Publications:
A Framework
for Adult Numeracy Standards:
The Mathematical Skills and Abilities Adults Need
To Be Equipped for the Future
DATA: DATA ANALYSIS, PROBABILITY
AND STATISTICS, AND GRAPHING
In the workplace the common thing would be -- we measure everything. If someone
is measuring something and they are taking samples and they see that is it going
out of the acceptable margin. I mean, they need to be able to stop everything and
get someone to find out what is happening. Upper and lower limits, check that against a
blueprint and see that the upper and lower limits have been put in properly, then
compare that with how it was running earlier that day. Someone has got to understand;
it could be a supervisory level. Someone's got to be putting in the data properly. It
is computerized, of course, but it is only as good as the information that someone
is putting in. We try to tell people, numbers have got to make sense. They have
got to make sense. You have to be able to see if for twenty-five days it has been operating
like this and suddenly it looks like this. What does your gut tell you? There is
something wrong here. Something is going out, that kind of thing. Look at the chart.
People should have enough understanding and knowledge to read all the results of all
our quality measure that we post on a regular basis. And if they see something that
they don't understand, they need to question that. Say, 'what is that?' How does
that impact that? Where does that come from? Everyone of those things impacts something
else. In a workplace setting, there is this domino effect. Everything builds on
the next thing. From the time that raw material comes in the door and one process
after another through departments takes place. You are adding value, but you are also
adding costs. We need to catch those numbers if they start to go out of alignment.
Again going back to -- people need to see the big picture first. The numbers stand
out, how things operate. So they see the big math picture. You get to the big math picture
through all these tiny calculations.
Overview
Adults make decisions based on data in their daily lives and in the workplace. According
to Equipped for the Future, "Adults are also interested in learning and strengthening
the skills associated with using information to have an impact on the world. They identify the need to develop the problem solving and critical thinking skills that
have to do with analyzing and reflecting on information in order to make good decisions.
. ." (p. 24) Reading charts and graphs, interpreting the data, and making decisions based on the information are key skills to being a successful worker and an informed
citizen. Being an informed citizen includes understanding statistics and probability
as well. Adults
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cannot make reasonable decisions unless they understand from where the statistics come.
Charts and graphs are essential in the workplace. According to SCANS documentation,
tomorrow's workers must have reading skills that enable employees "to read well enough
to understand and interpret diagrams, directories, correspondence, manuals, records, charts, graphs, tables, and specifications. Without the ability to read a diverse
set of materials, workers cannot locate the descriptive and quantitative information
needed to make decisions or to recommend courses of action." (p. xvi)
Data from charts and graphs are used to make decisions. Graphs are useful tools in
that they organize data so that information becomes clearer. This organized information
can then be used to draw conclusions, to make decisions, or to influence others.
Data is organized in a variety of fashions, from charts and graphs, to computer-generated
spreadsheets.
In comparing the comments made by stakeholders --often individuals in managerial positions
-- with those made by adult learners, several interesting distinctions were noted.
Stakeholders tended to use the data in charts and graphs to make inferences and
decisions. Adult learners, on the other hand, were more inclined to use charts and
graphs in a more literal way - simply to gather information. Adult learners who created
charts and graphs used them to help themselves while stakeholders (management) used
charts and graphs to influence others. In addition, adult learners claimed either to
not have a use for charts and graphs or felt they used them when they needed information.
Stakeholders shared a concern for the lack of "chart literacy".
Key Findings
Data collection, analysis, and graphing are essential in the workplace. SCANS proposes
five competencies needed by employees for success in the workplace. The competency
Information clearly suggests that data analysis and graphing are necessary skills
for tomorrow's employees. An example of the level of proficiency for the competency
Information includes the ability to ". . . analyze statistical control charts to
monitor error rate. Develop, with other team members, a way to bring performance
in production line up to that of best practice in competing plants." (p. xx)
Many industries, manufacturing in particular, now use statistical control processes
(SPC) to monitor their processes in order to ensure quality products. Often the
front-line employee is required to collect the data used for charting the manufacturing
process; therefore, employees at all levels should be knowledgeable about and comfortable
with using a variety of charts. As more and more quality teams -- consisting of
a variety of employees -- are charged with the task of ensuring quality products,
employees will need to have an understanding of probability and sampling. During a focus
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group session, when asked how math is used in the workplace, an adult learner responded,
"Sometimes I have SPC graphs. It kind of determines if something is wrong with the machine and pretty simple things, nothing really major. One out of 6 is bad, shut
the machine down. A lot of times we don't count the parts. They'll just be in a
can and we write down on an overlay. You know, if you red tag some parts that are
no good, you tag -- nothing really major."
It is interesting to note that only stakeholders seem to be acutely aware of the need
to have the ability to read and interpret statistical process control charts. "There
are two other areas and we mentioned this before about statistical process control.
Our industry is moving into really using numbers to determine whether the production
process is functioning or not. And they are using the concept of time as well as
numbers. How fast it takes to do a particular process. Budgetary hourly rates is
another phrase that is kicked around. . . " Yet another stakeholder commented, "In the
workplace today, employers want everyone to understand quality. Any chart or graph
that shows production uses statistics."
Other forms of charting are also used in the workplace to make decisions as well as
gauge accuracy. One learner shared how he uses blueprints to determine whether a
part is within tolerance: "Basically at work every day, you know, just looking at
parts, I use a blueprint. That gives you a tolerance, a couple thousandths here, couple
thousandths there, sometimes 5, -2, and if you've got a part that's right on the
borderline of t |
