Math Study Skills
Pierce College Math Learning Communities
Table of Contents
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Lesson
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Page
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1
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Syllabus
Search
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3-5
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2
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What Makes
Math Different and Math Anxiety
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6-8
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3
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Listening and
Classroom Skills
|
9
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4
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Reading a Math
Textbook
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10
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5
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Homework
Skills
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11-14
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6
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Note Cards and
Review Sheets
|
15-16
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7
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Test
Preparation
|
17-19
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8
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Test Taking
Skills
|
20-21
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9
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Post Test Analysis
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22-24
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10
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Mid-semester
Check up
|
25-26
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11
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The Final Exam
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27
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Lesson 1
Syllabus
and Keeping a Notebook
The syllabus contains
important information about the course material. For any class
you take it is very important to understand the details of the syllabus given
by your instructor, so you should read it thoroughly and carefully.
Many times students miss points in the class because they have not
carefully reviewed the syllabus. Most of
the questions you have about the details of the class can probably be answered
by just looking over the syllabus. After
reading the syllabus, if you find that you still have questions about the
course do not hesitate to ask your instructor for more clarification.
Things to remember when reading the
syllabus:
1. Read
through the syllabus.
2. Underline/star
the parts that the instructor has emphasized.
3. Highlight
the important dates to remember.
4. Put
question marks next to things you may be unclear about.
Do no lose the syllabus. Keep it for your records and refer back to it
throughout the course to stay on top of things.
One way to avoid losing the syllabus is to keep a notebook/binder for the class. If your notebook has a transparent front
jacket, it is a good idea to place it there for quick reference. If not, you can place it as the first page of
your notebook/binder. You should use the
notebook/binder to take notes in the class in an organized manner. Start each page by writing the important
information like the date and section(s) to be covered that day. These class notes should be reviewed
periodically and also when you are preparing for quizzes or exams.
Lesson 1 Activity:
Syllabus Search
Directions: Use your class syllabus to answer the
following questions.
My instructor’s name is _______________________________________
I can contact my instructor by:
Phone: _______________________
Email:_____________________________
My instructor’s office is located in: ___________
My instructor’s office hours are:
_______________________________________
Matching my schedule with my instructor’s office hours, the
times that I will be able to meet with my instructor are:
____________________________________
The website address for
this class ___________________________________ (leave blank, if none provided)
The required textbook for this class is titled
________________________________________________________________
and I can buy it on campus at
________________________________________
For this class I need a
(circle one) scientific/graphing calculator such as a _______________.
Other materials I need
are:___________________________________________________________________________
The attendance policy is:
____________________________________________________________________________
The cheating policy is:
______________________________________________________________________________
Course Grading Policy
I plan to earn a(n)
A/B/C_____________ in this course.
The grading scale will be:
A=________B=________C=________D=________F=________
My course grade will be based on my scores on
_________________, ________________,
and _____________________.
Homework is graded using
___________________________________
Each homework assignment is worth _____ points and all
homework is worth _______points total for the course.
This class has ______tests
that are scheduled on ________________________
Each test is worth
_________points.
The Final Exam
is scheduled on ____________and is worth __________points.
Other requirements
are: ________________________________________________________________________
_______________________________________________________________________________
Resources for this Course
If I need help in this course, I can use the following
resources:
1
_______________________________________________________________
2 _______________________________________________________________
3
_______________________________________________________________
4
_______________________________________________________________
If I need a tutor for this course, I can call
_______________________________
or go to_________________________________
If I need accommodation
due to a disability I need to _________________________
If I need to contact a
classmate from this class I would call or email
1
_______________________phone: _____________email:________________
2
_______________________phone: _____________email:________________
3
_______________________phone: _____________email:________________
A good time for me to
meet with a study group is_________________________
Questions for my instructor about
the grading policies:
________________________________________________________________________________________________________________________________
Lesson 2
What Makes Math
Different and Math Anxiety
What Makes Math Different
1. Math requires
a different study process. You must not only learn the material, but understand it, and then apply it to solve problems.
2. Math is a linear learning process. What is used one day is used the next, and
so forth. In a history class you can
learn chapter 2, but not 3 and possibly do fine on chapter 4. In a math class, you must understand the
material in chapter 1 before you go on to chapter 2. In other words, you need to retain everything
you learn and build on it.
