation of adult education programs in mathematics? What are the best tools or assessments for evaluating these outcomes?

  5. What practices exist in professional development and certification requirements for teachers of adult mathematics education that are worthy of replication?

  6. What types of programs have been implemented at the state and local levels through federal funding that incorporate or focus on adult mathematics instruction?

  7. What types of programs have been implemented at the state and local levels through federal funding that focus on adult mathematics instruction related to adult English language acquisition learners?

This review addresses the first five research questions by summarizing key findings from the literature. The report that will incorporate the findings from the environmental scan will address the final two research questions concerning mathematics instructional programs.

Organization of the Review

This literature review is the first report of the Adult Numeracy Initiative and lays the foundation for the other substantive activities in the project’s first phase. It strives to answer the first five research questions posed by the Statement of Work. The review summarizes the definitions, theories, and research around adult numeracy to organize what is known and to point the way for future research and development. We have organized the literature review into five parts:

  • Issues in Conceptualizing Adult Numeracy addresses the first and second research questions and presents an overview of the competing approaches to defining adult numeracy. The section then reviews the main theoretical approaches toward teaching and learning mathematics for adults that reflect these definitions. The concepts and theories in this section provide a background and context for the research in instruction and assessment presented in subsequent sections.

  • Adult Numeracy and Mathematics Instructional Approaches and Interventions reviews the small number of studies done on ABE students, supplemented with an also small number of studies on adults in community college developmental education programs, on the effects of different types of instructional approaches on mathematics learning among adults. In response to the third research question, this section presents the instructional approaches, findings, and methodologies of these studies.

  • Assessment Issues in Adult Numeracy endeavors to respond to the fourth research question as it summarizes the existing knowledge base regarding assessment in adult numeracy, reviews the uses of assessment, analyzes the nature of assessment and how it can be improved, and summarizes the principles for designing effective assessments for adult numeracy.

  • Professional Development in Adult Numeracy deals with the fifth research question and discusses the state of professional development in ABE around numeracy. The section notes the low-level background of ABE teachers to teach mathematics, presents professional development approaches, and briefly discusses research on the characteristics of effective professional development.

  • Summary and Implications for Future Research summarizes the findings of the review and suggests future research and how the field of adult numeracy practice and research might progress. It also briefly suggests how research on children’s learning of mathematics may inform research on adults, thus also addressing the first research question.

Writing a literature review is one of the researcher’s more difficult tasks. Unless it is to be a life’s work, lines must be drawn around the topic to identify what is important, what is to be included, and how it is to be analyzed. This task is even more difficult in the field of adult numeracy, which Diana Coben has aptly called a “moorland,” where the lines, where they exist at all, are often indistinct and vaguely drawn. The Adult Numeracy Initiative’s research questions identified the general topics we were to cover. Within these topics, two goals guided our approach: (1) to identify the areas of greatest interest to furthering research and practice of adult numeracy instruction and professional development within the U.S. adult education system and (2) to set the stage for the other activities of the project.

The review suggests areas to pursue further in the environmental scan and commissioned papers, including ongoing work on the development of instruction approaches and curricula and professional development. The technical working group and the commissioned papers will also address many of the conceptual and theoretic issues identified in the review.

2. Issues in Conceptualizing Adult Numeracy

The construct “numeracy” does not have a universally accepted definition, nor agreement about how it differs from “mathematics” (Gal, van Groenestijn, Manly, Schmitt, & Tout, 2005).

This statement, by the authors of a recent international report on adult numeracy, indicates a fundamental problem for anyone reviewing the research literature in this area: there is as yet no consensus about the nature of adult numeracy. Numeracy is a deeply contested concept, beset by terminological confusion, especially when referring to adults. A plethora of similar and loosely related terms compete for attention: mathematical literacy, techno-mathematical literacy, quantitative literacy, functional mathematics, mathemacy, and so on. The resultant complexities are discussed in depth in Adult Numeracy: Review of Research and Related Literature (Coben, 2003).

The issues of the definition of numeracy may seem to be an academic exercise, with little practical value. However, how numeracy is defined has profound implications for all issues of concern to the Adult Numeracy Initiative. Definitions of numeracy have implications for what adults need to know, what should be taught, how students should be assessed, and what professional development teachers need, as a recent international comparative study of adult numeracy frameworks makes clear (Hagedorn et al., 2003). In this section, we summarize the conceptualizations of numeracy and learning theory related to how adults learn mathematics and numeracy.

