The differences between the students who fail in math and the students who get decent grades – C and above – are generally clear cut, and easily identifiable (unless there is a learning disability involved). Most of these differences aren’t even math specific… failing students in any subject can generally improve their grades by improving one or more of the following areas:

1)
Get organized

2)
Do (and turn in) assignments on time

3)
Be willing/able to seek help when needed

4)
Be willing to put in the time/effort necessary
to be successful

5)
Practice/Prepare for tests

6)
If the people you hang out with aren’t committed
to success, hang out with different people

7)
Don’t accept defeat easily (“If at first you
don’t succeed, try, try again.”)

However, I
recently found myself wondering about what sets the truly excellent math
students apart from the merely-great math students. I have a number of students earning a grade
of A or A- (at or above 90%).

Why do a
select few of these students

*consistently*earn grades near 100% (or above 100%, if extra credit is offered) in math class?
In analyzing
my students, I have noticed a few traits that differentiate merely-great math
students from highly successful math students.

1.
Merely-great math students tend to believe that
knowing a lot and being good at math is the most important component of good
test taking.

Highly successful math students understand that
knowing a lot and being good at math is actually the

*second*most important component of test taking. The most important component is being able to successfully__communicate your knowledge and math excellence to your teacher/professor__.
There are many merely-great math students who turn
in tests containing problems with ambiguity in the solutions. Their brains might have been doing all the
right steps, but their work is suspect.
Highly successful math students provide complete solutions that are

*clearly*mathematically sound. As a result, they tend to receive higher scores on their tests.
Laziness also plays a role in this. Many merely-great math students seem to
follow the philosophy, “When in doubt, show less work.” Most highly successful math students follow the
philosophy, “When in doubt, show more work.”

2.
Merely-great math students don’t tend to place a
high value on neatness.

Highly successful math students tend to make
neatness a priority.

I can’t count how many times I’ve been grading work
and discovered that a student got the wrong answer due to a mistake caused by
poor handwriting. I’ve seen “4” turn
into “9”, “z” turn into “2”, “7” turn into “1” and a myriad of other sloppy
mistakes. These mistakes often prove to
be the difference between a 95% test and a 100% test.

3.
Merely-great math students use lectures and
class time to learn what they need to know in order to succeed.

Highly successful math students also use lectures
and class time to learn what they need to know, but they tend to use this as a

*starting point*in their learning process. They are adept at looking in textbooks for additional examples in order to enhance the material covered in a lecture. They are also eager to explore alternative methods and they have a desire to know WHY a particular method works or doesn’t work.
4.
Merely-great math students do their best to find
out what material will be covered on a test.
(Some are even quite assertive in trying to get specific review topics
from their instructors.) They then review
this material diligently to make sure they can complete the test successfully.

Highly successful math students emphasize material
they know will be covered on a test when studying. However, they also attempt to review/practice
all of the other concepts from a chapter.
This is helpful in (at least) two ways:

1.
Since concepts are often interrelated, highly
successful students gain a deeper understanding of the “key concepts” by
broadening their review.

2.
Teachers who put extra credit items on their
tests will often draw from these “other” concepts. When these extra credit test items show up,
highly successful students are ready for them.

5.
Merely-great
math students sometimes put too much emphasis on being right at the expense of
focusing on what went wrong.

Highly successful math students attempt to learn as
much as possible from their mistakes so that they can avoid making the same
kind of mistakes in the future.

I can think
of a number of students who are experts at “nickel-and-diming” teachers out of
extra points. They submit work that is
good (but not great) and then have to verbally defend their work and try to
convince the teacher that they deserve 100% credit. They rejoice when their
arguments are fruitful and they receive a small increase in score… their
mission has been accomplished. Sadly,
these students tend to get in the habit of submitting less-than-stellar work
and find themselves arguing with their teachers a lot.

Highly successful math students, on the other hand, are
willing to admit when their work is less than ideal. They may argue the merits of their work with
their teacher in an attempt to get more points, but their chief concern is
learning how to produce stellar work in the future that will be above reproach.

The above
list of traits is not exhaustive – there are probably more traits of highly
successful math students that I’ve missed.
(If you’d like to add to my list, leave a comment below.)

Also, the
above list does not come from a scientific study. It is simply an anecdotal summary of my own
personal observations.

I hope it
will help you as you strive for true excellence.

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