Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
ALGEBRA: PATTERNS AND FUNCTIONS
My high school algebra class was really hard. I didn't know what I was doing and
I felt like I was the only person without a clue.
I've used every math skill I ve learned with the exception of algebra.
Algebra is the gatekeeper.
Overview
Should algebra be on the "honest list?" The Conference on Adult Mathematical Literacy
voted on "informal algebra" as one of four basic topics to include in adult numeracy
education. NCTM's Curriculum and Evaluation Standards, The Massachusetts ABE Math
Standards and other reform movements include it as a critical skill. But say the word
"algebra" to any group of adults (ANPN focus groups, for example) and the reaction
is negative, with personal stories of frustration and sheer agony spilling out.
Is the general perception that "there's really no use for it" a signal that we drop it
from the list of instructional topics or is the answer simply to improve instructional
practice? This area of mathematics presents a challenging dilemma, because what
appears to be a case of the experts want it but the people say no, may be more a case that
the two groups are talking about apples and oranges.
When adults reflect upon what it means to do algebra, they tend to recall formal methods
of equation solving, age problems, and a lot of x's and y's. But mathematics educators
at all levels have begun a dialogue with a very different emphasis, one that "moves away from a tight focus on manipulative facility to include a greater emphasis
on conceptual understanding, on algebra as a means of representation, and on algebraic
methods as a problem-solving tool." (NCTM, 1989, p. 150) They are not talking about
the mechanical high school algebra but algebraic reasoning that allows us to think
about and express patterns, relations and functions and which ultimately gives many
more people access to technology (e.g., spreadsheets and relational data bases).
Key Findings
Many frustrations are connected to past experiences with algebra. "I remember my
father standing over me at the dining room table attempting to drill into my head
the algebra x, y, and x + y. I couldn't understand how anyone could understand it
and why anyone would want to." (Stakeholder) So many adults cite algebra as a major stumbling
block in their earlier mathematics education, the place where they got stuck. "Math
is pretty easy (division); but algebra, forget it." "Algebra in ninth grade was
hard for me. The teacher would do a problem and I was lost. I really felt out of place."
"Algebra is hard." Whatever the reason, many learners report an incredible disconnect
at the
53
point when algebra is traditionally introduced. "I never had any trouble
with math in school until I got to algebra." " Math was pretty decent, and then when
you got to algebra it was like they totally switched it all the way around."
There is a widely held notion that algebra is not practical, relevant or useful. "What
is it used for? You don't use it unless you're teaching it or you're going into
some kind of manufacturing type deal where you actually make diagrams, but otherwise
it's no use. I use math everyday, fractions and so on and so forth, but I just don't
use algebra or geometry."
Algebra is a bridge between arithmetic and more broadly generalized mathematical situations.
Mathematics is the study of patterns. "Learning to recognize and analyze patterns
and number relationships connects math to the world." (Massachusetts ABE Math Standards, p. 42) These generalizations can be expressed in the notation of formulas
and graphs.
Many life and work experiences can be expressed in algebraic terms. While most adult
learners do not see the relevancy of algebra, and many teachers see the academic
relevancy, employers and other workers do see application to today's workplace.
"Our union has a formul |
