ERIC Identifier: ED392316
Publication Date: 1996-02-00
Author: Ciancone, Tom
Source: National Clearinghouse for
ESL Literacy Education Washington DC.
Numeracy in the Adult ESL Classroom. ERIC Digest.
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
In developing a methodology for numeracy instruction, an instructor must
consider not only the nature of mathematics learning, but also the nature of
adult learners. Determining appropriate instructional methods depends both on
learners' mathematical skills and on their attitude toward mathematics. For the
ESL learner, proficiency in English will be an additional factor. Although
mathematical concepts may be generalizable to many languages and cultures, these
concepts must be learned and expressed through particular languages. Whereas "2
+ 2 = 4" may be widely understood, the English expression "two plus two equals
four" is not. Thus a learner's difficulties in numeracy may be due in part to a
lack of proficiency in English.
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 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. [graphic representations/examples of long division not provided
Because there are often multiple ways to solve problems, it is usually best
to observe how learners approach problems and then to build on that. However,
adult ESL learners may ask to learn the ways commonly used in Canada or the
United States so that they may help their children in school.
ESL and Literacy Instructors
In addition to addressing learner needs, instructors need to consider their
own attitudes about numeracy (Kallenbach, 1994; Leonelli & Schwendeman,
1994; Stoudt, 1994). Many ESL and adult literacy educators may not be
comfortable with math and may teach math skills as discrete and isolated rather
than "relevant, contextualized, and essentially linked to overall literacy"
(Stoudt, 1994, p.11).
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
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:
Class math activities should be collaborative, involve problem-solving, and help
learners develop reasoning skills.
Diagnostic assessment tools need to be developed to inform all
stakeholders--learners, instructors, evaluators, and program funders.
Support for professional development for teachers is needed (Gal & Schmitt,
GUIDELINES FOR TEACHING NUMERACY
To facilitate numeracy
learning in an ESL literacy program, Ciancone and Jay (1991), Kallenbach (1994),
Leonelli and Schwendeman (1994), and Lucas, Dondertman, and Ciancone (1991)
offer the following suggestions:
Encourage looking for patterns rather than finding the right answer.
Stress the possibility that there may be many ways to solve the same problem.
Encourage peer-group collaboration. The best way to clarify one's own
understanding of a concept is to explain it to someone else.
Encourage learners to write journals about the math skills they are learning and
their feelings about learning math. Using the language of mathematics reinforces
both the mathematical concepts and proficiency in English.
Although numeracy is an everyday coping skill, mathematical concepts can be
quite abstract; the more concrete and visual the explanation, the more easily
understood the abstract concept.
Each numeracy lesson should provide a balance between skill building and
functional needs. A lesson may begin with a problem (e.g., a mistake on a
paycheck) that provides a context for learning new skills (such as subtracting
decimals), or the lesson may start with a skill (e.g., adding decimals) followed
by practical applications (such as adding sales tax to a fast food bill).
Include math in literacy instruction from the beginning. Even learners who have
almost no proficiency in English need to learn numbers for such basic activities
as shopping and riding the bus.
SOME NUMERACY ACTIVITIES
As learners develop language
skills, they can also develop skills such as estimating, measuring, and
analyzing data. Activities for numeracy learning can range from recognizing
numbers to calculating percentages, from reading a bus schedule to baking a
cake. The two activities described below have been useful for helping beginning
numeracy learners understand number systems.
The place-value chart reinforces the essential mathematical concept of place
value while helping ESL learners to read large numbers. It is a series of
adjacent columns with headings that designate their value. From right to left
the headings are "Ones," "Tens," "Hundreds," "Thousands," and so on as high as
"Billions," if needed. The chart can be used in a variety of ways. The
instructor can simply dictate numbers and ask the learners to write them in the
correct columns on the chart. Or this exercise can be combined with questions,
such as, "How many days are there in a year?" or "What is the population of
Ontario?" If a class is reading a newspaper article that involves large numbers
(e.g., corporate profits), the instructor can have learners underline numbers
and then copy them onto the place-value chart. The chart can also be used when
writing numbers in words, as required in writing checks.
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.
A unit on metric measurement can include topics of length, distance, area,
volume, and weight to teach functional language skills related to dimensions and
mathematical skills involving decimals. The following activity presupposes a
preliminary understanding of metric units, a reasonable expectation of learners
educated outside the United States. U.S. measurements can also be used, or an
activity can be done comparing the two systems of measurement.
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:
How long is the table?
It's about "2 meters" long.
Let's measure it.
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
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
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
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. (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. (ED 383 879)