Adult Numeracy Development is part of the Series on Literacy: Research, Policy and Practice published by the National Center on Adult Literacy at the University of Pennsylvania. Iddo Gal, editor and the author of several chapters, served as the director of the Numeracy Project at NCAL, where he began work on this book. He currently teaches in the Department of Human Services at the University of Haifa, Israel. In his preface, Dr. Gal states:

"In developing this volume... [w]e sought colleagues able to address both theoretical aspects and classroom realities and to reflect on the challenges and dilemmas involved in implementing new as well as proven teaching methods when working with diverse types of adult students." (p. ix-x )

Adult Numeracy Development is a terrific resource for math teachers and other practitioners; it succeeds in balancing research and practice, and innovation and proven approaches. While many of the participating authors come from the United States (and some from Massachusetts), contributors also come from the United Kingdom, Netherlands, Israel, Australia, Canada, and Malaysia. And while there are many differences in the contexts from which each author writes, there are also many similarities: adult educators who teach math often lack prior training in math teaching and mathematics itself; they are challenged to "meet the math-related goals and needs of adult learners, as well as to satisfy the increasing demand by public agencies, community organizations, or business organizations to improve adults' numeracy or mathematical literacy." (p. 1)

Adult Numeracy Development is divided into four sections: Perspectives on Numeracy, Approaches to Instruction, Reflecting on Practice and Learning, and Assessment. Each section has chapters written by practitioners and researchers, and by US and international authors. For this review, I am focusing on two chapters: "Journey Into Journal Jottings: Mathematics as Communication," by Donna Curry and "Assessment of Adult Students' Mathematical Strategies," by Mieke van Groenestijn.

Writing About Math
"Journey Into Jottings" really bridges the research and practice divide. The author, Donna Curry, provides straightforward descriptions of how to implement journal writing in a math class and what she and her students learned by asking them to write about math.

Donna's brings years of experience teaching math in a variety of ABE contexts to her writing. This chapter reflects her experiences as a member of the Massachusetts ABE Math Team where she explored the National Council of Teachers of Mathematics (NCTM) standard-Mathematics as Communication-while teaching in a workplace education program and doing teacher research. Donna wanted to know if journal writing would increase her students' understanding of mathematical concepts, confidence in tackling math problems at work and at home, and comfort with speaking the language of math. Students in Donna's class were preparing to pass a required standardized test for the workplace. She chose journal writing because "it would address the writing skills for communicating mathematically and provide opportunities for students to reflect on and clarify their own thinking about math." (p. 241) She felt that journal writing would be easy to implement in a structured class.

Having students keep daily math journals led to four changes in Donna's classroom:

• Students increased their use of math language in the classroom.
• The teacher was able to engage in ongoing student assessment more easily.
• Students gave Donna more feedback on the classroom techniques she used.
• Students reported to Donna examples of their application of math learning to everyday life.

Research also led Donna to other questions: How can I encourage students to write more? How do I make sure students aren't just writing what they think I want to hear? How can I tell which specific activity helped students gain confidence and learn new skills? How do I help students who are afraid of being wrong?

Math Assessment
"Assessment of Adult Students' Mathematical Strategies" describes the math interview process, the "Supermarket Strategy," used nationally in the Netherlands to assess ABE students. Written by Mieke van Groenestijn, a professor in adult and special education, the chapter summarizes the growth of Realistic Mathematics Education (RME) in the Netherlands in the early 1980s. RME "emphasizes the use of realistic context problems, representations of reality, and models to relate classroom instruction and learning to the student's real environment and real experience." (p. 336)

With the adoption of RME came the need for assessment tools that would let teachers analyze learners' mathematical strategies and skills. The resulting Supermarket Strategy was developed to be used nationally for placement, ongoing assessment, and post assessment. Considerations in developing this tool included that it "must consist of functional problems in an everyday-life context that can be solved in different ways. The student must be free to use his or her own methods . A good answer is important, but the process by which the student solves the problem gives more information about his or her way of thinking and the quality of his or her calculations." (p. 337)

The Supermarket Strategy
The Supermarket Strategy tests three skills areas (basic skills, proportions, and measurement and geometry further subdivided into seven fields of knowledge) across six levels of complexity (elementary, intermediate and advanced, each broken into two levels). The assessment process consists of a 30-45 minute interview/observation with each student using a special advertising leaflet developed in collaboration with a large supermarket chain and a selection of 60 "context-rich" problems. Three types of questions are asked on each problem: "How are you going to do it? How are you calculating/what are you doing now? How did you do it?" Since observing the process by which students arrive at an answer is so critical to understanding mathematical reasoning, interviewers are allowed (actually encouraged) to help students when they get stuck in certain ways. The interviewer can structure the task, give a similar but easier task, provide concrete materials, or try calculating together with student. Parts of a sample assessment interview conducted with an ABE student from Morocco are included in the chapter and provide an opportunity to really understand what the Supermarket Strategy is and how the process works. The description paralleled my experiences with Massachusetts students and reminded me of how much more I learned working and talking with math learners than I did by administering a paper-and-pencil computational test.

The Netherlands found that "well-trained teachers using appropriate adult assessment instruments such as the Supermarket Strategy are the staring points for quality in math education in ABE." (p. 100) Unfortunately Adult Basic Education services have merged with Further Education and Vocational Education services in the Netherlands as part of a national scheme to reduce unemployment, and a new assessment is being developed. This new written test yields a standardized score and a grade level. Since the new test has a number of problems, however, the use of the Supermarket Strategy is again increasing. Maybe there's hope for the US, too.

Sally Waldron works as the Director of the SABES Central Resource Center at World Education. She taught math for more than 15 years. She can be reached at 617-482-9485 or by e-mail at: swaldron@worlded.org