Teaching Math and Other Subjects to
Developmental Students
Dr. Paul and Kimberly Nolting
Academic Success Press, Inc. 2006
www.academicsuccess.com
Variables Contributing to Student
Academic Achievement (Bloom, 1976)
Placement
Aptitude
Grades
Math history
LD
Cognitive Entry Level Skill
+
IQ
Quality of
Instruction
Learning styles
24/7 Web accesses
Tutor training
Self-concept
Locus of
Control
Attitudes
Anxiety
Study Habits
SES
Learning speed
Math study skills
Self-regulated Learning
Workshop Agenda
Guidelines for integrating study strategies
into the classroom
Guiding students to develop study systems
for learning mathematics.
Student study strategies
Study strategies transformed into
teaching/learning strategies for classroom
Guidelines for Integrating Study Strategies
Select what works best for
you at the beginning.
Integrate one or two at a
time and continue using
them at least two weeks.
After two weeks, try
different study strategies.
Make the students use
them.
Students need opportunities
to practice a study strategy
several times.
Guidelines for Integrating Study Strategies
Require students to
practice study
strategies outside of
class.
Reward them for
using the study
strategies.
Continually tell students that
study strategies help them save
time in the long run and learn
more productively.
Study System Overview
Students need strategies for the following learning activities.
Class Lectures
Homework
Tests
Textbooks
Test Preparation
Class Note-taking System
Learning from Homework
Ten Test Taking Steps
Textbook
Learning System
Homework/Test Reviews
Test Taking Errors
Practice Tests
Test Analysis
Study Strategies to Empower
Students’ Learning Experiences
1. Learning Outside of
Class: Homework and
Textbook
2. Note taking
3. Test preparation
4. Test taking
Learning out of Class
Understand the concepts behind the math
problem.
Complete problems with the speed that will be
required when taking a test. Master the math.
Review frequently to keep what you have
learned fresh, in long term memory, and easy
to retrieve.
Learning from the Textbook
Different reasons to use the textbook:
Before class: Become familiar with vocabulary and concepts.
Helps you collect all the details during class.
After class: Helps glue all the details together or fill in the details
you missed.
Before homework: Reading the textbook and reviewing notes
before starting homework reduces the number of times you flip the
pages.
Visit your instructor
during office hours and
ask for a system for
using the textbook.
Try some of the
strategies from this
workshop.
Reading (Study) Strategies
Set up a section in a notebook for vocabulary. Collect the vocabulary
words as you read and then as they are discussed in class. Remember
that everyday words may mean something different in math. Math is a
foreign language!
Use the learning objectives in each chapter to make sure you are learning
everything you need to learn. Can make note cards of each learning
objective with vocabulary words listed and sample math. Explain the math
to yourself or someone else like another student you study with.
Organize your class notes, using the learning objectives.
Review older material 15 minutes each day by skimming a section of the
textbook.
Reading a math
textbook = studying the
material, learning it, and
storing it in long term
memory.
Reading a math textbook
takes more time. You can’t
skim the book when you are
reading to understand. It
might take an hour to work
through 4-5 pages.
Modeling Textbook Learning
Small group quiz: Without book, students list as
many of the new vocabulary words as possible.
Require students to be ready to tell the class
where a particular vocabulary word, concept or
problem can be found in the textbook. (during
presentation of information) (game)
Set up a system for reading a chapter or
subchapter and model it in class.
Modeling Textbook Learning
Organize notes using the learning objectives
from the textbook (homework assignment)
Insert vocabulary, rules, etc. into their notes.
They can use a different color of pencil so that
when you peruse their notes, you can easily
catch what they have done. (Students can check
each others notes.)
Learning from Homework
Understand the concepts behind the math
problem.
Complete problems with the speed that will be
required when taking a test. Master the math.
Review frequently to keep what you have
learned fresh, in long term memory, and easy
to retrieve.
Ten Steps to Doing Math Homework
1.
2.
3.
4.
5.
6.
Review related textbook material.
Review appropriate lecture notes.
Do homework neatly.
Write down every problem step.
Understand reasons for problem steps.
For difficult problems repeat 1 -5 and
review similar problems, call another
student, use other references, see a tutor
or teacher.