Definitions of Numeracy

The term numeracy originated in the United Kingdom in the Crowther Report on the education of children ages 15–18. As “the mirror image of literacy,” numeracy was a way of bridging scientific and literary cultures (Ministry of Education, 1959, ¶. 389). The definition entailed “not only the ability to reason quantitatively but also some understanding of scientific method and some acquaintance with the achievement of science.” Literacy and numeracy, at a basic rather than an advanced level, have been yoked ever since, with numeracy often subsumed within literacy.

Definitions of numeracy have proliferated. One view equates numeracy with mathematics and computational skills, in much the same way that literacy is viewed as mastery of basic reading and writing. A much broader view focuses on people’s capacity and propensity to interact effectively and critically with the quantitative aspects of the adult world (Gal, 2002a). Similarly, in relation to literacy, some argue that numeracy is subsumed in literacy, whereas others argue that debates about numeracy within the context of literacy limit the full operationalization of both concepts. Gal and Schmitt (1994) reported that “some people prefer to use the term ‘mathematical literacy,’ believing that ‘numeracy’ is too…limiting in scope. Others feel just the opposite, taking ‘numeracy’ to be the mirror image of literacy…while viewing ‘mathematical literacy’ as a sub-area of mathematics” (p. ii). Appendix A presents a sampling of definitions of numeracy.

Maguire and O’Donoghue’s (2002) organizing framework (Exhibit 1), developed through discussions with researchers and practitioners in Adults Learning Mathematics – A Research Forum (ALM), offers a way of bringing some order into the conceptual confusion surrounding adult numeracy. In the framework, concepts of numeracy are arranged along a continuum of increasing levels of sophistication. In the formative phase, numeracy is considered to be basic arithmetic skills; in the mathematical phase, numeracy is “in context,” with explicit recognition of the importance of mathematics in everyday life. The third phase, the integrative phase, views numeracy as a multifaceted, sophisticated construct incorporating the mathematics, communication, cultural, social, emotional, and personal aspects of each individual in context.

Exhibit 1.
Adult Numeracy Concept Continuum of Development

Phase 1

Phase 2

Phase 3

Increasing levels of sophistication


(basic arithmetic skills)


(mathematics in context of everyday life)


(mathematics integrated with the cultural, social, personal, and emotional)

A continuum of development of the concept of numeracy showing increased level of sophistication from left to right (from Maguire & O’Donoghue, 2002)

Formative Phase

Conceptions of numeracy following the Crowther Report lost the sophistication of the original definition. For example, “numeracy” first appeared in the UNESCO International Standard Classification of Education in 1997 as “Literacy and numeracy: Simple and functional literacy, numeracy.” The designations “simple,” with respect to content and skills, and “functional,” with respect to purpose and application, are telling: numeracy in these definitions refers to basic mathematical, or sometimes specifically numerical or quantitative, skills, which adults are deemed to need to function effectively in society. In this view, numeracy is a basic skill normally acquired in childhood; in some versions of numeracy, what adults are deemed to need is simple arithmetic. Evans (2000) calls this the limited proficiency model of numeracy, a hangover from the Victorian period when the “3Rs” of reading, (w)riting, and (a)rithmetic held sway in elementary education. As a corollary, because the content is seen as simple, numeracy may also be thought to be easy to learn, a view roundly rejected by Ma (1999). This view of numeracy is located in Maguire and O’Donoghue’s formative phase.

Mathematical Phase

A broader view of numeracy may also be traced back to the United Kingdom, in the 1982 Cockcroft Report. This view epitomizes Maguire and O’Donoghue’s mathematical phase, with its emphasis on the use of mathematics in daily life:

We would wish “numerate” to imply the possession of two attributes. The first of these is “at-homeness” with numbers and an ability to make use of mathematical skills, which enable an individual to cope with the practical mathematical demands of his everyday life. The second is ability to have some appreciation and understanding of information which is presented in mathematical terms, for instance in graphs, charts or tables or by reference to percentage increase or decrease. (Department of Education and Science/Welsh Office, 1982,¶. 39)

In this phase, numeracy often includes number, money, and percentages; aspects of algebraic, geometric, and statistical thinking; and problem solving based on the mathematical demands of adult life. This view of numeracy has been influential in the Anglophone world, including the United Kingdom’s Adult Numeracy Core Curriculum (Basic Skills Agency, 2001). In the United States, this approach appears as part of “functional literacy” approaches, exemplified in the CASAS framework (2004), in several states’ mathematics instructional content standards, and in the National Adult Literacy Survey (NALS) (NCES, 1992) and it successor, the National Assessment of Adult Literacy (NAAL) (NCES, 2005). These national surveys measure “quantitative literacy,” a concept that clearly falls within this applied mathematics phase.