3. Math is much like a foreign language. It
must be practiced EVERY DAY, and often the VOCABULARY is unfamiliar.
4. Math in college is different from math in
high school. You may not have class every day.
Attendance may be optional. There
are usually only a few midterms a semester and your grade is based almost
exclusively on your exam grades. What
took a year to learn in high school is now covered in only fifteen weeks.
Lesson 2 Activity A: Study Strategies for Math
Directions:
Given the four differences above, make a list of specific study strategies you
will use in studying for this math class.
1.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
2.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
3.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
4.____________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________________
Math Anxiety
Math anxiety is an emotional reaction to
mathematics based on a past unpleasant experience which harms future learning.
A good experience in learning mathematics can overcome these past feelings and
success and future achievement in math can be attained.
How
to overcome math anxiety:
1. Overcome negative
self-talk. Never say “I can’t...” or “I’m no good at...”
2. Ask
questions.
3. Consider
math a foreign language -- it must be practiced.
4. Don't
rely on memorization to study mathematics. Aim for understanding the concepts.
5. READ your
math text, working out the examples as you go along.
6. Study
math according to YOUR
LEARNING STYLE.(Auditory, Visual, or Kinesthetic)
7. Get help
the same day you don't understand a topic.
8. Be
relaxed and comfortable while studying math.
9.
"TALK" mathematics. Communicate
with your classmates using proper terminology.
10. Develop
responsibility for your own successes and failures.
Lesson 2 Activity B:
Do you have Math Anxiety?
Directions: Rate your answers from 1 to 5 by circling the
desired number; add them up and check your score below. (1) = Strongly
Disagree, (5) = Strongly Agree.
- I cringe when I have to go to math
class. 1 2 3 4 5
- I am uneasy about going to the
board in a math class. 1 2 3 4 5
- I am afraid to ask questions in
math class. 1 2 3 4 5
- I am always worried about being
called on in math class. 1 2 3 4 5
- I understand math now, but I worry
that it's going to get really difficult soon.1 2 3 4 5
- I tend to zone out in math class. 1
2 3 4 5
- I fear math tests more than any
other kind. 1 2 3 4 5
- I don't know how to study for math
tests. 1 2 3 4 5
- It's clear to me in math class, but
when I go home it's like I was never there. 1 2 3 4 5
- I'm afraid I won't be able to keep
up with the rest of the class. 1 2 3 4 5
CHECK YOUR SCORE:
40-50 Sure thing: you
have math anxiety.
30-39 You're still
fearful about math.
20-29 On the fence!
10-19 Wow! Loose as a goose!
If
you scored above 20 points make sure you review again “How to overcome math
anxiety” from above and list 3 or more changes you will make during this math
course to improve your math success.
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
________________________________________________________________
Lesson 3
Listening
and Classroom Skills
Success
in math starts in the classroom. You
need to make sure that you are prepared to learn and have all the materials
that you need. You should pay attention
to where you sit so that you can best see the board and hear the instructor
without distractions. You also need to
come to class prepared. This means
bringing your notebook, textbook and any other needed materials (pencils,
colored pens/pencils, ruler, calculator, etc.) EVERY DAY as well as being
mentally prepared. Below is a check list
to help you.
Where
to sit: “The
Golden Triangle”: Choosing
where to sit is the first step you take to ensure your success. In the front of the classroom there are fewer
distractions and it is easier to see the board.
The point in the back of the triangle is good for auditory learners because the instructor’s
voice will project to this point. Do not
hesitate to try out different positions until you find the spot that works for
you. Also, communicate with your
instructor- if there are distractions in the classroom that are interfering
with your learning, such as other students’ talking, noise or glare from
outside, etc., let him/her know so that they can help you.
Warm up for class:
- Review
the previous days’ notes.
- Read
the section to be covered.
- Review
your homework.
- Prepare
questions.
- Work
out a few problems from the previous lesson.
Active listening:
- Repeat
important information to yourself.
- Listen
for main ideas.
- Ask
appropriate questions.
- Mark
your notes at points you need to go back to or ask about.
Note taking: The goal is to record as much information as
possible with a minimal amount of notes.
