Not Just a Number: Critical Numeracy for Adults.
by Kerka, Sandra
"It is difficult to understand why so many people must struggle with
concepts that are actually simpler than most of the ideas they deal with
every day. It is far easier to calculate a percentage than it is to drive
a car." (Dewdney 1993, p. 1) To many people, the words "math" and "simple"
do not belong in the same sentence. Math has such an aura of difficulty
around it that even people who are quite competent in other areas of life
are not ashamed to admit they can't "do" math. Innumeracy is more socially
acceptable and tolerated than illiteracy (Dewdney 1993; Withnall 1995).
Rather than discussing specific ways to teach math to adults, this Digest
looks at emerging perspectives on numeracy and their social, cultural,
and political implications as a context for new ways of thinking about
adult numeracy instruction.
WHAT IS NUMERACY?
Numeracy involves the functional, social, and cultural dimensions of
mathematics. Numeracy is the type of math skills needed to function in
everyday life, in the home, workplace, and community (Withnall 1995). Although
not always recognized as such, math is used in many everyday situations--cooking,
shopping, crafts, financial transactions, traveling, using VCRs and microwave
ovens, interpreting information in the media, taking medications. Different
people need different sets of math skills, and their numeracy needs change
in response to changes in life circumstances, such as buying a car or house
or learning a new hobby (Gal 1993; Withnall 1995). Like literacy, numeracy
"is not a fixed entity to be earned and possessed once and for all" (Steen
1990, p. 214), nor a skill one either has or doesn't have. Instead, people's
skills are situated along a continuum of different purposes for and levels
of accomplishment with numbers.
Beyond daily living skills, numeracy is now being defined as knowledge
that empowers citizens for life in their particular society (Bishop et
al. 1993). Thus, numeracy has economic, social, and political consequences
for individuals, organizations, and society. Low levels of numeracy limit
access to education, training, and jobs; on the job, it can hinder performance
and productivity. Lack of numeracy skills can cause overdependence on experts
and professionals and uncritical acceptance of charlatans and the claims
of pseudoscience (Dewdney 1993). Inability to interpret numerical information
can be costly financially; it can limit full citizen participation and
make people vulnerable to political or economic manipulation. Like people
with low levels of literacy, those lacking numeracy skills sometimes manage
to avoid using math, relying on social support networks and coping tricks
adapted to their environment (Steen 1990).
MATH MYTHS...AND REAL-LIFE NUMERACY
Why do people avoid math, and why does such a seemingly abstract subject
arouse such high emotions? Many myths cloud the perception of math and
numeracy (Bishop et al. 1993; Gal 1992; Willis 1992); the realities are
discussed in this section.
NUMERACY IS CULTURALLY BASED AND SOCIALLY CONSTRUCTED.
The math mystique is fed by stereotypes suggesting that white males and
Asians are innately better at math and that math originated in Western
civilization (Zaslavsky 1994). However, a new field--ethnomathematics--is
emerging to refute these ideas. Researchers in this field are demonstrating
that all cultures have math and use it (like language) as a system for
making meaning of the world (NUMERACY IN FOCUS 1995). Math principles and
numeracy practices are not universal. Like literacy, numeracy is a set
of cultural practices that reflect the particular values of the social,
cultural, and historical context (Joram, Resnick, and Gabriele 1994). From
the mental math of bazaar merchants to the navigational practices of South
Pacific islanders to the astronomical calculations of ancient Mayans, "an
enormous range of mathematical techniques and ideas have been developed
in all parts of the world" (Bishop et al. 1993, p. 6). Some math activities
are widely practiced across cultures--counting, measuring, locating, designing,
playing (gambling, guessing), and explaining but there are cultural differences
in these "universal" activities (ibid.). Academic math may look the same
in many societies because a competitive economic and political ethic demands
a competitive math curriculum and dominant cultures may have imposed their
math forms on other societies (ibid.).
MATH REFLECTS A PARTICULAR WAY OF THINKING. Why is a computer
program considered "real" math and the calculations in knitting a sock
are not (Zaslavsky 1994)? Why do people think that math requires special
intelligence or a "math mind"? As a particular way of thinking about the
world, the math of a particular culture or group can be used as a gatekeeper
to restrict access to professions, disproportionately keeping out nondominant
groups such as women and minorities (Willis 1992). The behavior and attitudes
of the dominant group become the norm against which others are measured.
Those whose ways of thinking are attuned to this kind of math succeed where
it is used in school and work. Those who think in other ways may be considered
lacking in math ability, prompting Willis to ask whether math anxiety is
innate or culturally induced. Because math (and numeracy) relates to specific
cultural contexts, different cultural groups have different mathematical
strengths. Although academic math is used to regulate access to higher
education and occupations, academic aptitudes and skills are not necessarily
those needed on the job or in life (Gal 1992).
