STOP DOING MATH STOP DOING MATH LONG ENOUGH TO LONG ENOUGH TO

LEARN ITLEARN IT

Getting Started – Background InformationGetting Started – Background Information

Delano P. Wegener, Ph.D.Delano P. Wegener, Ph.D.

Spring 2005Spring 2005

Getting StartedGetting Started IntroductionsIntroductions Background/OriginBackground/Origin Studying vs DoingStudying vs Doing Statement of PurposeStatement of Purpose Mathematics vs ComputationMathematics vs Computation Algebra vs ArithmeticAlgebra vs Arithmetic Honest AssessmentHonest Assessment Time CommitmentTime Commitment

IntroductionsIntroductions

Delano P. Wegener, Ph.D.Delano P. Wegener, Ph.D.

del@delweg.comdel@delweg.com

Background/OriginBackground/Origin

This seminar came about as the result of This seminar came about as the result of many years of teaching mathematics, many years of teaching mathematics, studying fundamental principles of teaching studying fundamental principles of teaching and learning, and observing that more than and learning, and observing that more than 50% of students in elementary college math 50% of students in elementary college math classes fail mainly because they do not classes fail mainly because they do not properly study mathematics. properly study mathematics.

Background/OriginBackground/Origin Most students in elementary college math Most students in elementary college math

classes do not know how to study mathematics classes do not know how to study mathematics and consequently have had very little success and consequently have had very little success learning mathematics. They have probably learning mathematics. They have probably never had instruction on how to study math. never had instruction on how to study math. Without proper guidance they have developed Without proper guidance they have developed an unsuccessful strategy. In this seminar I an unsuccessful strategy. In this seminar I hope to take some small steps toward hope to take some small steps toward correcting that situation.correcting that situation.

Background/OriginBackground/Origin Reasons for developing this Reasons for developing this

seminar as well as credentials seminar as well as credentials which lend some credence to its which lend some credence to its contents may be roughly contents may be roughly summarized in the following pointssummarized in the following points.. Lessons learned during more than 30 years of Lessons learned during more than 30 years of

teaching mathematics.teaching mathematics. Observing less than 50% success rates in the Observing less than 50% success rates in the

first Algebra courses.first Algebra courses.

Background/OriginBackground/Origin A firm belief that every student can learn A firm belief that every student can learn

mathematics to any desired level of mastery.mathematics to any desired level of mastery. Seven years devoted to developing a Seven years devoted to developing a

successful program for teaching remedial level successful program for teaching remedial level mathematics to college students.mathematics to college students.

More than 30 years of studying what “teaching More than 30 years of studying what “teaching and learning” experts have to say.and learning” experts have to say.

More than 20 years of observing mathematical More than 20 years of observing mathematical ignorance in industry.ignorance in industry.

Studying vs DoingStudying vs Doing There is little doubt that Mathematics has a There is little doubt that Mathematics has a

bad reputation. Mathematics may be difficult bad reputation. Mathematics may be difficult but its reputation is not inherently deserved but its reputation is not inherently deserved from its own nature.from its own nature.

Listen to the words when students, teachers, Listen to the words when students, teachers, parents, and the general public speak about parents, and the general public speak about mathematics. Compare those words and that mathematics. Compare those words and that language to the words and language used language to the words and language used when other subjects are discussed.when other subjects are discussed.

Studying vs DoingStudying vs Doing Students Students studystudy history, social studies, history, social studies,

language arts, etc. They language arts, etc. They readread literature, history literature, history or other subjects. They neither study nor read or other subjects. They neither study nor read mathematics, but rather they mathematics, but rather they dodo mathematics. mathematics.

Teachers encourage their students to Teachers encourage their students to dodo their their math every day to avoid falling behind. Parents math every day to avoid falling behind. Parents check to insure their children have check to insure their children have studiedstudied their spelling, their spelling, readread their literature, their literature, studiedstudied their their

history, and history, and donedone their math. their math.

Studying vs DoingStudying vs Doing Students take their queue from this Students take their queue from this

language and routinely skip the reading language and routinely skip the reading material in a math book. They do not read material in a math book. They do not read and certainly do not study the concepts and certainly do not study the concepts presented. They do precisely what they presented. They do precisely what they think is expected of them: they turn to the think is expected of them: they turn to the problems and attempt to problems and attempt to dodo their math. their math.

Studying vs DoingStudying vs Doing The language of The language of doingdoing mathematics fosters mathematics fosters

and continually reinforces another more and continually reinforces another more fundamentally incorrect conception about fundamentally incorrect conception about mathematics. Because mathematics. Because doingdoing mathematics mathematics is equated with is equated with doingdoing the exercises in a the exercises in a mathematics textbook, mathematics soon mathematics textbook, mathematics soon translates into “getting the answer”.translates into “getting the answer”.

Statement of PurposeStatement of Purpose One of the objectives of this seminar is to One of the objectives of this seminar is to

equip you with the tools and habits to help equip you with the tools and habits to help you: you:

““Take Responsibility for Your Education”. Take Responsibility for Your Education”.