Your notes must be organized and neat.
One type of note taking that is particularly powerful in a math class is
the column system. You can use 2 or 3
columns. Make the columns before class.
- Start
each lecture with a clean sheet of paper, label it with the date and
course.
- Label
one column for examples, one for explanations. A 3rd
column can be used for key words and rules.
- Listen
for cues from the instructor about problems that may be harder or problems
that are already in the book.
- Show
ALL steps when copying problems from the board.
Lesson 3 Activity:
Note Taking
Directions: Use the 3 column system for the lecture on
_____________. Meet with your study group to compare your notes with the other
people in your group.
- What
were the main concepts? ______________________________
- Did
you all have the same examples? _______________
- Can
you understand the other’s notes? _______________ Can they understand
yours? ___________________
- Make
a list of how you can improve your notes._________________________________
Lesson 4
Reading a
Math Textbook
Your math textbook should be one of the most helpful
tools you use to successfully complete your math course. You should always read sections BEFORE the
lesson and then again after the lesson before you do the homework. Following is a summary of steps you can use
to become a more active reader of your textbook.
1)
You should be familiar with your
textbook.
a.
The answers are _______________
b.
The book has answers for
_________problems
c.
There are formulas________________
d.
Each chapter contains (circle all
that apply) chapter summary, chapter review, practice test, a list of formulas
and definitions for the chapter.
2)
Before each class: Survey the
section to be covered.
a.
Read paragraph titles.
b.
Read all bold faced words and
definitions.
c.
Look over examples.
d.
Note any information that is
boxed.
3)
After class: Survey the homework.
a.
Look at the assigned problems; note any definitions or key
words that are used.
4)
Read the section.
a.
Read it thoroughly!
b.
Either in your book, or on notes
(depending on if you plan to keep your book), work out any examples, make a
vocabulary list, note any examples or definitions you will need to ask about in
class or office hours.
5)
Survey again.
a.
Now survey the text and your
notes.
6)
Do the homework.
Lesson 4 Activity
A:
Directions: Fill in the blanks for step 1 above for
your textbook.
Lesson 4 Activity
B:
Directions: For section______________, read it as
described above and complete the following for your journal:
1)
Your vocabulary list for the
section.
2)
A list of questions about the
section (be as specific as possible.)
3)
A short summary of the main
idea/concept covered in this section.
Lesson 5
Doing the Homework
1)
Complete
your homework assignment every night, and certainly before the next class.
In college classes, each topic is
covered just once, and the next class session takes up a new topic.
2)
Read
the section in the book and your lecture notes before starting.
3)
Write
out step by step solutions to your homework problems neatly in a notebook, so
that you can use your solutions later for test preparation. Make sure to pay
attention to the following:
·
Never
do your homework in pen. Ink is the number one ingredient in the recipe for
sloppy homework.
·
Use
scratch paper for experimentation, and then write the solution in your
notebook.
·
Space
things out to allow for comments or questions about the problems.
4)
Read
the instructions for homework problems carefully. Similar instructions will be
used on the test, so you want to get used to the language. Think of doing
homework as practicing for the exam.
5)
If
a problem is too difficult, check the book and your notes for similar examples,
or a discussion that includes the same concepts or words in the problem. If you
become frustrated with a problem and you have genuinely exhausted every
possible resource for trying to solve it, work for 10 minutes beyond that point
and then, if you still don’t get it, put a question mark by the problem and
move on.
6)
Check
your work by using the back of the book for odd problems.
·
If
yours looks different from the answer in the book, check if your answer is
equivalent to the book answer, but in another form.
·
If
your answer is incorrect, try to find your mistake. It may be a single
arithmetic or algebra error, or a more substantial misunderstanding.
·
If
you cannot find your mistake, put a question mark by the problem and move on.
7)
Avoid
getting bogged down on the homework. Remember the available sources for help.
·
Find
classmates to do homework with.
·
Get
help from your teacher during office hours.
·
Ask
tutors in the Tutoring
Center about your
questions.
8)
Take
short breaks while doing homework. Getting up, walking around, stretching,
getting a snack, or thinking about something fun helps. For each 30 to 40
minutes of studying, you can take a 5 to 10 minute break.
