As a department chair from 1990-1997,
I counselled most of the students to do not succeed in our department's
engineering majors. Most students who fail academically, do so
because of a few critical errors in judgement and in how they
approach their studies. As a student (again) myself from 1984-1988,
I became an avid student of "how to study" mathematically
based subjects. I had the good fortune to learn some of the secrets
of studying mathematically based subjects (such as statistics
and engineering) and developed a few new techniques of my own.
I have shared these methods with students on an individual basis
and in numerous workshops and presentations. Students who have
used these techniques report excellent results.
The most effective way of communicating
these techiques is in a workshop format. Unfortunately just reading
this document leaves too much to the imagination. However,
if you take the time use these methods you will see that they
actually work! I look forward to sharing this information
with others in a workshop format in the future.
This guide focuses on the basic strategies for being an effective
math, science or engineering student. These strategies cover
three phases of student life:
Phase I - Planning - Planning ahead and choosing classes Phase II - "Inside class" activities - Note
taking, listening, test taking, attendance Phase III - "Outside class" activities - Using
notes, studying, homework, term papers and projects, visiting
instructor office hours, etc.
In this paper you will learn:
How to get better grades and have more
personal time (the "Big Picture") - Do's and Don'ts.
How to organize yourself for school.
The three basic strategies for taking
How to study.
How to take tests.
What policies you need to understand
to succeed at the university level.
Strategies for choosing classes and
Reasons why capable students fail.
How to study "non-mathematical"
Survey of Available Resources - Much has been written
on how to be a good student--but very little on how to be a good
math, science or engineering student. On my shelf are twelve
books and articles I have collected on how to be a good student
or how to study. Only two of them give any special attention
to "mathematics". All of the other books are directed
to students majoring in non- mathematically based majors.
What Is Different About Studying Mathematically Based Subjects
- The study of math (or related subjects such as engineering,
science, or statistics) is a process that requires progressive,
step-by- step learning of fundamentals or the "order"
of things. Engineering goes beyond just learning "order"
and further emphasizes the "design" process. The goal
of engineering education is to learn, understand, and use laws
of science within the discipline of a profession and the needs
Math and science are filled with "ordered" structure.
This truth makes them different from the study of humanities
and social sciences where philosophy, creativity and inference
may be of more concern. Unfortunately most students try to use
the same methods in all classes. This approach usually leads
to a deficient approach to learning math related subjects. In
most cases this deficiency is compensated for by a innate intelligence,
added time to the task, or persistently repeated failed courses.
In many cases, however, this deficiency is not compensated for
and the student fails somewhere along the way.
My belief, based on experience,
is that 99% of the students who enter engineering have the brain
power to graduate. Those who fail to graduate because of non-outside
forces (eg. health, finances, personal problems, etc.) usually
do so because of poor strategy, planning, study habits and methods.
Math Skill Self Survey
An on-line survey is linked below for the purpose of self-assessment
and introducing some of the concepts that will be presented later.
It is suggested you take the survey and look at your score. The
lower the score, the more you may need to re-assess your methods.
If your your score is very low, do not be discouraged. Finding
out new strategies that allow you to succeed that actually take
less of your time can be very invigorating!
The following steps should ideally be
done before even deciding to go school. School needs to "fit
into" your life, not "become" your life at all
costs. This concern becomes larger as we get older and more involved
with job and family. This step-by-step process can be done on
your own or with the help of a parent, spouse, faculty advisor
The Big Picture - The Big Picture is really your life.
Your studies should fit into your life in such a way that you
can sustain yourself for as many years as it takes to graduate.
PLAN your week so that you have enough time to study properly
and have a BALANCED life. You need to balance your academic,
financial (career/work), personal, family, social, and spiritual
life. If you are spending more than 60-70 total hours per
week on school plus work, then you may be out of balance.
Use a Time Picture - There are 168 hours in a week. Use a "Time
Picture" to determine how much time you can devote to school.
Then use that information to determine how many classes you can
take. Below are the steps for constructing a "Time Picture".
Following is an example time picture. Use the blank "Time
Picture" provided at the end to go through the steps yourself.
