Adult Numeracy
11/19/16

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ADULT NUMERACY

Iddo Gal (shown above) is a leader in bridging adult numeracy, statistical reasoning and statistical literacy. Dr. Iddo Gal is ILI Special Senior Advisor for Literacy/Numeracy Assessment. He was previously the Director of the Numeracy Project at the National Center on Adult Literacy (NCAL): a federally-supported R&D center at the Graduate School of Education at the University of Pennsylvania, Philadelphia. He was the editor of Adult Numeracy Development: Theory, Research, Practice. 

Key Websites:

Conferences: Adults Learning Mathematics (ALM).   Proceedings

Looking for research on Adult learning Mathematics?
Searchable Index of all ALM conference proceedings papers now available at http://www.alm-online.net/useful-links/resources/alm-proceedings-index/
The database has been compiled by Prof Kathy Safford Ramus, Saint Peter’s University, Jersey City, New Jersey. (ksafford@saintpeters.edu)

Key publications in Adult Numeracy:

Unlatching the Gate

By Katherine Safford-Ramus (188 pgs, 2008pb). Unlatching the Gate: Helping Adult Students Learn Mathematics by Katherine Safford-Ramus Associate Professor, Mathematics Department Saint Peter's College, Jersey City, New Jersey.

Teaching mathematics to children can be a challenge. Reteaching mathematics to older students who have not mastered it in previous educational attempts can be equally challenging.

Unlatching the Gate was written primarily for the thousands of adult education and postsecondary mathematics educators who teach adults studying mathematics in the United States each year. It summarizes the major learning theories from educational psychology, adult education, and mathematics education, as well as research in adult mathematics education that can inform their classroom practice. This book would be ideal for use as a primary or supplementary text for a graduate course or seminar in adult mathematics education or as outreach via a distance learning course or instructor study circle.

About the Author: Katherine Safford-Ramus is an associate professor of mathematics at Saint Peter’s College, the Jesuit College of New Jersey. She holds a Bachelor of Science in Mathematics from Chestnut Hill College, a Master’s of Arts in Mathematics Education from Jersey City State College, and a doctorate in Mathematics Education from Rutgers, the State University of New Jersey. Dr. Safford has been teaching mathematics at the tertiary level for 24 years, beginning her career teaching introductory mathematics evening courses to adult students at a community college. It was only when her schedule shifted to daytime classes that she became intrigued by the subtle and striking differences between traditional and adult students. Her current research interests center on the impact of student perspective on the learning/ teaching processes and on the significance of social learning theories in the mathematics classroom. From October 2005 to October 2006, Dr. Safford served as the co-director of the Adult Numeracy Initiative, a project of the United States Office of Vocational and Adult Education, a division of the Department of Education.

ISBN13 Hardcover: 978-1-4363-5121-8; ISBN13 Softcover: 978-1-4363-5120-1; 186 pages. To Order: Contact your local bookstore, call 888-795-4274 ext. 7876, or order online at www.xlibris.com, www.bn.com, www.borders.com, or www.amazon.com. Published by Xlibris..

The Components of Numeracy by Lynda Ginsburg, Myrna Manly, and Mary Jane Schmitt.  National Center for the Study of Adult Learning and Literacy (NCSALL) Occasional Paper   Dec., 2006

"we propose three major components that form and construct adult numeracy:

  1. Context — the use and purpose for which an adult takes on a task with mathematical demands

  2. Content — the mathematical knowledge that is necessary for the tasks confronted

  3. Cognitive and Affective — the processes that enable an individual to solve problems, and thereby, link the content and context "

"there are noticeable differences in the frameworks’ treatment of use or purpose. The adult-focused frameworks use three different approaches as to how they position context:

(1) context as the primary organizing principle;

(2) math skills as the organizing principle, while paying attention to context throughout; and

(3) math skills as the organizing principle, yet paying little explicit attention to context.

An example of the first approach—context as the primary organizing principle—is found in the Australian Certificates in General Education for Adults. The authors state that the framework is based on the idea that “skills development occurs best when it is within social contexts and for social purposes” (http://www.aris.com.au/cgea/).  Learning outcomes are organized into four different “numeracies” depending on their purpose:

  • Numeracy for Practical Purposes … addresses aspects of the physical world to do with designing, making, and measuring.

  • Numeracy for Interpreting Society … relates to interpreting and reflecting on numerical and graphical information of relevance to self, work or community.

  • Numeracy for Personal Organization …focus is on the numeracy requirements for the personal organizational matters involving money, time and travel.