9)
Try
to do as many assigned homework problems as you can. Your goal is to feel
completely confident, so that you can work similar problems efficiently on the
test. After completing the assignment, do the following:
·
Close
the book and list the skills and concepts you learned. Then open the book and
edit your list.
·
Make
note cards with challenging problems and /or main concepts.
·
Prepare
your list of questions to ask including any problem that you still can not work
and any points that seem unclear to you.
10) When asking
questions, try to understand the process
of doing problems. Don’t memorize steps or look for “short cuts”. They may not
apply to all situations.
11) Make sure you go
back and complete (correctly) ALL homework assignments!
12) Keep a problem
log in your notebook that lists problems from each homework assignment that you
have consistently missed.
Lesson 5 Activity A: Homework
Skills worksheet
Directions:
Do the following worksheet with your study group and keep the answers in your
journal.
Below,
evaluate your current approach to homework.
Use as much detail as possible.
Why do
homework?
Why do math teachers
assign homework?
Who benefits when you
do homework?
How does practice help
you improve a skill?
What are the advantages
of doing homework?
How can your graded
homework be useful to you?
Lesson 5 Activity B: Doing Homework
Directions:
Each group member should take out their last math homework paper and pass it to
another member of the group.
Looking
at your classmate’s homework paper:
List 3 good things.
1.____________________________________________________________
2.___________________________________________________________
3.____________________________________________________________
List 3 things that could be improved.
1._______________________________________________________________
2._______________________________________________________________
3._________________________________________________________________
Share
your results with your group. Is there
one common area in which you all could improve?
Answer
each of the following questions individually and then discuss your answers with
your group members.
1. When do you usually
do your math homework?
2. Where do you usually
do your math homework?
3. What is going on
around you when you do your math homework?
4. What would be the
optimal environment for you to do your homework?
5. What do you do if
you get stuck on a homework problem?
6.
When you finish a homework assignment, what does the paper look like?
7. How do you feel when you finish a homework
assignment?
This table lists several practices that students use
when doing math homework. Check the ones
you usually do. In the next column,
check the practice that will help you succeed in this class.
Homework
Practice
|
I
usually do
|
Will help me succeed!
|
|
Do
homework where there is help available.
|
|
|
|
Write
my name at the top of the paper.
|
|
|
|
List
the assignment at the top of the page.
|
|
|
|
Number
each problem.
|
|
|
|
Keep
problems in order.
|
|
|
|
Write
neatly and legibly.
|
|
|
|
Show
all work--not just answers.
|
|
|
|
Refer
to similar examples in text or notes.
|
|
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|
|
|
|
|
|
|
|
|
|
|
|
|
|
|
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Save
my homework to review before test.
|
|
|
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Feel
proud of my work.
|
|
|
Homework
Grades
How much of your course
grade is based on homework?
How often is your
homework assigned?
When is your homework
due?
How much does each
assignment count toward your homework total?
Does your teacher
require you to do your homework in a specific format? If so, what is it?
Where do you turn in
your homework?
Describe the scoring
system used by your teacher to evaluate your homework.
Will your teacher
accept late homework? Is there a
penalty?
Lesson 6
Note
Cards and Review Sheets
Many students feel that
they understand the homework, but then don’t perform as well on exams. One possible problem is retention. In a math class, you must understand the material, apply
it, and retain it! There are many techniques to help you retain
and remember information. Following are two
very useful tools for a math course: note cards and review sheets. Both of these techniques help you in several
ways. First of all, the act of reviewing
the information and choosing what is important is a great review. Then, the actual creation of the cards and/or
review sheet helps reinforce the material and of course, you now have cards and/or
a review sheet to study from.
I.
Note Cards: You can buy a pack of any size note
cards. The goal is to make a set of
cards that will be useful to study from and quiz yourself on. In order to accomplish this, follow the
guidelines below.
a.
Use note cards for vocabulary, formulas,
and example problems.
b.
Put only one (1) word/formula/example/etc.
on a card.
c.
Use the front for the vocabulary word,
title of the formula, or the problem, then on the back put the definition,
formula, or solution to the problem (with all steps).
d.
Organize your cards by category, and
have fun quizzing yourself out loud or in writing.
e.