- Block out personal time -
Using vertical lines or arrows, block
out personal time first. Personal time includes sleeping,
eating, personal hygiene, dressing, exercise, watching your favorite
TV program, hobbies, reading, prayer and meditation, etc.
You need proper food, rest, and mental freshness in order to
function properly in all the other areas of your life.
- Block out work time -
Block out your job or work time if it
is something you have little or no control over. Include driving
or transportation time.
- Block out time you need for personal priorities and balance
Next block out your spiritual, family,
and social time. Block out time for church, dating, recreation,
family outings, coaching a sports team, helping children with
homework, etc. THIS STEP IS IMPORTANT. These things need
to go in before school work because having these needs satisfied
and being at peace with this will release you to perform properly
in your school work. You will make better decisions in your life
if you are not worrying about the other areas and do not feel
like you are "depriving" yourself.
- Block out school time -
Finally block out time for taking classes,
studying, and for Flexible Time. Flexible time is a block
(or blocks) of time that can be used for either school, family,
or personal--whichever needs it the most. For example, Saturday
morning from 8 am - 12 noon can be flexible time. You would normally
use it for family but could use it for doing a term paper or
studying for final exams if needed. Simply put, "flexible
time" allows you to be flexible and meet your personal,
family and educational needs. Plan your study time for the hours
when you are fresh. My experience is that the earlier in the
day you study, the better. After you have been awake for 15 hours
your mind's ability to concentrate on and comprehend difficult
math concepts diminishes rapidly. Do not expect to get difficult
homework problems solved rapidly late at night.
- Determine how many units of classes you can take.
If you are married you should discuss
the results with your spouse. How flexible time can be used is
the major concern here. For example, if your spouse or child
wants you to do something with them or for them that goes beyond
your scheduled family time, you could use the flexible time to
meet the request or reschedule study time into the flexible time
block. Also, if you have a job which requires a flexible work
schedule you should show the time picture to your supervisor
or manager to get any agreements you can about scheduling work
hours, overtime, travel, and vacation. It is difficult to imagine
being able to go to school for two to five years without some
- Estimate your school workload.
As a rule of thumb, you should plan
for four hours of time for each unit of college credit. The four
hours covers times for lecture, fixing up and transcribing notes,
doing homework, studying for quizzes and exams, library research,
laboratory time, working in small groups, travel to school and
seeing your instructor during office hours. For example: Suppose
you have 24 hours available for school. Then 24 ÷ 4 =
6 units. This means you could take two 3 unit classes or one
4 unit class and one 2 unit class. If you wanted to take 7 units
for some reason, you could consider it based on the nature and
expected difficulty of the class. The length of time it will
take you to graduate will primarily depend on how many units
you can comfortably take each quarter.
- Plan ahead for your last year.
If at all possible begin planning a
way that you can be a full-time student during your final year.
If you can, by planning two or three years in advance, manage
to go to school full-time during your last year you will reap
many benefits. This practice would, for example, shorten the
time to degree significantly, make it easier to take all those
"hard to get" classes, enable you to complete your
senior project on time, and give you more time to concentrate
on your senior level classes. Remember, the classes you take
in the last year are the hardest, require more reports and presentations,
and are the most related to the degree.
SAMPLE TIME PICTURE
The sample below happens to be for a part-time
summer school student taking Chemistry (3 units) and Math (4
units), working two part-time jobs and in a leadership position
with an extra-curricular activity.
6 - 7 am
7 - 8 am
8 - 9 am
9 - 10 am
10 - 11 am
11 - 12 noon
12 - 1 pm
1 - 2 pm
2 - 3 pm
3 - 4 pm
4 - 5 pm
5 - 6 pm
6 - 7 pm
7 - 8 pm
8 - 9 pm
9 - 10 pm
10 - 11 pm
11 - 12 midnight
12 - 6 am
Work: Work (21 hours) + Rose Float (11 hours) = 32
School: CHM 121 (3 units) + MAT 012 (4 units) = 7
units. Allowing 4 hours per unit for all school needs = 28 hours
Total Hours for Work and School: 32 + 28 = 60 hours.
Analysis: This is an example of a balanced schedule.
