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Slide #1
How To Study Math
BCC Cocoa Math Lab
Coordinator: Denice Lewis
"The essence of mathematics is not to make simple things
complicated, but to make complicated things simple." -- S.
Gudder
Before We Get Started . . .
Slide #2
Introductions
 On the sheet of paper,


Answer the question “I’d like to learn,
___________________”
What are we going to Cover in
this session
Slide #3

Planning the journey
Assess where you are currently
 Determine what you would like to accomplish
 Figure out how to get from A. to B.


Taking the trip
Learning the Language of Math
 Learning how to read a Math book
 Discovering your resources
 Building a learning circle

"One person's constant is another person's variable." -- Susan Gerhart
Where are you now?
Slide #4


Do you know what your internal and external
variables are?
Internal variables





Do
Do
Do
Do
you
you
you
you
know your learning style?
experience math anxiety?
go through text anxiety?
have a math learning disability?
External variables

What are you trying to juggle at the same time?



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Family/friends
Work
School
Any thing else?
Slide #5

How do I Know What My
Learning Style is?
What is a Learning Style?

A learning style is an individual's
preferred means of acquiring
knowledge and skills

Handout, “What are my
Learning Strengths?”

Time Limit: 10 minutes
“If people do not believe that mathematics is simple, it is only
because they do not realize how complicated life is.”
-- John Louis von Neumann
Do you have . . . ?
Slide #6

Math anxiety is a learned emotional response to one or more of the
following:
1. Participating in a math class
2. Discussing mathematics

3. Working through problems
4. Listening to a lecture
Test Anxiety
“ If your anxiety is a direct result of lack of preparation, consider it a normal,
rational reaction. However, if you are adequately prepared but still panic, "blank
out", and/or overreact, your reaction is not rational. While both of these anxieties
may be considered normal (anyone can have them) it is certainly helpful to know
how to overcome their effects.”

Math Learning Disability


If you have problems with basic math e.g. adding, subtracting, dividing, etc.
you may have a math learning disability.
If you are having problems in Algebra, you may have an issue with reading,
writing, language, or sequential processing.
Information courtesy of
http://www.lemoyne.edu/academic_advisement/academic_support_center/mathanx.htm and
http://www.couns.uiuc.edu/brochures/testanx.htm
Math Anxiety Web Sites
Slide #7

http://www.mathacademy.com/pr/minitext/anxiety/
http://www.mathpower.com/anxtest.htm
 http://mtsu32.mtsu.edu:11064/anxiety.html


http://www.math.com/students/advice/anxiety.html
“What we know is not much. What we do not know is immense.”
--Pierre-Simon de Laplace
Test Anxiety Web Sites
Slide #8
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http://www.studygs.net/tstprp8.htm
http://www.healthyplace.com/communities/Anxiety
/treatment/test_strategies.asp
http://www.couns.uiuc.edu/brochures/testanx.htm
http://www.testtakingtips.com/anxiety/index.htm
http://web.mit.edu/arc/learning/modules/test/testanxiety.html
http://www.sparknotes.com/testprep/books/newsat/powertactics/strate
gies/chapter4.rhtml
http://www.howtostudy.org/resources_skill.php?id=16
 The “How to Study” website presents several links to
other websites that reference test anxiety. Certain links
may require additional time, information, pre-tests, etc.
“Obvious' is the most dangerous word in mathematics.”
--Eric Bell Temple
What do I do if I have . . . ?
Slide #9


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The Office of Students with Disabilities (OSD) is here to help
you. If you have a diagnosed disability or other questions,
please contact Chris Pierce (OSD Disabilities Services
Specialist, 433-7295).
NOTE: OSD is located in Building 9, Room 108.
If you have any questions regarding learning disabilities,
please contact Nancy Malta (Learning Specialist, 433-7297).
Slide #10

Handout, “What are my
external variables?”


