Teaching Math and Other Subjects toDevelopmental Students

Dr. Paul and Kimberly NoltingAcademic Success Press, Inc. 2006

www.academicsuccess.com

Variables Contributing to Student Academic Achievement (Bloom, 1976)

Cognitive Entry Level Skill

+

IQ

Self-conceptLocus of ControlAttitudesAnxietyStudy HabitsSES

Quality ofInstruction

Placement

Grades

Math history

LD

Aptitude

Learning speed

Learning styles

24/7 Web accesses

Tutor training

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

Textbooks

Homework

Test PreparationTests

Class Note-taking System

Textbook Learning System

Learning from Homework

Homework/Test Reviews

Practice Tests

Ten Test Taking Steps

Test Taking Errors

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) StrategiesSet 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 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.

Reading a math textbook = studying the material, learning it, and storing it in long term memory.

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. Review related textbook material.2. Review appropriate lecture notes.3. Do homework neatly.4. Write down every problem step.5. Understand reasons for problem steps.6. 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?

Problem Steps

Rules, terms, properties, etc.

How do I check my answer?

Answer:

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 SystemThree 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 pre-made 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 Explanation

Note taking System

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

“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.”

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

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. Misread Directions

2. Careless Errors

3. Concept Errors

4. Application Errors

5. Test Procedure Errors

6. 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 self-worth.

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 anxietyStudents 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_Trends.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