The student should have plenty of time for both part time jobs,
a major extracurricular activity and two math/science classes
AND STILL HAVE A BALANCED PERSONAL LIFE. The student should cut
back on something if he wants to take more units.
Strategy For Graduation Planning - Follow these basic
guidelines and you will minimize your difficulties in completing
Know your curriculum. Understand which courses are prerequisites
for others, when courses are traditionally offered, what electives
you want to take, and what options you have. Know what courses
are on the "critical path" and make sure your are on
track for taking them.
Balance classes by degree of difficulty - Categorize courses
into the three categories discussed later in this paper. Balance
your class load so that your are not taking courses all in one
category (if possible).
Be prepared for classes - Do not take courses for which
you do not have the necessary prerequisites or skills. This practice
takes the fun out of learning, leads to delays and frustrations
and may result in having to repeat the course. If you have to
repeat the course you have not gained anything anyway.
Time your prerequisites - Try to take courses just after
their prerequisite if possible.
Try to plan your curriculum one year in advance - If possible,
always be looking ahead for one year of classes and roughly plan
your coursework out to graduation. If your department has a forecast
of classes or a historical pattern, then use it to plan. Know
what substitutes, if any, are commonly being allowed by your
department. Also, every department has unwritten policies
and procedures. Get to know people who can help you understand
what these policies and procedures are.
See your advisor with your proposed schedule - Do not
ask your advisor to make your schedule--he or she does not have
time. They can, however, critique a schedule you have already
Understand University Policies and Procedures as specified
in the University Catalog. Especially know what the catalog
says about adding and dropping classes, probation and disqualification,
staying enrolled, repeated courses, holds, academic integrity
(cheating), credit by examination, course load, leaves, withdrawing
from the quarter or university, graduation requirements, graduation
with honors and paying fees. You should own a University
Catalog and at least be familiar with the list of topics found
in the first 100 or so pages.
Understand Your Learning Style - Learning styles vary from person to person.
Traditional college "lecture" courses favor verbal
learners. Some instructors may have teaching styles that are
aimed at visual learners. Very few courses are aimed at
active learners who favor doing and learning by discovery.
The beauty of the techniques taught here is that they will help
learners with ANY learning style become successful by
compensating for imbalances. It has been my experience that this
methodology can even help overcome certain types of mild learning
disabilities (Note: On many campuses students can obtain a very
comprehensive assessment of learning disabilities they may have.
If you have struggled in school for any length of time and cannot
seem to figure out why, consider getting an assessment). One
of the better learning styles questionnaires available on the
web is at:
Strategy for Learning and Taking Classes - To "properly"
learn math, science, or engineering you should plan on spending
2 to 4 hours of outside study for each hour of class. The nature
of these courses is that the material is cumulative in two ways:
Each course builds on the previous
one. A poor grade in an early class could doom you to a low grade
in the next course because of lack of mastery of concepts--the
ability to perform quickly.
Each lecture builds on the previous
lectures. This factor makes it imperative to stay on top of the
material during the quarter. Good attendance and completion of
assignments is essential.
The methodology explained below is designed
to give the student tools to effectively learn the material in
a progressive manner rather than by "cramming" (Cramming"
is the practice of not keeping up with class assignments and
then trying to learn the course material the night before a quiz
or test. Some students in non mathematically related courses
or curriculums manage to "pass" some of their classes
this way. In addition to the obvious possibility of failing a
class, the main disadvantage of cramming is that the retention
rate for the material is practically zero--which hurts later
on). In order to have time to learn progressively the student
needs to have a balanced class load because some class types
will require more time than others. A "balanced" load
is a mixture of types and difficulties of classes. For example,
it is not desirable to be taking all engineering science classes
or all general education classes.
Try not to take more than one pure math or statistics class at
a time. These are not subjects you can cram because you are building
and training all the time. Certain engineering classes should
not be taken together in the same quarter because they can be
very difficult and time consuming. In particular the "engineering
sciences" are traditionally very difficult. These classes
include statics, dynamics, strength of materials, fluid mechanics,
thermodynamics, metallurgy, operations research, etc. In fact,
many students find themselves having to repeat some of these
classes because a C- or better is required to continue the sequence.
