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.
research on Adult learning Mathematics?
Searchable Index of all ALM conference proceedings papers now available at
The database has been compiled by Prof Kathy Safford Ramus, Saint Peter’s
University, Jersey City, New Jersey. (firstname.lastname@example.org)
2015 July 12-15.
Washington DC USA.
2013 July 1-4.
Univ. New South Wales, Newport, Wales/UK.
2012 June 26-29.
2011 June 26-29.
2010 June 28-30
ALM-17 Oslo Norway.
Presentations: Titles, Presenters.
2009 July 6-9
ALM 16 London England. Incorporating LLU+ 7th
National Numeracy Conference at the LLU+ / London South Bank University
2008 June, 29- July 3
2007 June, 26-29
Ireland. List of Presenters
2006 July, 16-20
ALM-13 Belfast, Northern Ireland.
2005 July, 3-7
ALM-12 Melbourne, Australia .
2004 June 29 - July 2
ALM-11 Kungälv, Sweden.
2003 June 29 - July 2
ALM-10 Strobl, Austria
2002 July, 17-20
ALM-9 London, UK
2001 June, 28-30
ALM-8 Roskilde, Denmark
2000 July 30 - Aug 6 ICME-9 Tokyo, Japan (ALM
2000 July, 6-8
ALM-7 Boston/Medford, USA
1999 July, 8-10
ALM-6 Sheffield, UK
1998 July, 1-3
ALM-5 Utrecht, Netherlands
1997 July, 4-6
ALM-4 Limerick, Ireland
1996 July, 5-7
ALM-3 Brighton, UK
1995 July, 7-9
ALM-2 Exeter, UK
- 1994 July, 22-24
ALM-1 Birmingham, UK
Key publications in Adult
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
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
"we propose three major components that
form and construct adult numeracy:
Context — the use and purpose for which an
adult takes on a task with mathematical demands
Content — the mathematical knowledge that is
necessary for the tasks confronted
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
(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:
Practical Purposes … addresses aspects of the physical world to do
with designing, making, and measuring.
Interpreting Society … relates to interpreting and reflecting on
numerical and graphical information of relevance to self, work or
Personal Organization …focus is on the numeracy requirements for the
personal organizational matters involving money, time and travel.
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."
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)
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.
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)
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,
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)
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 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.
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
Table of Contents:
Section 1: Numeracy in Adult Basic Education.
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.
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.
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.
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.
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
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,
Section 4. Development of a numeracy program in ABE.
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
Conclusions and Discussion.
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
Development: Theory, Research, Practice edited
by Iddo Gal
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
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....
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
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.
tasks, such as activities that are drawn from the context of real life
National Center on Adult
Literacy (NCAL). University
Adult Numeracy @ TERC or
Proficiency in Adult Learners
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.
(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