What are all the external
variables that you’re juggling?
What are all the things and who
are all the people that you
commit time to?
Time Limit: 10 minutes
"Don't say you don't have enough time. You have exactly the same number of hours
per day that were given to Helen Keller, Pasteur, Michelangelo, Mother Teresa,
Leonardo da Vinci, Thomas Jefferson, and Albert Einstein."
-- H. Jackson Brown
Using a personal example
Slide #11
Denice’s scheduled for Fall 2006
NOTE: These times
do not include
running errands e.g.
shopping (grocery,
etc.), car
maintenance (gas, oil
change, wash the
car), cooking etc.,
etc.!!
NFL
NFL
Setting Priorities . . .
Slide #12
Where are you now?
 Now that you know . . .

Your current state
 Why you feel tired
 Why there just doesn’t appear to be enough
time in one day 

It’s time to set some priorities . . .
 Keep in mind that for every hour you spend
in the classroom, you’ll spend 2 to 4 hours
outside of class.

Slide #13
What things are important to
you?

On a blank sheet of paper, list
the people, places, things,
goals, etc. that are important
to you.

Time Limit: 3 minutes
Plotting Your Course
Slide #14

What grade do you want to
make in your Math class?






“A”
“B”
“C”
“D”
“F”
It’s time to figure out “How
do I get an “ ____ “ with all
of the things that are on my
plate and with my current
personal priorities?”
Slide #15
How do You Plan to Study or
Learn Math?

Handout, “What are your
study and planning
habits?”

Time Limit: 5 minutes
“The mathematical sciences particularly exhibit order, symmetry, and
limitation; and these are the greatest forms of the beautiful.”
-- Aristotle
Slide #16

Definitions of Proactive &
Reactive
Proactive[proh-ak-tiv]
adjective  serving to prepare for, intervene in, or
control an expected occurrence or situation, esp. a
negative or difficult one; anticipatory: proactive measures
against crime.

Reactive [ree-ak-tiv]
adjective  1. tending to react. 2.pertaining to or
characterized by reaction. 3.Electricity. pertaining to or
characterized by reactance.

We’ll review a couple of different scenarios to see
where you fit on the Proactive/Reactive Scale. . . .
Do you plan for things to happen?
Do things happened to you?
Are You Proactive or Reactive?
Slide #17

Handout, “Are you
proactive or reactive?”

Time Limit: 5 minutes
Slide #18
•
Proactive Planning versus
Reactive Planning (Summary)
If you’re proactive,



You are actively
endeavoring to learn.
You know what you
know and what you
don’t know.
You’re continually
planning for success.
•
If you’re reactive,



You are taking a class.
You don’t have a clue
where to go or how to
get there.
You’re on your way to
failure.
Break time!
Slide #19

It’s time to take a
7 minute break.

Please be sure to
be back on time!
In the Classroom
Slide #20


Make sure your awake and aware during class.
Get to know other people in your class.


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
Create a study group
Share notes
Take notes during class!
Be sure to at least write down legibly what
information is covered in class. If writing is an
issue, ask the instructor if you can bring a tape
recorder to class.
“For the things of this world cannot be made known without a knowledge of
mathematics.”
-- Roger Bacon
Outside of the Classroom
Slide #21

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Read your book
Go to class
Review your notes
Do your homework
Go and get help
when you need it
Go to
class.
Read your
book.
Go and get help
when you need it
Review
your notes.
Do your
homework.
“I have had my results for a long time: but I do not yet know how I am to arrive at
them.”
--Karl Friedrich Guass
Making the Connection
Slide #22

You may be asking yourself, “Why do I need to
know my preferred learning style(s)?”

Now that you know what your learning style is,
it’s time to be proactive in the classroom.
The Auditory Learning Style
Slide #23
Learn through hearing
 From a math perspective . . .