Again, try to only take one "engineering science" course
Another type of class to take without being hampered by a heavy
class load are what I call "critical path" classes.
A critical path class is a major class that is embedded in a
long series of prerequisites. If you were to fail a critical
path class, for example, it could delay your graduation from
one quarter to one year, depending on how often it is offered.
Critical path classes are often considered very important in
your major and you would do well to learn the material thoroughly.
Below is a sample classload:
Quantity & Type of Class
Note Taking Method
one math, statistics, or difficult
engineering science class
calculus, statistics, statics,
transcription (one transcription
course per term recommended)
some classes are both a math
class and a critical path class for most engineers
one engineering science or critical
path major class
physics, statics, dynamics, thermodynamics,
transcription or non- transcription
classes are problem solving type classes
one major (with or without lab),
support (with or without lab), or general education class
MAT 114 Calculus I
MAT 115 Calculus II
MAT 116 Calculus III
MAT 214 Multivariate Calculus I
MAT 215 Multivariate Calculus II
MAT 216 Differential Equations
STA 309 Probability and Statistics
IME 312 Probability and Statisitics for Engineers
IE 311 Math for Engineers
IE 327 Systems Engineering
IE 416 Operations Research I
IE 436 Advanced Production Planning
Strictly speaking, several of these classes could be taken concurrently
(eg. STA 309 can be taken concurrent with MAT 215). The problem
then becomes taking two heavy math courses at the same time.
Major classes that are engineering science that actually should
be taken prior to IE 436 include:
IE 417 Operations Research II - IE 429 System Simulation
(on the list of core courses) ME 214 Statics - ME 215 Dynamics - ME 218 Strength of Materials
- ME 219 Strength of Materials
ECE 231/251L Electric Circuits - ECE 333/383LElectrical
All of the above classes should be taken with the Transcription
Method (explained later) of note-taking except IE 436 and
the ECE classes. (Note: If I were a full-time student I would
include the physics classes here and use the transcription method
with them as well).
Most of the rest of the core and support courses are technical
as well and the Non-transcription Method of note-taking
should be used.
Several core and support classes and most of the GE classes can
be taken with using the "St. PIE" Method of
There are 17 total lab classes (assuming that chemistry and physics
classes and labs are taken concurrently). Therefore, it should
not be necessary to take more that two lab classes in any one
Analysis: If I were a full-time, freshman IE student I
would try to take the critical path classes close to the order
shown (several can be switched) and schedule everything else
around the critical path. I would balance the other engineering
science and lab classes so that I was not over loaded in any
If I were a part-time student, I would map out the critical
path, other engineering science courses, and classes with labs
so that I never had more than two of them in any one quarter.
If I were a transfer student, I would make sure I had
all lower division lab classes and ME classes out of the way
early so I would not get caught with scheduling conflicts and
difficult schedules later on. I would try be a full-time student
(non-working) my last three quarters if at all possible.
Next we discuss "In Class" (Phase II) and "Outside
Class" (Phase III) activities. Your ability to be successful
here depends on the study habits described below and whether
or not you have set yourself up to be successful in planning
your time and classes (Phase I activities). The three areas covered
a. Note-taking skills (Phase II &
b. Study skills (Phase III)
c. Exam techniques (Phase II)
The Importance of Notes and Note-taking Skills - The focal
point of this study technique is the development and use of your
notes. Properly developed
notes typically reflect the ideas, concepts, methods, examples,
and "do's & don'ts" that your instructor believes
to be important and will expect you to know well.
Mastery of your notes will be the best use of your time and is
much more efficient than basing your study around the textbook.
I recommend three different note taking strategies--depending
on the class and/or instructor.
2. Non transcription method (for most technical major
classes and technical GE classes)
3. St. PIE method (for humanities, social science, and
other non-technical classes)
Each strategy uses the two-column system to start with. What
you do after that is what makes the three methods or strategies
different. The two-column method is adapted from a notetaking
format developed at Cornell. The following illustration shows
how 8 x ll, three-hole paper is used for taking notes.