7. Finish by working a problem successfully.
8. Recall or write down important concepts.
9. Make up note cards for difficult concepts.
10. Don’t get behind.
Learning from homework
= Doing homework
Expanded Homework System:
Learning the Concepts
Problem:
What do I ask
myself to get to
the first and
subsequent
steps?
How do I check
my answer?
Problem
Steps
Answer:
Rules, terms, properties, etc.
Complete this process
for key representative
problems, those which
will be like the test
questions.
Keep these in a
section in your
notebook. This is an
excellent tool to learn
the material and make
quick review tools.
Need motivation? Break up your learning goals into small ones. Focus on the
strategies you are using—not the test in the future. Reward yourself when you
are disciplined to complete learning tasks using these strategies.
Chapter Review Sheets:
Learning the Concepts
Learning
Objectives
Sample
Problem
Explanation of steps and list
of vocabulary, rules, and
important points made by
the instructor
More Bang for the Buck!
Learn
Organize notes and problems
Tools for Review
Self-test
Seem like a great deal of work? Find a few collegial friends you trust and
divide up the chapter. Make copies and you have the entire chapter. Or, do
them together, combining a little social life with studying.
Modeling Learning from Homework
Select a key representative problem. In small
groups, students complete one of the previous
expanded homework strategies. Excellent time
to do this is at the end of a learning objective.
Assign students to complete one on their own
after they have learned how to do it. This can be
done with small groups outside of class. (Good
way to introduce idea of study groups.)
Using Language to Learn Math
Vocabulary Cards
Students keep 3x5
vocabulary cards with
definitions in their
own words and
sample on the back.
Quick review.
Compare/contrast
terms to see how they
work together.
Vocabulary Section in
Notebook
Two columns, one with
word and other with
definition and sample.
Keep up with it in class.
Quiz themselves by
folding back column.
Modeling Vocabulary Strategies
Allow time for students to make vocabulary
cards. (small groups) (good way to close a
class)
Ask students to group cards they already have
for a particular unit to show how they relate to
one another.
Class Note-taking System
Three Column Method
Math Problem
Key Words/Rules/
Properties
Examples/Problem Steps
Explanations and questions I
need to ask myself
Integrating Note-taking System into
Classroom Learning
Option One
1. Use 3 column method on the board or use premade 3-column board work on overhead. Do
this for a few classes.
2. Use 3 column method, asking students to fill in
the keywords/rules column. Do same with
Explanation column. Do this for a few classes.
3. Organize lecture and remain sequential so that
students can listen and take notes in three
column fashion.
Keywords
Examples
Note taking System
Explanation
Scaffolding: Math – note-taking
Three column note-taking method on the board.
1.
Instructor models the method for 2 weeks or so.
2.
Instructor provides outline for the students. Students must fill in details
during class.
3.
Instructor provides the process column. Students discuss the
questioning column. Students fill in vocabulary, rules outside of class.
4.
Instructor still organizes presentation of information in a way that
students can use the 3 column, but does not model it on the board. Time
is provided for students to compare notes at end of class.
Reviewing to Maintain Information in
Long-term Memory
Use chapter review sheets or expanded homework or vocabulary
lists for daily 15-30 minute reviews.
Rework your notes, inserting vocabulary, rules, and properties
where they belong.
Review more when the material is more difficult.
Reread the textbook.
Get together with a friend and discuss through your notes and other
review tools.
Preparing for Tests
Review all the time.
Practice master learning.
Make up mental cheat sheets and
memorize them.
Ask instructor for practice tests.
Make a practice test with other
students. Let instructor review for
accuracy.
Memorize vocabulary. Use them
while reviewing problems.
Study what you do not know.
Take a practice test using the Ten
Steps to Test Taking.
One of the best “pieces
of advice” is to assume
you are preparing for the
test whenever you are
working math—in class,
as homework, as review.
Modeling Test Preparation Strategies
Allow time for students to make mental cheat sheets on
note-cards.
As a class, make up a practice test. Students select test
questions. Lead discussion as to why some are good
test questions while others are not. Put the test together
and give to students to take outside of class. Use as a
guide to know what they need to study more.
Students take the practice test using ten steps to test
taking.