You may want to bring a tape recorder to class
 Viewing DVDs or listening to audio tapes may be
helpful


If you wish to enhance this style, you will
need to sit away from noisy distractions such
as the TV, open windows, or crowded areas.
“Pure mathematics is, in its way, the poetry of logical ideas.”
--Albert Einstein
The Visual Learning Style
Slide #24
Learn by sight
 From a math perspective,

Graphs, charts, etc. may help you understand key
concepts
 Ask the instructor/tutor to graph it for you or
demonstrate the concept visually


To enhance this style,
Review everything on the board
 Pay attention to key points in the book while
reading

Slide #25
The Kinesthetic Learning
Style
Learn by doing
 From a math perspective,

Do as many problems as you can
 Have someone demonstrate to you different
methods for solving the problem


To enhance this style,
Participate in class
 Ask questions if you don’t understand how
something was done

Take a moment
Slide #26

On a blank sheet of paper,
write 2 things that you can do
differently inside and/or
outside the classroom.

Time Limit: 3 minutes
The Language of Math
Slide #27

These are the things that you need to know in order
to succeed in Math, feel prepared to take an exam,
and basically, know what you don’t know. . .
Terminology
 Definitions
 Notation
 Theorems

Factual Knowledge
 Procedural Knowledge
 Conceptual Knowledge

“In mathematics, you never understand things; you just get used to
them.”
--John von Neumann
Discovering the Language of
Math (Terminology)
Slide #28

The first step in learning Math is understanding the
words being used in Math.

If you don’t know what a polynomial is, could you
“Factor the polynomial(s), circle the binomial, and
underline the monomial.” given the following:
•
•
•
2
x -9
2
x + 2x + 1
2x
“Since Mathematics is intermediate between natural and divine science, it is
more certain than either of them.”
-- Thomas Aquinas
Slide #29
Discovering the Language of
Math (Definitions)

Next, you need to know what each word means.

Do you know what a derivative is? A polynomial?
An integral? A matrix?

If you’re sitting in your Math class and it feels like
your teacher is speaking another language, it’s
time to review the terminology & definitions.
Slide #30
Discovering the Language of
Math (Notation)

The language of Math includes words and symbols.

Understanding the notation that is being used is
the next step in understanding the language of
Math.
½
X

X
Do you know the difference between set notation
and interval notation when calculating the
domain/range of a function?
{x | x ≤ 1 } ≈ (-∞,1]
Slide #31

Discovering the Language of Math
(Theorems & Factual Knowledge)
Just like other languages, there are rules to Math.
Theorems (Pythagorean Theorem)
 Properties (Additive Property: a + b = b + a )
 Equations

y
= mx + b (Equation of a line)
2
 y = ax + bx + c (Equation for a parabola)

Factual Knowledge is essential facts and figures
that you’ve memorized
cos, sin, tan of 0, p/6, p/4, p/3, p/2
0
 x =1

Slide #32
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

Discovering the Language of Math
(Procedural Knowledge)
There are a number of different ways to solve certain
Math problems
The more methods you know, the better off you are.
For example, to factor a polynomial, you could use the
following:


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Grouping
Completing the square
The AC Method
The quadratic formula
Plug and play
A combination of the above
Slide #33


Discovering the Language of Math
(Conceptual Knowledge)
When you know the what, why, when, where and how
behind any mathematical concept, you have reached
nirvana and conceptual knowledge.
Example:




Not only do you know what a derivative is, you know how to
calculate it for any given function.
You understand that the derivative is the rate of change of a
function and gives you the slope of the graph at any given point.
You can discuss derivatives with your instructor.
Integrals come easy to you because you know reverse engineer
calculating the derivative.
Slide #34





The Language of Math . . .
Practical Application
If you feel as if the teacher is speaking another language, it’s
time to review the Terminology and Definitions.
If it looks like the instructor is solving a problem using ancient
script, it’s time to review the Notation.
If you find yourself missing problems because you don’t know
the cos 45˚ํ or you forget your multiplication tables, is time to
pull out the flash cards to memorize the Factual Knowledge.
If you can’t follow how the instructor solves the problem, you
may want to check your Procedural Knowledge and what
you know about Theorems.
If you’re in any math class beyond Pre-Calculus including
Statistics having a Conceptual Knowledge of each
concept/subject will enable you to solve problems more
efficiently and effectively.
Reading for Understanding, I
Slide #35

Know the important sections in your book.