The problems you put down are a great
source for creating your own practice testJ
II. Review
sheets: These are best done to study for
an exam. The goal is to include all the
important information on only one sheet of paper. Give yourself a time limit for the creation
of the review sheet, and do it all in one sitting.
a.
Survey all the material for the exam:
notes and text. Look for comments you made in your notes about problems and
concepts the instructor noted as important.
b.
Consider any important vocabulary terms.
c.
List any relevant formulas.
d.
Make notes/hints for yourself for
problems that are particularly difficult for you.
e.
Predict the types of questions that will
be on the exam, and include some examples.
Lesson 6 Activity:
Directions: Use the above techniques to complete the following for your
journal.
1.
Create
at least 15 note cards for section _______________________. Then write
an honest appraisal of the experience.
Do you think it would be helpful enough to
you personally to start doing it for
every section? Why or why not?
2. Create a review sheet for the material on
test___________________. Then after
the test, discuss how
the technique worked for you. How did you create the
sheet? How did you organize it? And did
creating it have a positive effect on your retention for the exam? Do you think
you’ll use this technique in the future? Why or why not?
Lesson 7 Test
Preparation
Most cases of “math anxiety” are not caused by math,
but are actually the result of test anxiety, due to inadequate study and
test-preparation skills. Imagine how you would feel if you were giving a piano
recital, and you hadn't practiced the piece you have to play. You would probably feel the same anxiety you
might feel when confronted with a math problem you weren't prepared to solve.
Anxiety during a
test can cause the dreaded “mental
block.” A mental block occurs during a test when there is inadequate
preparation before the test. The trick
to avoiding mental blocks is to prepare
for the test so thoroughly and comprehensively that you build your
confidence to a high level, based on a high level of knowledge.
Have you ever been
in a situation like this?
“I studied 19 hours for my math test
and only got a 37% on it.”
If you receive a
low grade on a test after putting in a lot of time studying, it usually
indicates that you have used ineffective study methods to prepare for the test.
You will get better results if you use your time wisely and efficiently.
Math Test Study Plan
Start your test preparation early--at least several
days before the test. Successful test
prep involves several steps and you need
sufficient time to complete each one.
1. Homework Review. Check that you have completed every
homework assignment that the test
will cover. Not completing every assignment causes holes
in your body of knowledge.
Make sure that every problem is
understood and done with integrity. Integrity means
that
work
has not been copied from the student solution manual, and problems for which help
was received have been redone to guarantee
that you can do them yourself!
2. Test
and Notes Review. Review your class
notes and the textbook sections that deal with the
topics on the test. Pay particular attention
to any questions you wrote in the margins of your notes
or textbook. By the time of the test, you must
get all of these questions cleared up.
Also
Review the
Chapter Summary in your textbook to make sure you understand all the key
concepts. Write out a list of important facts,
formulas and definitions that you will need on
the test. Make sure that you can write any
formulas from memory.
3. Topic
List. Go to each section and write out a list of all the topics the
test will cover. Make your
“topic list” as specific as
possible. Phrase your topics by describing actions to be
performed,
such as “Find the equation of a line through two points,” or “Solve mixture
problems.” For each topic, choose a representative problem that best typifies it. Write
this problem on the list or on a
3x5 card, being sure to list the section and problem
number where you found it. Write
the answer on the back of the list or cards. If you use
the 3x5 cards put them together to create your own practice set for the exam.
4. Topic Problems. Now work on mastering each topic by working the problems you chose on that
topic. Check your answers with
those on the backs of the list or cards. You must get to
the point where you can work out
the entire solution to the problem without consulting
your notes or book. It is critical
that you work on one topic at a time. It is not enough to get
a general idea of how the problems
work; you must develop total confidence in your ability
to work problems on each topic.
To
guarantee success, you must master all the topics on your list before
you work
on
any practice tests.
5.
Practice Test. Once
you have completed steps 1 through 4, you are ready to take a practice
test, perhaps one
your teacher has given you or one in your textbook. Or if you study with a
partner or a group, you could make
and exchange practice tests. Then write out the
solutions to your practice test
under test conditions: no notes, no books, and no help!