  • Numeracy for Knowledge …deals with mathematical skills needed for further study in mathematics, or other subjects with mathematical underpinnings and/or assumptions (Butcher et. al., 2002, p. 215).

An example of the second approach—math content as the organizing principle, while paying attention to context throughout—is the Adult Numeracy Network’s (ANN) framework, which categorizes numeracy by mathematical content and processes consistent with the National Council of Teachers of Mathematics approach. However, the ANN framework adds a category: relevance. The inclusion of this extra category was motivated by an analysis of stakeholder focus group discussions examining the important mathematics adults do in their lives.

An example of the third category—math skills as the organizing principle, while paying little attention to context—is the United States’ National Reporting System (NRS), in which the description of outcome measures focuses only on mathematics computational skills, even though the category is labeled “numeracy” rather than “mathematics.” Some states that organize their frameworks based only on math skills are Florida, Washington, and West Virginia."

"it is the focus on, and prioritization of, context that differentiates an adult numeracy framework from a formal school mathematics framework."

REFERENCES

  • Assessing Mathematical Knowledge of Adult Learners: Are We Looking at What Counts?   Joy Cumming, Iddo Gal, Lynda Ginsburg (1998) identifies 13 instructional strategies that address issues of assessment, development of mathematical skills, and development of problem-solving skills. The strategies reflect research on how adults learn, the cognitive processes involved in learning mathematics, and the mathematical concepts that are important for adults to learn for educational and real life purposes.   (Technical Report: TR98-05, 17 pages)

  • What does 100% juice mean? Exploring adult learners’ informal knowledge of percent   Ginsburg, L., Gal, I., & Schuh, A. (1995). [Technical Report No. TR95–06]. Philadelphia, PA: National Center on Adult Literacy (NCAL), University of Pennsylvania.  Summary.

  • Who Counts in Adult Literacy Programs? A National Survey of Numeracy Education Iddo Gal, Alex Schuh (1994) collected baseline information about numeracy provision in the United States in order to facilitate planning and prioritizing of numeracy-related educational activities. Results point to the need to significantly enhance staff training, consider changes in reporting procedures, change assessment practices, and improve the use of technology for instruction.  (NCAL Brief: TR94-09, 2 pages) Summary

  • The Role of Literacy in the Wealth of Individuals and Nations by Sue E. Berryman (1994), primarily based on data for the United States, describes what is known about the relationships between adults' verbal and mathematical literacy, employers' investments in training, employee wages, unemployment probabilities, unemployment duration, technological change, productivity, and economic growth. (Technical Report: TR94-13, 13 pages)

  • Use It or Lose It? The Problem of Adult Literacy in Skill Retention by Daniel A. Wagner (1994) is a literature review that covers what is known about (a) cognitive skill retention across the life span, (b) studies of literacy and basic skills retention, and (c) policy implications of skill retention work. The main conclusion is that little research has been done on the topic' questions to guide future work are provided in the final section of the report. (Technical Report: TR94-07, 15 pages)

  • Issues and Challenges in Adult Numeracy by Iddo Gal (1993), discusses the place of numeracy in adult education, examines conceptions of what numeracy and numeracy provisions might include, and explores links between literacy and numeracy provision. Questions pertaining to teacher preparation and instructional frameworks are raised, and tentative implications for policy and practice are discussed.  (Technical Report: TR93-15, 53 pages)

The Inclusion of Numeracy in Adult Basic Education (2002) Vol 3, Ch 5 by  Dave Tout and Mary Jane Schmitt 
National Center for the Study of Adult Literacy  (NCSALL)

In the ALL [Adult Learning and Literacy] framework, numeracy involves much more than the "quantitative literacy" described in the IALS [International Adult Literacy Survey]. Numeracy has to do not only with quantity and number but also with dimension and shape; patterns and relationships (such as being able to generalize and represent the relationship between where one lives and the cost of housing); data and chance (such as being able to understand how polls are based on sampling); and the mathematics of change (such as being able to represent how prices fluctuate and populations vary). The ALL team argues that people need to identify, interpret, act upon, and communicate about mathematical information, and the framework details the ways mathematical information can be represented; it also recognizes that to be numerate, adults need not only mathematical skills but also literacy and problem-solving skills. In this view, numeracy is also dependent on disposition, such as anxiety or self-confidence, which affects how one responds in situations requiring use of numeracy skills.