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The Table of Contents outlines what information will be
covered, in what order and what page you can find a
particular topic.
The Index is a quick way to find information. If you’re
looking for where polynomials are discussed, go to the
index to find the page number.
The Glossary gives you the definitions of terms used in
your textbook.
Most math textbooks have the answers to the odd
problems in the back of the book.
“There are no deep theorems -- only theorems that we have not understood very well.”
--Nicholas P. Goodman
Reading for Understanding, II
Slide #36


Reading a math book is not like reading a fictional
novel or a humanities textbook. You will be
reviewing/reading each more than once!!!
Review your textbook to see how the author
presents the information. NOTE: Some authors
explain how to use the book in the beginning.

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Are key words/terms bolded?
Are theorems, methods in separate squares?
How are example problems presented?
Review the section first to see what new terminology
is being presented as well as to highlight any new
notations used.
Reading for Understanding, III
Slide #37

After understanding what terminology & notation is being
used, read through the section carefully.


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When an example is presented, cover the answer and try to
work it out on your own.

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Every word, dot, symbol, etc. counts!!!
If you don’t understand a word used by the author, stop and look it up
in a dictionary.
If you can’t, review each step of the example to understand the
method being used.
If you can’t figure it out on your own, know your resources and get
help.
Obtaining the student solutions manual may help you
understand how to solve the problems.
Ask yourself, “Is my book working for me?” If it’s not, don’t
be afraid to go to the library, a bookstore, online or even to
your professor to find another book that will work for you.
Slide #38

Reading a Math Book
Web Sites
http://home.sandiego.edu/~pmyers/textbook.html

http://www.stonehill.edu/compsci/History_Math/math-read.htm
http://www.maa.org/t_and_l/exchange/ite3/reading_reiter.html

http://wc.pima.edu/~carem/Mathtext.html

http://academic.cuesta.edu/acasupp/AS/704.htm


http://www.newark.osu.edu/osunmathlab/pdf/handouts/howto/pdf/read
math.pdf

http://oakroadsystems.com/math/sdrdbook.htm

http://www.maa.org/t_and_l/exchange/ite3/TaalmanProblemzero.htm
“Obvious' is the most dangerous word in mathematics.”
--Eric Bell Temple
What other books can I use?
Slide #39

There are several books that were made to support
education/learning. A few series are listed below:

Demystified series
http://shop.mcgrawhill.com/landingpage.php?template=testprep

Schaum’s Outlines
http://books.mcgrawhill.com/searchseries.php?series=Schaum's+Outline+Series
&template=schaums

Schaum’s Easy Outlines
http://books.mcgrawhill.com/searchseries.php?series=Schaum's+Easy+Outlines&
template=schaums

Dummies
http://www.dummies.com/WileyCDA/Section/id-100171.html

Cliff Notes
http://www.cliffsnotes.com/WileyCDA/Section/id-106156.html
Pictures courtesy of the websites listed above.
Are there any free resources?
Slide #40
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Always use your instructor as a free resource.
Visit the Math Lab (Cocoa Campus, Building 9, Room 106)
for help or as a quiet place to study.
Learning Labs (Palm Bay, Melbourne, Titusville) on other
campuses have Math tutors. NOTE: The hours vary per
campus.
You can check out books for free at the library (BCC, public
libraries, etc.). Also, in the Reference section of the BCC
library, there are a number of math-related VHS and DVDs
that you can take blank VHS tapes in and copy.
Also, if you are a registered BCC student, you can go online
and use SMARTHINKING an online tutoring service.
Free Math resources online
Slide #41

Free math resources: Articles, Glossaries, Cheat Sheets, and
more.