Taking the Test:
Ten Steps for Taking a Test
1. Memory Data Dump
2. Preview Test
3. 2nd Memory Data Dump
4. Test Progress Schedule
5. Answer Easy Questions
6. Skip Difficult Questions
7. Review Skipped Questions
8. Guess at Remaining Questions
9. Review All of the Test
10. Use all the Test Time
“The first student done with the test
may not be the smartest in the class.
Often the smart students are the ones
that take the entire time to make sure
they do everything accurately. Be
brave. Stay in the room and make sure
you complete everything accurately.”
Modeling Test Taking Strategies
Provide practice tests in library, learning center,
math department for students to practice using
the test taking strategies.
Write the strategies on the board during the test.
Six Types of Test-taking Errors
1.
2.
3.
4.
5.
6.
Misread Directions
Careless Errors
Concept Errors
Application Errors
Test Procedure Errors
Study Errors
This is why
they invented
the eraser!
Use the eraser wisely. Sometimes it is better to scratch something out
at first and then make sure the correction is right. Go back and erase,
leaving the correct information. Sometimes when we are nervous, we
may change a correct a right answer. We erase the right answer, go
on to other problems, check the test and discover we changed an
answer incorrectly and have forgotten the right answer.
Modeling Test Analysis
Train tutors, learning assistants to work with
students on the test analysis.
Require students who make a B or lower to go
to the academic support centers and complete
the analysis.
Managing Test Anxiety: Causes
Association of grades with selfworth.
Develops from different types of
fears.
Can stem from feeling of lack of
control and change a situation.
Previous embarrassment from
teacher, students, family.
Placed in the wrong class.
Past and continued negative
experiences.
Consequence of perfectionism.
Fear of timed tests.
Poor study and personal habits.
Anxiety strikes
all types of
students
Test Anxiety: Myths
Students are born with it.
Test anxiety is a mental
illness.
Test anxiety cannot be
reduced.
Any level of test anxiety is
bad.
All students who are not
prepared have test
anxiety
Students with test anxiety
can’t learn math
Students who are well
prepared don’t have it.
Intelligent students don’t
have it.
Attending class and doing
homework should reduce it.
Being told to relax will make
you relaxed.
Doing nothing about it will
make it go away.
Reducing test anxiety
guarantees better grades.
Calm Yourself Right before the Test
When you get to the
classroom and you want to
avoid all the panicky talk
going all around you, try the
“Palming” technique.
Place your palms on your
forehead. Think of a place
that is very relaxing to you.
Pretend you are there. Or,
you can think about your
memory “mental” cheat
sheets.
The other benefit is that the other
students will think you have a
headache and will leave you alone.
Tensing and Relaxing Technique
Relax all
your
muscles.
Tense your muscles.
Pull up with your arms
tight.
Press down with you feet
and legs.
Hold for a few seconds.
Relax.
Repeat one
more time if
necessary.
Strategies for Repeating Students
• Enhanced course sections just for repeaters/LD
• Required tutoring/SI/PAL for students
• Required Math Study Skills/Life Skills course
• Appropriate accommodations, identification and
instruction of students with disabilities (LD, ADD)
Web Resources
• Student Life Skills Report (Data Trend31) by Dr Patricia
Windham, Associate Vive-Chancellor for Evaluation
(850-245-9482):
www.fldoe.org/CC/OSAS/DataTrendsResearch/Data_Tre
nds.asp
• Student Math Practice and Learning Sites
http://www.academicsuccess.com
• Title 3 Practice Placement Test Resources (Accuplacer)
http://www.mccfl.edu/pages/1484.asp
• Title 3 Research and Presentation by Dr. Paul Nolting
and others
http://www.mccfl.edu/pages/2092.asp
Web Resources
• American Math Association of Two Year Colleges
http://www.amatyc.org
• Beyond Crossroads by the American Math Association of
Two Year Colleges
http://www.bc.amatyc.org
• Math Research and Study Skills by Dr. Paul Nolting and
others
http://www.academicsuccess.com/research/math.php
• National Developmental Education Association
www.nade.net
Contact Us for Follow-up Conversations
Noltinp@mccfl.edu
941-752-5239