In this new light, numeracy is seen as the bridge between math and the real world. It is an umbrella term that expands both the breadth of the mathematics that is considered and the contexts in which adults use that mathematics. Numeracy is about making meaning of mathematics, at whatever level of mathematical skill, and mathematics is a tool to be used in a variety of applications in both education and life. "Numeracy is not less than mathematics, but more" (Johnston & Tout, 1995, p. xiii).

In further explaining the concept of numeracy, it is helpful to contrast the way in which the new numeracy might be taught with the way math tends to be taught in a traditional classroom. Very generally, when teachers teach math, students use a textbook or workbook and do lots of repetitive practice, they prepare for tests and exams, and they learn formal rules, often by rote, with little consideration of why and how the skills they are expected to learn can be put to use in the real world. When teachers teach numeracy, they are more likely to teach math from a more authentic, contextual point of view, one in which math is derived from some actual or modeled activity, in which investigations and projects are used as vehicles for learning. Teachers of numeracy are also more likely to take into account the students' various informal ways of doing math, allowing the understandings and strategies amassed in and out of school to serve as valid resources.

This essential difference between the teaching of math and the teaching of numeracy is the reason why terminology is important. And it is the reason why the term numeracy, as described above, should be used to indicate what it is we do when we teach math in ABE. It is a way forward. As Schmitt (2000) writes: "Adult basic education and GED [General Educational Development] 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" (p. 4).

Research: Research in adult numeracy in the United States is thin. We need to develop a research culture. Research should focus on issues of cognition and attempt to ask questions about both the numeracy demands of society and the ways in which adults can develop numerate thinking to meet those demands.

CONCLUSION: Numeracy, as defined in this paper, should be viewed as part of the core skill base of any literate individual. ABE advocates need to share that view as well, and this new "language, literacy, and numeracy" perspective should be clearly articulated in federal, state, and local policy and public relations documents. Only then will policy documents and the necessary teacher training programs and curriculum and assessment practices provide a platform from which comprehensive and successful numeracy instructional programs can be developed. Without the emphasis on numeracy as a core essential skill, one that is critical for adults in society, ABE will be unable to fulfill its promise as a second chance for all the adults who choose to participate. Numeracy needs to be brought to the fore.

A Gateway to Numeracy: A Study of Numeracy in Adult Basic Education by Mieke van Groenestijn (2002)

The main question in this study is: What content should be offered in a numeracy program for learners in adult basic education and how should it be organized?  To find an answer to this question, four subjects will be explored and elaborated thoroughly in four sub-studies.  The first three studies provide the building blocks for the fourth study.  The first study concerns the questions "What is numeracy?" and 'Who are the learners in Adult Basic Education (ABE)?" In the second study, the question [is] "What do learners in ABE know about mathematics when they enter ABE?" In the third study, we focus on the development of a theoretical basis for learning mathematics by adults in ABE in the frame of functional numeracy.  In the fourth study, a framework has been developed for a program on functional numeracy education for learners in ABE, based on the information acquired in the first three sub-studies. 

 

Table of Contents:

Section 1: Numeracy in Adult Basic Education.

  1. Development of Adult Basic Education in the Netherlands.     1.1 Introduction, 1.2 Development of ABE in the Netherlands,  1.3 The Population in Adult Basic Education, 1.4 Development of Mathematics Education in ABE, 1.5 Research Questions.

  2. Numeracy: A Dynamic Concept.   2.1 Introduction, 2.2 Developments in the field of adult literacy and numeracy,  2.3 Numeracy, a dynamic Concept,  2.4 Components of Numeracy, 2.5 Levels of Numeracy, 2.6 Conclusion.

Section 2. Numeracy Skills of Adults in ABE.

  1. Numeracy Assessment in Adult Basic Education.  3.1 Introduction,  3.2 Characteristics of the ABE population,  3.3 Development of Assessment in School Mathematics,  3.4 Goals for Numeracy Assessment in School Mathematics, 3.5 Criteria for numeracy assessment tools in ABE,  3.6 Development of numeracy assessment tools in the Netherlands, 3.7 Summary.

  2. Numeracy Skills in Adult Basic Education.  4.1 Introduction,  4.2 Quantitative Results,  4.3 Content Analysis [4.3.1 Numbers, 4.3.2 Proportions (proportions, fractions, percent), 4.3.3. Measurement and Dimensions, 4.3.4 Money,  4.3.5 Reading and Understanding Simple Data],  4.4 Conclusions.

Section 3. Numeracy Learning and Teaching in ABE.