Your practice test will probably be
longer than an actual test, because you have
included all possible problem
types. Nonetheless, estimate a reasonable time deadline
for your practice test so that you
will get used to working under time pressure. Then
get your practice test corrected, and work on any remaining
weaknesses in your list of
problems.
Final Preparation Tips
·
Do
not try to learn new material the night before the test.
·
Group
study sessions are very valuable, but do not let them substitute for your own
individual study time.
·
Get
a good night’s sleep the night before the test.
·
Eat
a healthy breakfast on the morning of the test.
Lesson 7 Activity A: Practice Test
Directions: Complete step5 from above for the test on
_________. Keep both your original
practice test and the corrected one in your journal.
Lesson 7 Activity B: Test
Preparation Exercises
Exercise 1. Use the checklist below to analyze the
test prep you used on your last test and then design your strategy to prepare
for your next test!
|
Strategy
|
My prep for last test (yes, no,
or “sort of”)
|
Countdown for next test (Check
these off as you complete them)
|
|
Test prep
started several days before the test
|
|
|
|
Every
homework assignment completed
|
|
|
|
Every
problem understood
|
|
|
|
Every
problem completed with integrity
|
|
|
|
Class notes
reviewed
|
|
|
|
Chapter
Summary reviewed
|
|
|
|
One problem
chosen for each objective
|
|
|
|
My Practice
Test worked
|
|
|
|
Chapter
Review/ Chapter Test worked
|
|
|
|
Resources
for help used
|
|
|
To be better
prepared for the next test I need to:
a.
Continue what I’ve been doing_____
b.
Make a few changes to my test prep strategies_____
c.
Make major changes to my test prep strategies_____
Exercise 2. List the resources
available to you to support your test prep:
_____________________________________________________________________________
_____________________________________________________________________________
Exercise 3.
Write 2 topics of a Topic
List for your next Test, following these instructions.
1. Choose a
section of your textbook and list 2
topics covered in that section. Use the subheads of the
section as an outline to get you started. Be
sure to include the section number and page with your topics.
2. Go through
the homework assignment for that
section of the text, and under each
topic from step 1, write down the directions for the type of problem that
matches it.
3. Choose one or
more problems from the group of
assigned problems you identified in step 2,
and note them down under the topic they go
with.
4. Make a list
of all the skills you encounter in
the problem instructions, such as “Factor
completely,” or “Solve for the indicated
variable.”
Topic 1: _____________________________________________________________________
Hw
directions:
_____________________________________________________________
Hw
problems:__________________________________________________________
Skills
needed: _______________________________________________________________
Now repeat for topic 2.
Lesson 8
Test-Taking
Skills
Stress Reduction
You have already
taken steps to reduce stress by preparing thoroughly for the test. Here are a
couple more tips for the day of the test:
- Make sure you have all the required materials in your
backpack: pencils, erasers, highlighters, calculator, notes,
Scantron/bluebook/graphing paper or other writing materials and any
assignment you need to turn in.
- Pack “comfort items” such as
tissues, water, sweatshirt.
- Do some simple exercises
and/or stretches before the test. Exercise helps reduce stress.
- Always arrive a little early
for the test. Leave yourself time to get settled and get your materials
together. Arriving late will only make you flustered and make it harder
for you to concentrate.
Taking the test
1. Memory dump. As soon as you receive the test, write down
all the formulas or other
information you think you might forget.
2. Preview the test. Look through the entire test quickly and
briefly to see the kinds of
problems and their point values.
3. Second memory dump. Write down anything
else that was jarred from your memory
while doing the preview.
4. Strategy. Decide upon the best way to get the most
points in the least amount of time.
Do the easiest problems first and save the
hard ones for last. Make sure you tackle
problems with high point value.
5. Start working through the test as
quickly as you can while still being accurate.
Review your answers to make sure they make sense.
6. Clearly write down each step in the problems in
order to get partial credit.
7. Do not spend
too much time on any one problem. If you find a problem you don't
know how to work, automatically skip it and go on to the next one. When
you come to
the end of the test, go back to the problems you skipped. Mentally run through your
topic list to identify the type of problem
and how to begin.
8. Guess at any remaining problems or do
as much work on them as you can.
