The ACCLAIM Capstone
Mathematics Course
AMS Sectional Meeting in Lexington
Special Session on Mathematics Outreach
March 27, 2010
Michael Mays
Institute 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