However, the issue of functionality is not straightforward. Numeracy could be functional with respect to a wide range of contexts and purposes, and the practical mathematical demands of everyday life may require more than basic numeracy. This complexity is acknowledged in Maguire and O’Donoghue’s integrative phase.

Integrative Phase

All of the most recent, influential approaches to defining adult numeracy fall into Maguire and O’Donoghue’s integrative phase. In this phase, numeracy is viewed as a complex, multifaceted, and sophisticated construct, incorporating the mathematics, communication, cultural, social, emotional, and personal aspects of each individual in context. FitzSimons and Coben (in press) argue that numeracy in this sense may empower individuals as “knowledge producers” as well as “knowledge consumers”that is, to become technologically, socially, personally, and/or democratically numerate.

Steen (1990) exemplifies this phase when he outlines five dimensions of numeracy, distinguished in terms of their purposes and associations:

  • Practical, concerning mathematical and statistical skills that can be put to immediate use in the routine tasks of daily life

  • Civic, where the focus is on benefits to society

  • Professional, because many jobs require mathematical skills

  • Recreational, for the appreciation of games, puzzles, sports, lotteries, and other leisure activities

  • Cultural, concerned with mathematics as a universal part of human culture

Maguire and O’Donoghue’s integrative phase also encompasses critical concepts of numeracy that eschew any automatic association with low-level mathematics. For example, Johnston (1995) proposes that

To be numerate is more than being able to manipulate numbers, or even being able to succeed in school or university mathematics. Numeracy is a critical awareness, which builds bridges between mathematics and the real world, with all its diversity. [...] in this sense ... there is no particular level of mathematics associated with it: it is as important for an engineer to be numerate as it is for a primary school child, a parent, a car driver or gardener. The different contexts will require different mathematics to be activated and engaged in. (p. 34)

Coben (2000a) also emphasizes the individual’s judgments about the use (or not) of mathematics in a given situation:

To be numerate means to be competent, confident, and comfortable with one’s judgments on whether to use mathematics in a particular situation and if so, what mathematics to use, how to do it, what degree of accuracy is appropriate, and what the answer means in relation to the context. (p. 10)

Although integrative conceptions of adult numeracy dominate almost all current theorizing and thinking in adult numeracy, this view has only just begun to move beyond a limited core of numeracy researchers and practitioners. Most mainstream practice continues to reflect formative and mathematical approaches to numeracy. However, more integrative approaches to numeracy have become influential over the last few years, as illustrated by projects to define numeracy instructional content standards, the Program for International Student Assessment (PISA), and the Adult Literacy and Lifeskills (ALL) Survey. The numeracy definitions in these projects specify the intended cognitive outcomes of adult numeracy education and/or emphasize the need for the individual to adjust to the increasing technological demands of the knowledge economy.

The introduction of the National Council of Teachers of Mathematics Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) helped fuel the instructional standards reform movement in mathematics and numeracy (discussed further in the next section). These standards emphasized conceptual understanding and the development of problem-solving and decision-making skills, rather than rule-based learning. This view of mathematics and numeracy has had an impact not only in the teaching of mathematics to children but also in adult education and has helped prompt a movement toward the development of content standards for teaching adult mathematics. The state of Massachusetts (Leonelli & Schwenderman, 1994) and the Adult Numeracy Network’s (ANN) mathematics standards framework were among the first attempts at developing an integrative numeracy framework for adult instruction. The following seven themes were proposed to serve as the foundation for the development of numeracy standards (Curry, Schmitt, & Waldron, 1996):

  • Relevance/Connections

  • Problem-Solving/Reasoning/Decision-Making

  • Communication

  • Number and Number Sense

  • Data

  • Geometry: Spatial Sense and Measurement

  • Algebra: Patterns and Functions

Several states have moved toward developing mathematics content standards, using basic computational, functional, or integrative approaches, and eight states have already developed mathematics standards. OVAE’s Adult Education Content Standards Warehouse project ( has supported states’ efforts to develop standards, as has the National Institute for Literacy’s (NIFL) Equipped for the Future (EFF) project. EFF’s Math Content Standard states that adults should be able to “Use Math to Solve Problems and Communicate” (see Exhibit 2) after participation in adult basic education.

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