NUMERACY REFLECTS CULTURAL VALUES. Math is often seen as abstract
and neutral. In reality, it is a discourse--a way of talking or thinking--that
people use to give meaning to the world and therefore it reflects a particular
world view (NUMERACY IN FOCUS 1995). For example, consumer education typically
uses math to teach about credit, budgeting, and money management. Implicit
in these uses of math are the assumptions of a market economy about value
for money, investment, and consumption--a hidden curriculum whose values
are not shared by all cultures (ibid.).
NUMERACY IS NOT JUST ABOUT NUMBERS. Numeracy is a socially based
activity that requires the ability to integrate math and communication
skills (Withnall 1995). It is intricately linked to language: words are
the tools for translating numerical code and giving it meaning. Words can
have everyday meanings as well as math meanings: for example, "and" is
a conjunction, but in math it can also mean "plus." Some words are math
specific: numerator, multiplicand, divisor. Interpretation of these words
can cause confusion for people with low literacy levels or those attempting
to become numerate in a second language.
MATH EVOLVES AND CHANGES. Despite the myth that mathematical
principles are fixed for all time, new discoveries and theories about math
continue to emerge. The uses of math in the world evolve as societal needs
change. For example, computers are changing the need for some kinds of
math skills and creating the need for others (Bishop et al. 1993).
NUMERACY IS ABOUT PROCEDURAL, PRACTICAL KNOWLEDGE. This type
of knowledge is perceived as less important or prestigious than abstract,
theoretical knowledge. Practical, everyday math is considered the "lower
end" of the mathematical hierarchy.
NUMERACY INVOLVES DIFFERENT WAYS OF SOLVING PROBLEMS. There is
not just one way to get the one right answer. "The students found it helpful
to discuss the sort of strategies they use in their real lives. The reinforcement
of these strategies not being wrong gave them a lot of confidence. The
students were convinced that there was only one way to carry out a process
in maths" (Halliday and Marr 1995, p. 75). In traditional teaching, the
teacher/authority hands down knowledge to blank-slate students who memorize
multiplication tables and formulas and mechanically apply rules to solve
problems. However, real-world problems are not as cut and dried as textbook
math (Zaslavsky 1994). Intuition, mnemonics, tricks, and other "home-grown"
problem-solving methods can complement abstract, formal approaches (ibid.).
IMPLICATIONS FOR ADULT EDUCATION
Numeracy has an uncertain place in adult basic education. Instructors
(often volunteers) are not always prepared to teach math and may even share
some of their students' anxieties about it. Adult math instruction often
focuses on preparation for the General Educational Development Test, which
is based on high school math and perhaps "cannot serve as a complete road
map for what adult numeracy provision should encompass" (Gal 1992, p. 22).
The concepts of numeracy and math explored in this digest suggest that
numeracy instruction should be based on the belief that everyone can do
math and everyone uses numeracy practices that may go unrecognized. Taking
a broad view of numeracy, educators take learners' existing reasoning skills,
experience, and literacy and language abilities as the context for what
learners need to learn (ibid.).
Literacy and numeracy should be linked and contextualized. Math is better
understood if learned in familiar contexts that may provide cues to enhance
problem solving. Familiar contexts may make math more accessible for those
who have been alienated from it (NUMERACY IN FOCUS 1995). Having learners
keep journals develops language and math skills together, helps them verbalize
their thought processes, and enables them to express emotional reactions
and feelings about math (Halliday and Marr 1995). Contextualized math applies
a constructivist approach to learning, in which people relate new knowledge
to what they already know, construct their own understanding, and make
new meanings. This approach can help learners recognize the math characteristics
of everyday situations (Gal 1992). Contextualized math can also help those
learners with different ways of thinking. Individual learning style preferences
should be considered in numeracy instruction (Zaslavsky 1994).
Adult educators should also consider their philosophical approach to
education as well as numeracy. Critical numeracy means that learners empowered
with functional skills can participate fully in civic life, skeptically
interpret advertising and government statistics, and take political and
social action. In opposition to the perspective that blames innumerate
people for their own difficulties, educators can use language, literacy,
and numeracy as vehicles for examining how society positions people and
treats them differently (Shore et al. 1993).
Teaching from the perspective of adult education as a tool for social
justice, instructors seek to change the system in which math serves as
a barrier and to "equip people with the knowledge and tools that will enable
them to examine and criticize the economic, political, and social realities
of their lives" (Zaslavsky 1994, p. 217). An inclusive approach to instruction
recognizes the different power relations in the way math and numeracy are
viewed and used and seeks to give people a voice and more control over
life circumstances (Shore et al. 1993). At the same time, educators can
also empower learners with the numeracy skills needed to function in the
technological society and workplace. As more learners acquire those skills,
the cultural practices that are numeracy as well as the way math serves
society can be changed.
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