Ideal Math Students
1)
Are aware of
where they stand in regard to necessary prerequisite skills, realizing that
weaker skills require a greater time commitment to the course at hand.
2)
Show up on time
and stay to the end of class.
3)
Act respectfully,
like they are in an institution of higher learning. Ideal math students behave
in a manner that does not inhibit the instructor from teaching or other
students from learning.
4)
Take
responsibility for absences and are aggressive in making up work missed. They
do not fall behind.
5)
Have a positive
attitude toward the subject matter at all times, realizing that mathematics is a vital part of the
preparation for life, work, and on-going education.1 More
specifically, they understand that:
·
The workplace requires ever-increasing analytical and technical skills.1
·
The problem-solving and quantitative skills that they develop in any
rigorous mathematics course are invaluable to other disciplines, such as the
social, biological, and behavioral sciences.1
·
Public policy issues often contain a quantitative component. Thus, as
an integral part of an informed electorate, the ideal math student must be able
to reason quantitatively.1
·
The skills they learn can be passed on to their children’s children’s children, thereby opening doors to rewarding
career opportunities for generations to come.
6)
Recognize where
they stand in regard to the rate at which they work mathematical exercises.
They continually strive to improve their processing speed without compromising
accuracy.
7)
Work in pencil,
doing all problems sequentially downward in a neat and organized manner.
8)
Do their own work! They understand what is expected of them in
regards to academic integrity.
9) Will work ahead, rather
than procrastinate. This includes doing as much of an upcoming assignment as
possible prior to the instructor lecturing on it. After a session concludes,
the ideal math student will:
·
Review notes taken, highlighting important formulas, processes, and
examples for study later on.
·
Complete the related homework assignment, going so far as to take on
extra problems related to weaker areas.
·
Try to minimize the need to view a problem’s answer before finishing
the problem.
·
Seek help immediately whenever necessary, either directly from the
instructor, or from a tutor or classmate. Ideal math students take advantage of
the opportunities to utilize additional resources.
·
Begin working on the next assignment by reading the textbook, following
the author’s examples, and attempting some to all of the assigned problems.
·
Grade the completed problems by first self-checking, then by checking
against the author’s or instructor’s solutions, if available.
10)
Follow up graded
material appropriately, by thoroughly going over an assignment after it is
returned. Ideal math students make note of content that was not understood or
just partially understood on a homework assignment, quiz, or test, and then
commit to immediately taking on the necessary extra practice and/or study, in
order to strengthen skills to a proficient level.
11)
Actively
participate in class. This includes, but is not limited to, being attentive
100% of the time, asking questions to gain clarity, taking quality notes,
diligently practicing when instructed to do so, volunteering answers to
instructor’s questions when appropriate, taking a lead and setting a premium
example during group work, and constantly anticipating where the instructor is
heading during a lecture.
12)
See more to a
problem than greets the eye. For instance, the text may read:
·
“Evaluate vt – 16t2 when v = 24
and t = 2.” The ideal math student sees “Determine the numeric value of the
expression vt – 16t2
after substituting 24 for the variable v and 2 for the variable t.”
·
“Solve x2
= 12x,” but the ideal math student sees “Find the two solutions to the quadratic
equation x2 = 12x by first getting 0 on one
side.”
·
“Use a calculator
to determine a four-decimal approximation to ln 87.” The ideal math student sees “To the nearest ten-thousandth,
use a calculator to find the number that one raises “e” to in order to arrive at 87.” Learning to see more than greets
the eye will improve test scores.
13)
Follow sound strategies
for preparing to take a test. They will:
·
Set aside an
appropriate amount of time each day for 3-5 days, longer if studying for a midterm
or final (always erring on the side of longer) to prep for a test.
·
Review notes,
committing to memory key formulas and/or processes.
·
Study reviews
provided in the textbook and/or by the instructor.
·
Go over related
quizzes and worksheets, re-trying all the problems, whether wrong or correct.
·
Practice!
Practice! Practice! Ideal math students do problems in the chapter reviews
and/or teacher-suggested exercises, paying particular attention to their
directions. When doing this necessary practice, ideal math students set up an
environment that will be similar to the actual test-taking environment.
·
Grade for
correctness all practice done to prep for a test.
14)
Follow an
appropriate test-taking strategy. When taking a test, ideal math students will:
·
Read directions
very carefully.
·
Think about the
solution before getting started.
·
Map out, either
in writing or in their mind’s eye, the steps required to complete a problem.
·
Finish every test
or quiz in four phases by:
1)
Doing the
easiest, least time-consuming problems first.
2)
Doing the medium
problems, those that they are somewhat less confident about, but are not
baffled by, or those problems considered easy, but more time-consuming.
3)
Doing as much as they
can on each of the hardest exercises (for possible partial credit).
4)
Checking as much
as time permits, especially those problems categorized as being medium. Ideal
math students do not erase or cross-out a solution unless they are more
confident about an alternative solution and, have the time to completely
display the alternative for grading.
1 From “The
Argument for Raising the Mathematics Requirement,” by The