The tools and habits presented in this The tools and habits presented in this seminar are designed to help you learn seminar are designed to help you learn mathematics.mathematics.

Statement of PurposeStatement of Purpose A second objective of this seminar is to A second objective of this seminar is to

change your idea about the nature of change your idea about the nature of mathematics. It seems unreasonable to mathematics. It seems unreasonable to expect success in learning mathematics if expect success in learning mathematics if you don’t know what it is.you don’t know what it is.

A third objective of this seminar is to explain A third objective of this seminar is to explain what you are expected to learn about what you are expected to learn about mathematics. mathematics.

Mathematics vs ComputationMathematics vs Computation Mathematics and computation are not Mathematics and computation are not

synonyms. Computation is a tiny little subset of synonyms. Computation is a tiny little subset of mathematics. All but the simplest computations mathematics. All but the simplest computations are now relegated to calculators and are now relegated to calculators and computers. computers.

Very little mathematics, other than computation, Very little mathematics, other than computation, can be done by calculators or computers. can be done by calculators or computers. Every year significant advances are made in Every year significant advances are made in the attempt to teach computers to do the attempt to teach computers to do mathematics, but don’t expect too much.mathematics, but don’t expect too much.

Algebra vs ArithmeticAlgebra vs Arithmetic Arithmetic is the branch of mathematics Arithmetic is the branch of mathematics

dealing with numerical computation. dealing with numerical computation. Arithmetical operations include addition, Arithmetical operations include addition, subtraction, multiplication, division, power subtraction, multiplication, division, power computation, and root extraction. computation, and root extraction.

A mnemonic for the spelling of "arithmetic" is A mnemonic for the spelling of "arithmetic" is "a rat in the house may eat the ice cream.""a rat in the house may eat the ice cream."

Algebra vs ArithmeticAlgebra vs Arithmetic The term Algebra comes from the title of an The term Algebra comes from the title of an

Arabic book - Al-jabr w'al-muqabala - written Arabic book - Al-jabr w'al-muqabala - written by Al-Khwarizmi (who lived around the year by Al-Khwarizmi (who lived around the year 800) which is all about algebra.800) which is all about algebra.

Algebra is a continuation and extension of Algebra is a continuation and extension of the rules of arithmetic to a more general the rules of arithmetic to a more general level.level.

Algebra vs ArithmeticAlgebra vs Arithmetic Algebra is the part of mathematics that Algebra is the part of mathematics that

deals with generalized arithmetic. Letters deals with generalized arithmetic. Letters are used to denote variables and unknown are used to denote variables and unknown numbers and to state general properties.numbers and to state general properties.

Algebra vs ArithmeticAlgebra vs Arithmetic Algebra is often described as an extension Algebra is often described as an extension

of arithmetic. Instead of using numbers, of arithmetic. Instead of using numbers, Algebra's operations of addition and Algebra's operations of addition and multiplication are applied to variables multiplication are applied to variables (symbols and or letters). (symbols and or letters).

Algebra vs ArithmeticAlgebra vs Arithmetic It is important for your success to observe It is important for your success to observe

that when moving from arithmetic classes to that when moving from arithmetic classes to algebra classes you are taking a algebra classes you are taking a

step up on the ladder of step up on the ladder of

generalization and abstraction.generalization and abstraction.

Honest AssessmentHonest Assessment If you are enrolled in Pre-Algebra, Beginning If you are enrolled in Pre-Algebra, Beginning

Algebra, Intermediate Algebra, or College Algebra, Intermediate Algebra, or College Algebra, you don’t have a history of success Algebra, you don’t have a history of success in mathematics. in mathematics.

It is probably true that your previous It is probably true that your previous techniques for studying mathematics have techniques for studying mathematics have not worked very well. not worked very well.

Honest AssessmentHonest Assessment Even if you were successful with Arithmetic, Even if you were successful with Arithmetic,

you may need to change your study habits you may need to change your study habits in order to be successful in Algebra.in order to be successful in Algebra.

National statistics indicate that about 60% of National statistics indicate that about 60% of beginning students need to change study beginning students need to change study habits.habits.

Honest AssessmentHonest Assessment What I want to encourage is that you imitate What I want to encourage is that you imitate

the study habits of those who have a long the study habits of those who have a long history of success in learning mathematics. history of success in learning mathematics.

Study the way mathematicians study, not Study the way mathematicians study, not because you want to be a mathematician, because you want to be a mathematician, but because it works.but because it works.

Time CommitmentTime Commitment You must make a significant time commitment if You must make a significant time commitment if

you wish to learn mathematics. you wish to learn mathematics.

A reasonable guide for the average student is A reasonable guide for the average student is three (3) hours of study outside of class for three (3) hours of study outside of class for every hour inside class. every hour inside class.

You should be realistic – don’t take 15 hours of You should be realistic – don’t take 15 hours of class work if you are working 30 hours per class work if you are working 30 hours per week.week.

End –Return to IndexEnd –Return to IndexThis concludes the preliminary portion of the

seminar.

Thank You for Your Attention

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