1. STOP DOING MATH LONG ENOUGH TO LEARN IT Getting Started – Background Information Delano P. Wegener, Ph.D. Spring 2005

2. Getting Started  Introductions  Background/Origin  Studying vs Doing  Statement of Purpose  Mathematics vs Computation  Algebra vs Arithmetic  Honest Assessment  Time Commitment

3. Introductions Delano P. Wegener, Ph.D. del@delweg.com

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

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

6. Background/Origin  Reasons for developing this seminar as well as credentials which lend some credence to its contents may be roughly summarized in the following points.  Lessons learned during more than 30 years of teaching mathematics.  Observing less than 50% success rates in the first Algebra courses.

7. Background/Origin  A firm belief that every student can learn mathematics to any desired level of mastery.  Seven years devoted to developing a successful program for teaching remedial level mathematics to college students.  More than 30 years of studying what “teaching and learning” experts have to say.  More than 20 years of observing mathematical ignorance in industry.

8. Studying vs Doing  There is little doubt that Mathematics has a bad reputation. Mathematics may be difficult but its reputation is not inherently deserved from its own nature.  Listen to the words when students, teachers, parents, and the general public speak about mathematics. Compare those words and that language to the words and language used when other subjects are discussed.

9. Studying vs Doing  Students study history, social studies, language arts, etc. They read literature, history or other subjects. They neither study nor read mathematics, but rather they do mathematics.  Teachers encourage their students to do their math every day to avoid falling behind. Parents check to insure their children have studied their spelling, read their literature, studied their history, and done their math.

10. Studying vs Doing  Students take their queue from this language and routinely skip the reading material in a math book. They do not read and certainly do not study the concepts presented. They do precisely what they think is expected of them: they turn to the problems and attempt to do their math.

11. Studying vs Doing  The language of doing mathematics fosters and continually reinforces another more fundamentally incorrect conception about mathematics. Because doing mathematics is equated with doing the exercises in a mathematics textbook, mathematics soon translates into “getting the answer”.

12. Statement of Purpose  One of the objectives of this seminar is to equip you with the tools and habits to help you: “Take Responsibility for Your Education”.  The tools and habits presented in this seminar are designed to help you learn mathematics.

13. Statement of Purpose  A second objective of this seminar is to change your idea about the nature of mathematics. It seems unreasonable to expect success in learning mathematics if you don’t know what it is.  A third objective of this seminar is to explain what you are expected to learn about mathematics.

14. Mathematics vs Computation  Mathematics and computation are not synonyms. Computation is a tiny little subset of mathematics. All but the simplest computations are now relegated to calculators and computers.  Very little mathematics, other than computation, can be done by calculators or computers. Every year significant advances are made in the attempt to teach computers to do mathematics, but don’t expect too much.

15. Algebra vs Arithmetic  Arithmetic is the branch of mathematics dealing with numerical computation. Arithmetical operations include addition, subtraction, multiplication, division, power computation, and root extraction. A mnemonic for the spelling of "arithmetic" is "a rat in the house may eat the ice cream."

16. Algebra vs Arithmetic  The term Algebra comes from the title of an Arabic book - Al-jabr w'al-muqabala - written by Al-Khwarizmi (who lived around the year 800) which is all about algebra.  Algebra is a continuation and extension of the rules of arithmetic to a more general level.

17. Algebra vs Arithmetic  Algebra is the part of mathematics that deals with generalized arithmetic. Letters are used to denote variables and unknown numbers and to state general properties.

18. Algebra vs Arithmetic  Algebra is often described as an extension of arithmetic. Instead of using numbers, Algebra's operations of addition and multiplication are applied to variables (symbols and or letters).

19. Algebra vs Arithmetic  It is important for your success to observe that when moving from arithmetic classes to algebra classes you are taking a step up on the ladder of step up on the ladder of generalization and abstraction. generalization and abstraction.

20. Honest Assessment  If you are enrolled in Pre-Algebra, Beginning Algebra, Intermediate Algebra, or College Algebra, you don’t have a history of success in mathematics.  It is probably true that your previous techniques for studying mathematics have not worked very well.

21. Honest Assessment  Even if you were successful with Arithmetic, you may need to change your study habits in order to be successful in Algebra.  National statistics indicate that about 60% of beginning students need to change study habits.

22. Honest Assessment  What I want to encourage is that you imitate the study habits of those who have a long history of success in learning mathematics.  Study the way mathematicians study, not because you want to be a mathematician, but because it works.

23. Time Commitment  You must make a significant time commitment if you wish to learn mathematics.  A reasonable guide for the average student is three (3) hours of study outside of class for every hour inside class.  You should be realistic – don’t take 15 hours of class work if you are working 30 hours per week.

24. End –Return to Index This concludes the preliminary portion of the seminar. Thank You for Your Attention Click the Thank-you to return to the index