9. Review the test for careless errors.
10. Use all the allotted test time. If you
have time left, check the solution to each
problem, or rework the problem on a
separate sheet of paper. Remember: A few extra
minutes during test time could save you from
having to repeat an entire semester!
Five Common Test-Taking Errors:
1.
Misunderstanding or not following the
directions.
2. Careless arithmetic or algebra errors.
3. Concept errors. These are errors made
when you don't understand the properties or
principles needed to work the problem. If not corrected, concept errors
will follow you from test
to test, causing you to lose points.
Students who have too many concept errors will fail the
course. It is not enough to find out how to
work that particular problem -- you must learn why
you missed that problem, and get help as soon as possible.
4. Application
errors occur when you “know” the concept but cannot apply it. Being able to
state a
rule or formula is not enough to be able to use it! To reduce
application errors, you
must practice the type of problem before
the test.
5. Strategy errors in test-taking itself.
Some examples are:
·
Not
completing problems to their last step.
·
Spending
too much time on one problem.
·
Leaving
answers blank
Everyone makes
some of these errors occasionally, but if you consistently make one or more
of these
mistakes, you need to consciously check for that error after you finish each
test.
Lesson 8 Activity: Test Taking
Skills
Directions: Respond to each
statement by checking Always(A), Sometimes(S) or Never(N)
A S
N
Before
the test
___ ___
___ I arrive on time or even early so I feel calm and ready.
___ ___
___ I set out the required materials so I feel prepared.
___ ___
___ If a problem in the rest of my life may interfere with my test
performance, I write it down on a card and zip it in my backpack until after
the test.
___ ___
___ I ignore others in the room--I do not want to pick up their
negativity or anxiety. I am prepared and confident.
___ ___
___ I check my inner voice. I turn any negative thoughts into positive
statements. “I am prepared; I’ve done what I can; I am ready to succeed; I can
do math!”
The test itself
___ ___
___ I do a “data dump” as soon as I get the test. I no longer need to
think about remembering these facts/formulas.
___ ___
___ I scan the test, reading all problems before I begin to work any.
___ ___
___ I read directions carefully – I circle, underline or highlight key
words and directions.
___ ___
___ I note easy problems and do them first to build my confidence and
ensure those points.
___ ___
___ If I can’t do a problem immediately, I write down anything I can
think of such as formulas, pictures, etc., and then I move on and return to it
later. The solution may come to me as I work on the other problems.
___ ___
___ I show all my work. I write
all steps, reasoning, and supporting evidence. This is really helpful when my
teacher awards partial credit.
___ ___
___ I check my work.
___ ___
___ I check answers. I make sure word problems have reasonable answers.
___ ___
___ I pace myself.
___ ___
___ I do not turn in my test early. I use the time to carefully go over
my work.
___ ___
___ I ignore others. I remember that those done early may be turning in
a blank test.
Stress reduction during
the test
___ ___
___ I check my inner voice. I turn any negative thoughts into positive
statements.
___ ___ ___ I imagine and visualize that I am in my
favorite pleasant relaxing situation.
___ ___
___ I take mental breaks.
___ ___
___I do stress reducing exercises.
___ ___
___ I do deep breathing.
___ ___
___ I do muscle tensing and relaxing.
Look
at your checklist.
·
Can
you think of any technique(s) that you use regularly that is not on the
checklist? Add it (them) in the spaces provided in the checklist.
·
Look
at the ‘Sometimes’ and ‘Never’ categories. List three techniques that you may
try during the next test.
1)___________________________________________________________________________
2)__________________________________________________________________________
3)__________________________________________________________________________
Lesson
9
Post- Test
Analysis
Learning From Your Returned Test
You can learn a
lot by going over your test when it is returned. If you are still hazy about
some of the
material on this test, it will make it difficult or impossible to master the
material on
the next test.
In any case, you'll see it all again on the final exam.
1. Locate all
your errors and write corrections on the test in a different color.
2. Identify any
careless errors and analyze why you might have made them. Were you working
too fast? Did you forget to check your
work?
3. If there are
some problems you still don't understand, get help from your teacher or tutor.
4. If there are
some problems or topics that caught you by surprise on the test, mark those
areas
in your notes and study them again.
5. Look for any
strategy errors you might have made and be aware of them on future tests.
