Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
NUMBER AND NUMBER SENSE
"Workers can't be afraid of numbers!"
GM Parts Plant Manager
Overview
Being able to handle numbers comfortably and competently is important to adults as
parents, workers and community members. This competence relies upon having developed
a kind of "number sense" about whole numbers, money, fractions, decimals, and percentages. Number sense includes calculation skills with numbers as well as a sense of number
and operation and an ability to appropriately use estimation, mental math, computation,
calculators or other tools. The learners, teachers and employers that were in the ANPN focus groups had lots of opinions about NUMBER. Learners ranked whole numbers,
estimation, and fractions/decimals high as important math topics (3rd, 4th, and 6th);
stakeholders concurred, ranking whole numbers fifth and estimation fourth. (Please
see the appendices for more information.)
Key Findings
Whole number computational skills are necessary but not sufficient. "If you don't
know whole numbers, that is the basis that everything else is built upon... I mean
how can you do any other type of thing if you can't do the simple whole number computations? ... Right there you're starting with one foot in the hole... " "I think whole
number computation is most important... it's a basic fundamental thing. For example,
there is a tree. If the root is weak, the tree's life will not be long. So we have
to know whole number computation first, because it's basic, the root of the tree."
The adult learners quoted above share a belief held by learners, educators and employers
alike about how important it is for adults to be solidly grounded in whole numbers.
What should be included in the root of that tree? What's the nature of a good solid understanding of number?
The Massachusetts ABE Math Standards states: "To be efficient workers or consumers
in today's world, adults must have a strongly developed conceptual understanding
of arithmetic operations as well as procedural knowledge of computation and number
facts. They must be able to perceive the idea of place value and be able to read, write and
represent whole numbers and numerical relationships in a wide variety of ways. Simple
paper and pencil computation skills are not enough. Adults must be able to make decisions regarding the best method of computation (mental math, paper-and-pencil, calculator/computer)
to use for a particular situation." (p. 38)
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But even deeper in the root of the tree, are some very basic understandings such as
sorting and classifying, comparing, ordering, counting and pattern recognition and
development. These "pre-number and pre-operational" understandings apply to all numbers.
One adult education math teacher reflected on how important it is to be able to do
those "pre-number things with fractions before one can make sense of the operations."
Other math educators included among the number/number sense basics:
Operation sense or understanding how the four operations (addition, subtraction, multiplication
and division) work means "recognizing conditions in real-world situations that indicate
that the operation would be useful in those situations." (NCTM, 1989)
"Multiplicative reasoning is basic as it leads to the understanding of multiplication,
division, and proportional reasoning. The notion of unitizing or forming units
of units where a person begins to group objects together and consider them as sets
or wholes, e.g., five candies per bag, six bags, gives 30 candies. The five candies
are considered a unit." (teacher)
Proportional reasoning was mentioned as critical to "people's ability to understand
and communicate about (rather than compute) what an average or percent is... Anything
that is decreasing/increasing or changing magnitude relies heavily on deep understanding of proportions, rates, ratios, relations and relative comparisons." (stakeholder)
All these elements add to a dynamic definition of what learners, employers and teachers
mean by being able "to do whole numbers."
Estimation and mental math are essential to sense making with numbers. ANPN focus
group members emphasized how critical the skill of estimation was. One
employer said: "I realize in the last few years in my career path, I use estimation
so much more now than I ever knew (I would).. you discuss something on the phone
and How much will I get paid for this and that? I can do a quick estimation, you
know. It is going to be about a thousand dollars commission here. Just being able to do
that -- I probably do estimation 80% of the time and there is 20% of the time when
I actually need to figure out a shipping charge or whatever. But most of the time
in dealing with all my sales reps and customer in general, most of the time, it is like estimating
90% of the time -- giving them a ballpark figure and they are comfortable with that.
I've actually had an awakening with estimation in the last couple of years. I didn't realize I was using it all the time. Yet someone right next to me says: How
did you know that, how did you figure that out? Obviously, I've learned the process
because I practice the process."
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The SCANS Report suggests that work competencies and skills require estimation. Workers
need to be able to "summarize information, set upper and lower limits and estimate
if it falls within acceptable range, understand precision both as consumer and producer, estimate time and costs, troubleshoot and anticipate consequences." (p. )
And the teachers who wrote The Massachusetts ABE Math Standards concurred. "Estimation
is probably the most used and useful skill for adults and continually plays an important
role in the adult learner's life. Adults use informal measurements in activities such as cooking, shopping, buying clothes or estimating the time required for daily
tasks |