  1. Functional Numeracy Education in ABE.  5.1 Introduction,  5.2 Adult Learning Related to Learning Math in ABE,  5.3 Numeracy Education in ABE,  5.4 Conclusions.

  2. Theory in Practice.  6.1 Introduction,  6.2 Setup of the learning program,  6.3 Content analysis of the Learning Program,  6.5  Quantitative results,  6.6 Conclusions.

Section 4. Development of a numeracy program in ABE.

  1. Developing a Program for Functional Numeracy Education (FNE).  7.1 Introduction,  7.2 Entry Level of Adults in ABE,  7.3 Program Design,  7.4 Objectives for an FNE Program, 7.5 Starting Points for an FNE Program, 7.6 The Setup of an FNE Program, 7.7 Learning and Instruction,  7.8 Evaluation, 7.9 Conclusions.

Section 5. Conclusions and Discussion

  1. Conclusions and Discussion.  Appendices

Developing Adults' Numerate Thinking: Getting Out From Under the Workbooks by Mary Jane Schmitt

The author makes a case for substantive change in how and what we teach in mathematics.  She argues that, "numeracy is the bridge between mathematics and the real world."  "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." She proposed this "mission statement for adult basic education: the development of adult numerate thinking."  Source: NCSALL Focus on Basics, Volume 4, Issue B, September 2000

Adult Numeracy Development: Theory, Research, Practice edited by Iddo Gal (2001)

  • Part I: Perspectives on Numeracy: 1.  The Numeracy Challenge (Iddo Gal);  2. Numeracy, Mathematics and Adult Learning (Diana Coben);  3. Building a Problem Solving Environment for Teaching Mathematics (Kloosterman et al.); 4. Preparing Adult Students to be Better Decision Makers (Robert Clemen and Robin Gregory).

  • Part 2: Approaches to Instruction:  5. Instructional Strategies for Adult Numeracy Education (Lynda Ginsburg and Iddo Gal); 6. Characteristics of Adult Learners of Mathematics (James Steele Foerch);  7. Adult Numeracy at the Elementary Level: Addition and Subtraction up to 100 (Wim Matthijsse);  8. Technology and the Development of Mathematical Skills in Adult Learners (Betty Hurley Lawrence); 9. Teaching Mathematics to Adults with Specific Learning Difficulties (Martha Sacks and Dorothy M. Cebula); 10. Writing About Life: Creating Original Math Projects with Adults (Karen Hicks McCormick and Elizabeth Wadlington).

  • Part 3: Reflecting on Practice and Learning:  11. Learning to Learn: Mathematics as Problem Solving (Leslie Arriola); 12. Journey into Journal Jottings: Mathematics as Communication;  13. The Challenge of Diversity in Adult Numeracy Instruction (Harriet Hartman);  14. Mathematics and the Traditional Work of Women (Mary Harris).

  • Part 4: Assessment: 15.  Assessment in Adult Numeracy Education: Issues and Principles for Good Practice (Joy Cumming and Iddo Gal);  16. Assessment of Adult Students' Mathematical Strategies (Mieke van Groenestijn). 

Extracts from Ch 1 The Numeracy Challenge (Iddo Gal).

Numeracy Situations by External Context or Activity:  "... adults need to manage multiple and diverse types of situations involving numbers, quantities, measurements, mathematical ideas, formulas, patterns, displays, probabilities and uncertainties, and events that unfold in time.  Key examples are 1. Home: Shopping, home repairs, cooking, coordinating schedules, understanding prescriptions labels; 2. Personal finance. Budgeting, filling tax forms, monitoring expenses, paying bills, negotiating a car loan, planning for retirement; 3. Leisure: Planning a trip or party, designing a crafts project, knitting;  4. Active parenting: Helping one's children with mathematical homework, understanding scores on standardized tests and statistics about the child's school;  5. Communicating with professionals: Talking with genetic counselors, obtaining medical advice, buying insurance;  6. Informed citizenship: Comprehending poll results, discussed on TV or crime figures reported in a newspaper; writing a letter to a public official;  7. Social action: Helping with a fund-raising or a survey of a local action group, debating environmental implications of a proposed development project; 8. Workplace: Shipping merchandise, measuring, computing materials needed, reading assembly instructions, retrieving data from a computer system, learning statistical process control, planning timetables; 9. Passing tests: Taking a college entrance exam or a technical certification test; 10 Further education: Studying college-level courses or taking technical training. [p. 10-11]