Cornell Notetaking Format
(2.5 inches wide)
Notes to tie concepts together
Capture Section (6 inches wide)
Write down all information:
Statements Proof Information Examples
(1 - 1.5 inches high)
Topics covered on page
People to contact
Transcription Method: Most math and engineering textbooks are not
easy to follow on their own so you need something additional
to study. Preparing proper notes can provide the proper study
materials. Take rough notes in class by copying everything down
on 8x11 paper with two lines (drawn either freehand or with a
straight edge ahead of time) following the Cornell format as
best you can (see above). Do not neglect to write down anything
because it may be important later (even though not obvious at
the time). Then later, outside of class, "transcribe"
(recopy) notes using the two-column system. Transcribing is where
you learn because it forces you to think things through for yourself-not
just follow the instructors thinking.
The two-column system - The two columns are mentioned
below. Subsequent notes explain the logic and use of the system.
On the last page is a sample page of notes using this system.
- This space is where you write in "cautions, observations,
verbal clues from the instructor, typical errors and mistakes,
or do's and don'ts resulting from homework, quizzes, and tests".
This column is also where you summarize rules or patterns that
govern the process. This information is usually added later after
you have identified all the steps. Also write rules on index
cards for review purposes and to study for tests. The index
cards can be carried with you in the car or anywhere and looked
at for memorization. This "spaced repetition" helps
you to internalize the rules.
- Record everything written on the board and whatever you can
that is said to explain the material. Include exercises and examples
in this column line-by-line. Whenever possible add references
to the textbook such as page and section numbers. Always write
the sequential page number and date that the notes were taken
in the upper right hand side. You will be amazed at how often
this information is useful.
- On the right side of the index area list the topics covered
on the page. On the left list any new "terms" or "vocabulary"
introduced. Also write any notes to yourself about who you should
see or what you should do about anything on the page.
Index or Table of Contents Page - Create an Index or Table of Contents by transferring
the index headings and page number it is on to a page at the
beginning of your notes. This "Table of Contents" for
your notes is invaluable when studying and taking open-note exams.
While transcribing you will find gaps in logic or things you
do not understand. Missing steps of proofs, errors or incorrect
statements, and undefined terms are just a few examples of questions
you will find only by using the transcription method. Identify
these questions in your notes so you can ask the instructor later.
This is done by using Post-it notes. Place the post-it with the
question written on it so it sticks out of the page. See your
instructor during their office hours and resolve your questions
by going through the post-it notes. You will find most instructors
will be very happy to help if you use this method.
In math there are two parts to learning:
"Can do" - What you can do
is given by the instructor.
"Can't do" - You add this
later in column 1. These are all the cautions and places where
mistakes can be made. After you see the homework solutions and
get back graded quizzes and exams, analyze the mistakes you made
and add cautions to your notes in column 1. This makes studying
for later tests (especially final exams) much more meaningful.
- Use color coding of notes to help you study and use your notes
efficiently. A suggested use of colored highlighters is:
Pink - Headings Green - Rules Yellow -
Cautions, things to memorize Orange - New words or items Purple (blue) - Examples
Optional Blue (purple) - Old rules and things you should know
Non-Transcription Method - The non-transcription method
is the same as the transcription method except that the you do
not rewrite the notes. Use the two-column ruled paper and write
your original notes as neatly as possible. Then color code and
fix up these notes as outlined above. This system works best
if you have an instructor that does not go to fast. A speedy
instructor forces you to get sloppy sometimes.
St. PIE Method - This method is from the excellent book
by Laia Hanau, Play the STUDY GAME for Better Grades, Harper
& Row, Fifth Ed. 1972. Briefly stated, use the Cornell Method
and write down everything you can in the capture area. When studying
you then try to classify the material in your notes as either:
Statement Proof Information Examples.
Thus the acronym St. PIE.
In a humanities or social science class, for example, you would
then make all the connections. The instructor does not always
"tie things together". They leave that to the student.
When you see a statement (postulate, theory, axiom, contention,
opinion, premise) for ask yourself where the proof, information,
and examples are in your notes. Tie them together with lines,
arrows, and notes. When you do this you are predicting the
test questions in advance. Aren't many test questions things
like: This is an example of ..., Give proof to support ..., etc.