6. Try to form
an overview of the test and see how the instructor views the material. What
topics did he or she emphasize? What kinds
of problems? What kinds of errors lost the most
points, and which were “minor” errors? This
should help you predict what the next test will
be like and help you study for it.
Save
your returned tests
(along with quizzes, homework, etc.) to help you study for the final.
Lesson 9 Activity: Test Analysis
Directions: Use the following descriptions to fill in the
chart. Answer the questions on a
separate sheet of paper and put it in your journal.
Look
at your graded test and analyze whether each point loss was due to a careless error, a concept error, or your having been unprepared for that problem.
A
careless error is one where you
understood the problem and knew how to solve it, but you made a relatively
minor mistake in calculations etc.
A
concept error is one where you
really didn’t understand the concept behind the problem. No matter how much time was available for a
problem like this, you wouldn’t have been able to do it because you didn’t know
how to approach it.
Being
unprepared for a problem means you
didn’t know how to do the problem because you hadn’t done/practiced the
homework that would have prepared you for it.
Fill
in the chart below putting the number of points missed on each problem
under the correct heading and then find the total in each column.
Problem
|
careless error
|
concept error
|
unprepared
|
|
1
|
|
|
|
|
2
|
|
|
|
|
3
|
|
|
|
|
4
|
|
|
|
|
5
|
|
|
|
|
6
|
|
|
|
|
7
|
|
|
|
|
…
|
|
|
|
|
|
Total
points
|
Total
points
|
Total
points
|
|
|
|
|
|
In
which column did you have the most missed points?
What
does this tell you about yourself?
What
can you learn from this exercise?
First, consider
the careless error points.
Careless errors
are often caused by hurrying during a test or by lack of concentration due to
test anxiety or over-confidence. So here are some strategies that have worked
for other math students:
- Do the easiest problems first. When you
first start on a test, look it over from beginning to end and note which
problems will be easiest for you.
Do all those problems first, to ensure that you don’t leave an easy
problem blank, just because it is at the end of the test. Finishing the problems you find easy
will help build your confidence! Then go through the rest of the test from
beginning to end.
- Work carefully and neatly. As you do
each problem try to focus on one step at a time.
- Review each problem to look for
careless errors
when you finish the test. Arithmetic mistakes and sign errors should be
found and corrected before you turn your test in.
- Whenever possible check the
problem.
A lot of points can be gained by slowing
down and being careful!
·
What
are two things you will do next time to prevent careless errors?
1.
2.
- Now take
half of your “careless” points and add them back to your test total.
- What could
your test grade have been? _____
- Would that
have changed your A/B/C grade? _____________
Now
consider the concept error points.
A high total in this column tells you
that you didn’t understand the concepts very well. As you do your work day–to–day
you might think you “get it”, but you don’t always verify that you understand
each problem in the homework completely. You may understand a math concept for
the two hours you’re working on the homework problems, but forget it by the
next day.
·
Review earlier
sections.
Make sure to spend some homework time reviewing earlier sections, instead of
saving all the review for test time.
·
Get the help you
need immediately!
Math concepts build on each other. Each
new idea is based on many previous concepts.
Make sure you get the help you need immediately, as soon as you find
yourself beginning to feel lost, so that the confusion doesn’t compound itself
– otherwise it can become like a snowball, getting bigger and bigger as it
rolls through the snow.
If your total loss due to concept errors
is fairly large, find out where you can get the help you need. Pierce has
places available just for you to get help with your math.
·
List
two places you can go to get help with your math:
1.
2.
A high concept error total is cause for
concern and must be addressed immediately to guarantee success!
What about the points lost because you were
unprepared?
Consider why you took the test without
being fully prepared. Oftentimes, activities and responsibilities in life interfere
with good intentions about being diligent in attending class, reading the
textbook, and doing all the assignments.
It may be time to:
·
Re-examine your weekly schedule and make sure you are devoting a
sufficient amount of time to this class.
Lay out a time management grid of your schedule making sure to schedule
your math study time.
·
Re-commit
yourself to succeeding in this class; think about your college and career
goals and remind yourself of how this course helps you get one step closer to
achieving them.
·
List
two steps you
will take to remedy being unprepared.
1.
2.