Numeracy Situations by Cognitive Activity: "Real-life numeracy situations are always embedded in a life stream with real, personal meaning to the individual involved.  The following are three key examples (with some subtypes) illustrate the range of numeracy situations. [p 13-14]

  • Generative situations require actors to count, quantify, compute or otherwise manipulate numbers, quantities, items, or visual elements and eventually create (generate) new numbers.  Such tasks involve language skills of varying degrees.  Two important and interrelated subtypes of generative situations are computational tasks and quantitative literacy tasks.  Computational tasks normally demand the generation of a single number...  Quantitative literacy tasks require that people apply arithmetic operations to information embedded in written materials, such as when computational operations have to be inferred from printed directions, or documents or newspaper prose....

  • Interpretative situations demand that people make sense of, and grasp the implications of, verbal or text-based messages that may be based on quantitative data but that do not involve direct manipulation of numbers....  The response expected of an actor is such a situation is often the creation of an opinion or the activation of a set of critical questions to be answered before  the information or arguments presented are accepted as credible, sensible or valid....

  • Decision situations demand that people find and consider multiple pieces of information in order to determine a course of action, typically in the presence of conflicting goals, constraints, or uncertainty.  Two key subtypes here are optimization tasks, which require the identification of optimal ways to use resources... and, choice tasks, which require a choice among alternatives...

Dispositional Aspects of Numeracy: "Many people ... report negative dispositions about learning math or addressing everyday mathematics tasks.... In realistic contexts, adults with negative mathematical self-concept may elect to avoid a problem with quantitative elements address only a portion of it, or prefer to delegate of subcontract a problem, by asking a family member or a salesperson for help.... A different facet of people's dispositions is related to their metacognitive habits.  In interpretative situations, for example, we want adults to be aware of critical questions that should be raised (e.g., about the credibility of the source of a message, about sample size or adequacy of sampling procedures used in a survey).  We also want them to foster a critical stance, which involves a propensity to spontaneously invoke, without external cues, the list of critical questions, and further invest the mental effort needed to ask penetrating questions, and try to answer them.  Without this stance, people might accept objectionable arguments and develop an incorrect world view." [p. 20-21]

"Numeracy education should present quantitative reasoning as  viable way to approach life's challenges, in order to increate the likelihood that learners feel confident to engage numeracy situations.  Numeracy education should serve as a gateopener, instead of a gatekeeper; learners, after leaving the program, should be motivated to further develop their numeracy skill and engage in lifelong learning through either formal or informal means." [p. 25]

"Teachers, administrators, and curriculum developers need to acknowledge that literacy and numeracy are inextricably connected an explore ways in which the development of people's literacy skills can also be promoted through instruction experiences seemingly more related to numeracy, and vice versa." [p. 26]   

Adult Numeracy Network: We are a community dedicated to quality mathematics instruction at the adult level. We support each other, we encourage collaboration and leadership, and we influence policy and practice in adult math instruction

Teaching and Learning Principles and Professional Development Principles

A high quality mathematics curriculum for adult learners should:

  • include the concepts of number, data, geometry, and algebra at all levels of learning so that students can develop and connect mathematical ideas.

  • weave together all the elements of mathematical proficiency – not only procedural fluency, but also conceptual understanding, ongoing sense-making, problem solving, and a positive attitude about learning mathematics.

  • feature worthwhile tasks, such as activities that are drawn from the context of real life experience.

Key sites:

  • National Center on Adult Literacy (NCAL).  University of Pennsylvania

  • Adult Numeracy @ TERC or Developing Math Proficiency in Adult Learners

  • EMPower  Extending Mathematical Power (EMPower) integrates recent mathematics education reform into the field of education for adults and out-of-school youth. EMPower was designed especially for those students who return for a second chance at education by enrolling in remedial and adult basic education programs, high school equivalency programs, and developmental programs at community colleges. However, the curriculum is appropriate for a variety of other settings as well, such as high schools, workplaces, and parent and paraprofessional education programs. EMPower builds interest and competency in mathematical problem solving and communication.

  • Project TIAN (Teachers Investigating Adult Numeracy) TIAN is a professional development initiative developing a model for standards-based mathematics professional development for adult basic education teachers.

  • TERC (Originally Technical Education Research Centers).   Our work in mathematics and science education includes research, curriculum and technology development, and implementation support in the form of professional development and assistance to districts and schools.  Contact: Mary Jane Schmitt

Surveys involving Adult Numeracy:

Papers on Adult Numeracy:

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This site was last updated 11/19/16