Journal of Educational Practice for Social Change 2012 | Page 11

The website run by the National Council of Teachers of Mathematics (NCTM) is filled with
classroom initiatives and researchers continue to produce results to support the newest fad in
mathematical instruction or testing techniques—and US student performance on these tests continues
to drop (Packer, J, 2009), to remain steady, or to increase by only a few points a year (National Center
for Education Statistics (NCES), 2011). Even the cases of improved scores leave something to be
desired. Is the “jump” from 263 to 284 in 21 years really that impressive, particularly when the
maximum score is 500 (NCES)? The lack of substantive improvement on the national scale means
despite several decades’ worth of effort, little progress has been made—and logical reasoning, not to
mention the new batch of proposals in my in-box, suggest positive change in mathematics is still being
predicted instead of being savored.
So what can we do? What should we change? Is the instruction incorrect? Are the tests invalid?
Are the students inept?
What are our objectives? Do we want higher scores? Do we want better test takers? Do we want
better mathematics students? Do we want better mathematics thinkers?
At its heart, mathematics is a subject grounded in logic, critical analysis, and pattern
identification. Skills build upon one another and progress with increased complexity. With the mastery
of one topic, additional ideas are presented, scaffolding the past with the future and ensuring that
students become grounded in the fundamentals of an intricate field.
But mathematics is also an art—as complexity increases we rely increasingly on intuition,
creativity, and a willingness to take risks in order to arrive at a solution. We don’t want to simply
present a result; we want to produce an elegant proof, a simple approach, a unique solution to a
common problem. Just as artists roll their collective eyes when someone looks at a piece of modern art
and says, “What’s the big deal? I could do that!” we as mathematicians, and instructors of
mathematics, know mathematics is more than crunching numbers. We know mastery of the material is
not possible without a deeper understanding of how the skills we instruct connect to one another.
Why, then, is so much emphasis placed on presenting the right answer and so little emphasis
placed on demonstrating the HOW and WHY behind the development of the answer? Why are
students encouraged to take multiple choices tests to demonstrate their skills? No one fills out multiple
choice tax returns or selects answer “A” when determining where to cut a piece of wood. Test-prep
companies abound and make tidy profits instructing students on how to beat the test. But where is the
emphasis on understanding and connecting skills? Our colleagues in the Social Sciences and literature
fields would be horrified if a student’s essay consisted of a topic sentence and a conclusion—yet in our
field we accept conclusions readily with little interest in how they were developed.
Not emphasizing the HOW and the WHY in testing means it won’t be emphasized in the
instruction. Shortcuts, tricks, and timesaving approaches receive the bulk of the attention--and for
good reason. With so much depending on testing scores (graduation rates, funding rates, salary rates),
it would be unwise to not instruct to the test. Is this the appropriate approach? I guess it depends on
the objectives.
US students walk out of Algebra classrooms and into Geometry classrooms not realizing the
two are related. Instructors then field questions such as, “Why are we solving for ‘x’ in Geometry? Isn’t
that an Algebra skill?” Standardized assessments such as the SAT and ACT also separate the two
subjects, further suggesting to the students how different the two topics are. This point was made
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