Math and Science Articles


http://www.dummies.com/WileyCDA/Section/id-100170.html
The Math website


http://www.cliffsnotes.com/WileyCDA/Section/id-110127.html
http://www.math.com/
A number of professors have their lecture notes or other
information online

Example: Bob Young, BCC (Palm Bay)
http://home.brevardcc.edu/youngr/

Google “notes on __________” e.g. “notes on algebra” and you’ll be
surprised how many different websites appear!
Other online resources
Slide #42

The Study Guides and Strategies web site
is authored, developed and maintained by Joe
Landsberger as an educational public service.
http://www.studygs.net
Building a Learning Circle
Slide #43
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
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“No man is an island, entire of itself; every man is a piece of
the continent.” John Doone
Get to know individuals in your class, friends/family
members that were good in math, other professors, etc.
Know







Who you can go to for what type of help
Which individual explains things in ways you can understand
Who you can study with
Who to go to when you need to vent or need advice
Who to stay away from
Basically, you want to develop your own support group.
Don’t focus on quantity. Focus on quality.
The quote was taken from http://www.quotedb.com/quotes/245
Reflection . . .
Slide #44


Go back to the initial paper
that you wrote, “I’d like to
learn ______”
Have we covered
everything?
The floor is open . . . .
Slide #45



Are there any additional
questions I can answer?
Are there any topics you’d
like to discuss further in the
time that we have?
One course that you may be
interested in is SLS1101,
Success Strategies for
College and Life!!!
My thanks . . . .
Slide #46
All of this would not be possible without the following people:









Dr. Amy Hendricks
Dean Leroy Darby
Quinn Hearn
Nelia Lake
Chris Pierce
Nancy Malta
Lisa Gill
Mark O’Hara
Penny Shannon







Dr. Michael Gallo
Marsha Lake
Skip Downing
Dr. Linda Krupp
Erica Anderson
All the students who
have visited the Math Lab
Fall 2006
Anyone that I may have
missed . . . Thank You!
Quick Tips (1)
Slide #47
Time Management
 There are different tools available that will
help you organize yourself, manage your time,
and be proactive.

Planner
 PDA
 Etc.


It doesn’t help if you have a tool and don’t
use it!
Quick Tips (2)
Slide #48

Time Management Websites

http://www.studygs.net/timman.htm
http://www.franklincovey.com/fc/index.jsp
http://www.ucc.vt.edu/lynch/TimeManagement.htm
http://www.couns.uiuc.edu/brochures/time.htm
http://www.managementhelp.org/prsn_prd/time_mng.htm

http://www.d.umn.edu/kmc/student/loon/acad/strat/time_manage.html

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
Quick Tips (3)
Slide #49
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

Test taking strategies
Your success in taking a test depends highly on your personal
belief in your knowledge and ability.
If you think you’re going to fail, you’re on your way there.
Prepare yourself as much as possible.
Have a test taking strategy for timed exams. You are being
tested on your knowledge of the subject area, time
management, and how efficiently & effectively you solve
problems.




As a result, do the problem you know how to do.
Circle the ones that you know how to do but will take considerable time.
“X” the problems where you have no clue.
Always go back and check your work for any arithmetic or other
errors!!!!!
Quick Tips (4)
Slide #50

Web sites for test taking strategies

http://www.d.umn.edu/kmc/student/loon/acad/strat/test_take.html

http://www.testtakingtips.com/test/math.htm


http://www.ncsu.edu/felder-public/Papers/testtaking.htm
http://www.bucks.edu/~specpop/tests.htm
http://www.ucc.vt.edu/stdysk/stdyhlp.html

http://www.studygs.net/tsttak1.htm




http://www.mtsu.edu/~studskl/teststrat.html
http://euler.slu.edu/Dept/SuccessinMath.html
http://www.msjc.edu/math/mathcenter/handouts/oncourse/T
est%20Taking%20Strategies.htm
Quick Tips (5)
Slide #51

BCC’s Math Courses