Study Skills - With math and applied mathematics fields
it is not enough to simply "know" or "understand"
material. You need to know the material well enough to perform
quickly-- without hesitation. Therefore, knowing involves
DOING AND DOING QUICKLY. Learning the rules well will help you
tremendously. Studying consists of studying the rules, trouble
spots, and practicing examples. Studying is not paging through
the book working problems. Math is a "doing" subject,
not a "reading" subject.
Study Steps - Write down the first line of an example
problem on a piece of scratch paper, close your book or notes,
then work as far as you can without looking. Then start over
and repeat the process four or five times until you can do the
example QUICKLY al the way through. By the time you have worked
through the example repeatedly you have the rules memorized.
The repetition in this process is the key to learning. This phase
of the study process is where you find the "can't do's"
to enter them into column one of your notes.
Now the homework should be the "frosting on the cake"
and should only take a few minutes. Contrast this technique to
the common practice of digging into homework without proper preparation.
The homework may eventually get done after a lot of "page
flipping", but the student still does not know the material
proficiently and rules are not internalized.
Study Time - How long should you plan on for studying
and how should it be used?
3/4 - 1 hours - to transcribe notes
and understand steps.
1/2 - 1 hours - to work examples over and over.
1/2 - 1 hours - to do homework.
These steps total to 2 to 4 hours of study for each hour of class.
You will experience two extremes when studying when using this
method: The frustration of not getting the homework done quickly,
and the reward of finally getting itout with a fair good understanding
and internalization of the material.
Closure - When you stop studying you should always allow
a few minutes to ask yourself what you have learned the last
hour and what the key points are. This step will help you solidify
what you have studied.
Exam Techniques -
Do's and Don't's when studying for an exam:
DO get a good night's sleep
DON'T cram in the morning
DO use index cards to review before the exam
DO take lots of breaks when studying. A five or ten minute break
or "cat-nap" for each hour of studying may keep you
fresh enough to continue fruitfully.
DO study during your most productive time. Each person has certain
times when they peak mentally. Try to use these periods to study
During the test:
Go through the entire test and decide
what types of problems there are.
_ Put a check mark next to those problems
you are good at.
a question mark next to those problems that are "maybes".
an X by those problems you are not good at.
Do the check-marked (_) questions first.
This builds confidence and helps you relax during the test. Your
strategy is to get the points you can get. These points (and
your grade) generally come from what you know, not from what
you do not know.
o Transcribe notes only on the front side of each page. Use the
back side of pages to enter examples, notes, and theorems from
the textbook that correspond to the open page of class notes.
If done properly, your notes will be a complete reference source
and you will not need to reference the text very often. Notes
prepared in the above fashion give you a sense of pride and are
considered very valuable.
o Always write the problem number, page and the problem itself
above your homework solutions. If not, you will always need your
text to make any sense out of your homework papers.
o Consider using a pressboard binder (the kind with two metal
strips that fit three hole paper) to store your pages as they
leave your 3-ring notebook. At the end of the course you will
have a completely "self-contained" reference complete
with notes and homework problems.
The Quality Student - Most students do not realize that
they can improve their GPA simply by demonstrating to the professor
that they are a serious, conscientious, hard-working student.
Why? Because the professor may give you the "benefit-of-the-doubt"
while grading quizzes or exams or even reward you for your good
attitude when determining your final course grade. The "Quality
Student" does the following:
1. Always attends class
2. Always takes the prerequisite courses
3. Always pays attention in class
4. Always takes notes
5. Always attempts and turns in their homework
6. Always notifies the instructor about difficult situations
that may be keeping them from optimum performance
7. Listens for helpful hints from the instructor
8. Keeps up with class material
9. Plans time to review and study for exams
10. Has a balanced life
11. Does their fair share on team projects
12. Does not "bicker" with the instructor over partial
13. Visits the instructor during their office hours with genuine
questions from class notes or attempted problems
14. Always buys and keeps their books, software, and other "tools"
15. Looks for the best in every situation
16. Is a student of "interpersonal communications"