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Numeracy in the Adult ESL Classroom
Numeracy is the ability to cope confidently with the mathematical demands of everyday life in the home, workplace, and community (Cockcroft, 1982; Withnall, 1995). The tools of mathematics provide adults with the resources to express facts and opinions and to analyze situations. Knowing how to calculate percentages, for example, is necessary for discount shopping and for figuring sales tax. For many adults, expressing and using the abstract concepts of mathematics is not an easy task, in part, because numeracy needs change as one's life circumstances change. However, like literacy, numeracy is not a case of one's either being proficient or not, rather individuals' skills are "situated along a continuum of different purposes and levels of accomplishment with numbers" (Kerka, 1995, p.1).
This digest examines numeracy for adults learning English as a second language (ESL) as well as for those who teach them. It focuses on learners with low literacy skills and provides curriculum ideas and resources for use in the classroom. While many suggestions are based on the author's experiences in teaching adult immigrants in Canada, they are applicable to adult ESL instruction in other English-speaking countries.
Assessing Numeracy Needs
Adult ESL Learners
Decisions regarding topics to be covered should be based on a needs assessment that takes into account both what the learners want to do and what they can do. Needs may be assessed in a number of ways, from asking about learners' experience in school mathematics to having them try math problems related to a skill they want to learn, e.g., calculating whether it is to their economical advantage to buy a monthly bus pass. To ensure that the class is meeting learners' needs, the instructor should continually monitor their progress and encourage self-assessment.
It is also important to be aware of differences in the use of mathematical symbols in learners' native languages and differences in methods of computation that result from their previous schooling. For example, there is variation in the world's languages in the use of the comma and the decimal point for writing numbers greater than a thousand and numbers as decimals. If a postal carrier earns $32,578.50 in Canada or the United States, most persons from non-English-speaking countries would write the salary as $32.578,50 -- i.e., with the point and comma reversed.
Another common difference is the method of writing out long division computations. For a class party, if 16 people wish to share equally the bill for some pizzas that cost $42.40, there are at least three different ways to do the division:
Writing 42.40 16 instead of 16 42.40 is not backwards; rather it is simply another way of symbolizing the operation of long division. Because there are often multiple ways to solve problems, it is best to observe how learners approach them and build on that. However, adult ESL learners may ask to learn the new way so that they may help their children in school.
Adult ESL and Literacy Instructors
Educators in the United States are beginning to form local and national groups to improve their own and others' math teaching practice. In 1992, 22 adult basic education (ABE), ESL, adult secondary education (ASE), general education development (GED), and workplace education practitioners in Massachusetts collaborated to form the ABE Math team. Using the standards from the National Council of Teachers of Mathematics as a model, they developed 12 math standards for teaching adults (Leonelli & Schwendeman, 1994) that stressed the importance of learning through discovery rather than through rote study of textbooks, the value of understanding over memorization, and the usefulness of such generally undervalued skills as estimating totals (Kallenbach, 1994).
In 1994, in Arlington, Virginia, 110 adult educators from 30 states met for a three-day working conference on adult mathematical literacy. Their recommendations included the following:
Guidelines for Teaching Numeracy
Some Numeracy Activities
A related activity is to make a large money chart. The headings on this chart are (from right to left) "Pennies," Dimes, "Ones," Tens," and "Hundreds, with the decimal point between the "Ones" and "Dimes." The columns are large enough to allow placement of real money or facsimiles on the chart. The money chart is an excellent tool for learners who have difficulty with carrying and borrowing in addition and subtraction.
The learners work in pairs, each pair with one meter stick or ruler, or both. A dialogue such as the following occurs in which learners take turns estimating the length or size of something in the classroom:
The learners measure the table and record the exact measurement. Then the second learner might ask, " How high is the ceiling?" and so on. From here more complex dialogues can be developed.
This activity provides a starting point for learning decimals. For example, learners may measure the width of a piece of paper as 21.6 cm with the ruler and see that 21.6 cm is just over halfway between 21 cm and 22 cm. In fact, 0.6 cm is six-tenths of one whole centimeter. Using the ruler as a concrete aid, the teacher can introduce the concept of decimal before the learners have mastered fractions.
Conclusion Numeracy includes a range of skills that are necessary for initial survival in a new country and for functioning as a fully literate person. In programs for adults learning English as a second language, both the mathematical skills and the language for these skills need to be integrated into the curriculum in order to prepare the learners to be successful. Instructors interested in integrating numeracy-related activities into their classes should evaluate their own perspectives on numeracy and advocate for training and professional development to improve their math teaching practice.
Ciancone, T., & Jay, C. (1991). Planning numeracy lessons for an ESL literacy classroom. Toronto, Ontario, Canada: Toronto Board of Education, Adult Basic Education Unit.
Cockcroft, W.H. (Ed.). (1982). Mathematics counts: Report of the Committee of Inquiry into the Teaching of Mathematics in Schools. London, England: Her Majesty's Stationery Office.
Gal, I., & Schmitt, M.J. (1995). NCAL Brief: Proceedings. Conference on Adult Mathematical Literacy. Philadelphia, PA: National Center on Adult Literacy.
Kerka, S. (1995). Not just a number: Critical numeracy for adults. ERIC Digest. Columbus, OH: Clearinghouse on Adult, Career, and Vocational Education.
Kallenbach, S. (1994, Spring). Massachusetts ABE Math Standards. NELRC News. Boston, MA: World Education.
Leonelli, E., & Schwendeman, R. (Eds.). (1994). The ABE math standards project, volume I: The Massachusetts adult basic education math standards. Malden, MA: The Massachusetts ABE Math Team. (ERIC No. ED 372 297)
Lucas, K., Dondertman, B., & Ciancone, T. (1991). A sequencing guide for numeracy: Whole numbers. Toronto, Ontario, Canada: Toronto Board of Education, Adult Basic Education Unit.
Stoudt, A. (1994, June). Enhancing numeracy skills in adult literacy programs: Challenges and new directions. NCAL Connections, 10-11. Philadelphia, PA: National Center on Adult Literacy.
Withnall, A. (1995). Older adults' needs and usage of numerical skills in everyday life. Lancaster, England: Lancaster University. (ERIC No. ED 383 879)
This document was produced at the Center for Applied Linguistics (4646 40th Street, NW, Washington, DC 20016 202-362-0700) with funding from the U.S. Department of Education (ED), Office of Educational Research and Improvement, National Library of Education, under contract no. RI 93002010. The opinions expressed in this report do not necessarily reflect the positions or policies of ED. This document is in the public domain and may be reproduced without permission.