The ACCLAIM Capstone Mathematics Course

AMS Sectional Meeting in LexingtonSpecial Session on Mathematics Outreach

March 27, 2010

Michael MaysInstitute for Math Learning

WVU Department of Mathematics

• NSF-CLT project: The Appalachian Collaborative Center for Learning, Assessment, and Instruction in Mathematics)

• Capacity building as outreach• In-service teacher training as outreach

• Capacity building: Three cohorts of students 2002 (6/13), 2004(5/15), 2007(17)

• Summers+distance education 20 courses, (6 mathematics)

• Doctoral dissertation at cooperating university

• History of Mathematics• Geometry• Discrete Math• Advanced Calculus• Abstract Algebra/Linear Algebra• Capstone: Elementary Mathematics from an

Advanced Standpoint

Felix Klein 1908

“At present my concern is with developments in the subject matter of instruction. I shall endeavor to put before the teacher, as well as the maturing student, from the view-point of modern science, but in a manner as simple, stimulating, and convincing as possible, both the content and the foundations of the topics of instruction, with due regard for the current methods of teaching.”

• 1. What is "An Advanced Perspective"?• 2. Real Numbers and Complex Numbers.• 3. Functions.• 4. Equations.• 5. Integers and Polynomials.• 6. Number System Structures. • 7. Congruence.• 8. Distance and Similarity.• 9. Trigonometry.• 10. Area and Volume.• 11. Axiomatics and Euclidean Geometry.

Problem analysis 1

• Basic algebra problem: Person A sets out in a car going at v = 50 mph. Starting h = 3 hours later, person B tries to catch up. If person B goes at w = 75 mph, how long does it take to catch up?

Parameter in/function out Intersection of functions

Problem analysis 2

• Basic algebra problem: Find two numbers m and n whose sum is 10 and whose product is 18.

RSA cryptography

• A stupid spy publishes N = 12007001 and E=7. Find the obvious factorization of N and use it to decrypt the "secret" message 3973692 165810 6506132 5228823 11249839 4543968

Research done in Israel with the nomenclature of probability in Hebrew, Arabic, and Russian suggests that it is more difficult for students to learn the mathematical meanings of words when the words have everyday meanings in their language than when the words do not possess everyday meanings (Tatyana Zaslavsky, Orit Zaslavsky, and Michael Moore, “Language Influences on Prospective Mathematics Teachers’ Understanding of Probabilistic Concepts,” Focus on Learning Problems in Mathematics 23:2 (Spring 2001) and 23:3 (Summer 2001). Discuss how this research might apply to the usual English names for sets of numbers.

See the attached printout from ERIC describing a study conducted about first graders in rural western Idaho. Suppose you want to adapt the study to students in your school district. Identify a mathematical concept that you would expect to be least understood, and explain how you would use topics covered in ACCLAIM mathematics courses to design an in-service activity for the experimental teachers to illuminate this concept.

Contacts, notes, more information

• http://acclaim-math.org/• http://math.wvu.edu/~mays/• http://www.math.wvu.edu/~mays/

ACCLAIM/Math_534.htm• mays@math.wvu.edu