What Does "Numeracy" Mean?
by Iddo Gal
This article appeared in the September/October 1995 issue of GED Items (ISSN 0896-0518; Volume 12, No. 4/5), published by the GED Testing Service of the American Council on Education. Iddo Gal is the former co-director of the National Center for Adult Literacy's Numeracy Project and a former Assistant Professor at the University of Pennsylvania's Graduate School of Education. He is now on the staff at the University of Haifa, Haifa, Israel.
Big Picture: What Does "Numeracy" Mean?
Numeracy is a term increasingly used in publications aimed at adult educators, yet its meaning and purpose may be unclear. This article briefly examines the importance of numeracy and the implications for those working with the GED Tests. Readers who are interested in a more in-depth discussion of the numeracy issue are encouraged to examine the publications listed under "additional reading."
The GED Tests measure the "major and lasting" educational skills and concepts learned at the high school level that contribute to successful functioning of adults in our society. What are the lasting outcomes of a high school's mathematics education component? In reflecting on this question, consider that high schools may aim at multiple goals. These would include activities aimed at:
- Handling functional tasks (e.g., shopping, home, crafts)
- Coping with workplace demands
- Further formal learning
- Gaining knowledge for self-development
- Being aware of trends and events of societal interest (regarding, e.g., pollution, crime, poverty, employment)
- Participating in public debate or community action
- Helping children with school work
How well do schools address this range of educational goals? So far, the mathematics curriculum in most high schools appears to have been geared mainly toward preparing students for colleges and post-secondary institutions; it places emphasis on abstract, college-related topics, mainly advanced algebra and calculus. Students who do not cope well with such topics, which many high school math teachers view as "real" math, are often banished into general mathematics courses, which these teachers often consider mathematically "uninteresting."
Advanced algebra and calculus courses hold obvious value for some students. Yet, more than half of U.S. 18-year-olds don't go on to college, and, of those who do, many will not take more math when they get to campus. For this reason, we need to examine how schools have been preparing students for the other types of life goals listed above, and whether the mathematical skills implied by such additional goals should also be considered part of the major and lasting outcomes of high school education. Below are some observations about the compatibility of traditional mathematics curricula with the goals listed above.
A. Certain topics included in the high school math curriculum, such as trigonometry, advanced algebra, or calculus, seldom come up in the lives of most adults. At the same time, insufficient attention is paid by schools to developing the estimation skills adults need to handle tasks which do not require precise calculations, and to "number sense" skills, relating the meanings people attach to numbers. Examples of "number sense" would include grasping the big numbers used in discussing corporate or government budget cuts, or small numbers, such as those involved in evaluating risks.
B. Most adults, regardless of their occupation or living environment, need to be able to plan, handle, and monitor the use of resources, such as money and supplies, or time and people. Such tasks require people to optimize the use of resources, often in the presence of conflicting goals and demands. The skills needed to handle such tasks often differ markedly from those needed to solve the word problems which schools use to simulate real-world dilemmas.
C. Adults often need to be able to handle functional tasks involving numbers embedded in text-comprehending a problem and choosing an action based on data from forms, schedules, manuals, technical, and financial documents. Most high school and adult mathematics instruction, however, tends to rely on textbooks and workbooks which use "distilled" language that does not replicate the types of texts and communicative demands found outside the school.
D. Mathematics instruction in the U.S. has traditionally emphasized procedural skills, and paid little attention to development of interpretive skills. Such skills are essential if students are to become informed citizens who can make sense of verbal or text-based messages that touch on quantitative issues but that do not involve direct manipulation of numbers. Consider the importance of an adult's ability to understand the results of a recent poll or medical experiment. Comprehending newspaper articles or statements on TV requires the student develop reading, writing, comprehension, and critical thinking skills, simultaneously with mathematical skills, and develop conceptual understanding, rather than computational prowess.
Numeracy is a concept without a precise definition. However, we use the term to make sure we focus on the goal of education (becoming numerate) as we contemplate the means of education (learning mathematics). The term numeracy describes the aggregate of skills, knowledge, beliefs, dispositions, and habits of mind-as well as the general communicative and problem-solving skills-that people need in order to effectively handle real-world situations or interpretative tasks with embedded mathematical or quantifiable elements.
The major and lasting outcome of the mathematical component of high school education should be much broader than knowing mathematical procedures and being able to solve brief word problems. Using the term "numeracy" as a term parallel to literacy should help us bear in mind that (a) the range of skills and dispositions required for effective functioning in most life contexts is much wider, and often quite different, than what has been traditionally addressed in K-12 mathematics education, and (b) in many life situations, adults need to seamlessly integrate the use of mathematical with linguistic or communication skills.
Similar to the goal of developing "mathematical power," advocated by the National Council of Teachers of Mathematics as part of its reform agenda, "numeracy" outlines an educational vision which should be embraced by the entire K-12 and adult education system. Evaluating the nature of students' numeracy requires tests that include much more than multiple-choice items, sophisticated as these may be. The communicative or text-related aspects of numeracy, and the need to ascertain people's ability to apply diverse tools and reasoning processes when solving problems that do not have right or wrong solutions, dictate that we continue to seek ways to improve the assessment methods now in use.
Gal, I. (1993). Issues and Challenges in Adult Numeracy. Technical Report TR93-15. Philadelphia, PA: National Center on Adult Literacy, University of Pennsylvania.
Gal, I. & Schmitt, M.J. (1993) (Eds.). Proceedings: Conference on Adult Mathematical Literacy. Philadelphia, PA: National Center on Adult Literacy, University of Pennsylvania.
Gal, I., Ginsburg, L., Stoudt, A., Rethemeier, K., & Brayer Ebby, C. (1994). Adult Numeracy Instruction: A New Approach. Philadelphia, PA: National Center on Adult Literacy, University of Pennsylvania.
National Council of Teachers of Mathematics (NCTM), (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.
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