Workshop on Mathematics Problem Solving
Mastery Project, Mathematics and Science Teacher Education in Yemen
May 16-21 2009
Schedule
Description:
The workshop will be about a mathematics problem solving course for secondary mathematics teachers. We will be using the materials from the EMAT 6600 Problem Solving in Mathematics course that I teach at the University of Georgia. It is one example of what such a course might be an it has been developed and implemented over an extended period of time at the University of Georgia. These materials and the syllabus included are the course as I have developed it. The materials have been used by other faculty at the University of Georgia and by faculty at other universities and adapted to their own courses.
In the process of our discussion over these few days I hope to describe to you what I try to accomplish in this course and the ways I go about it. In many respects I am sure you will find it non-traditional.
We are doing mathematics. This is about problem solving as an integral part of mathematics. I do not pursue discussions of the philosophy of mathematics or philosophy of mathematics problem solving outside of the context of being engaged in mathematics. We will be working from activities rather than abstract premises.
It would be good to keep in mind these OBJECTIVES I pursue in EMAT 6600:
To explore problem solving in mathematics as
. . . a curricular goal
. . . an instructional strategy
. . . the essential core of mathematics
. . . a process for doing mathematics
To develop a "can do" approach to mathematics problems solving.
To understand and describe mathematics problem solving as more process than product.
To become a mathematics problem solver.
To use technology to solve mathematics problems.
To use problem contexts to create mathematics demonstrations.
To use Contextual Teaching and Learning concepts.
To use problem solving to construct new ideas of mathematics for yourself.
To engage in mathematical investigations.
To engage in some independent investigations of mathematics topics from the secondary school curriculum or appropriate for that level.
To communicate mathematics ideas that arise from mathematics investigations.
To consider ways to assess problem solving performance.
As we work through the Workshop this week, we will be engaged with the mathematics problems from the web pages but we will use that as context for coming back to questions, issues, and discussions of these objectives.
One more limitation is in order: The mathematics problems I have included on my web page are all approachable with secondary school mathematics. That does not mean they are included in the secondary school curriculum but rather they are of a level that could be explored in secondary school. Consequently, even though more advanced mathematics and strategies could be applied to some of the problems, I want them explored with mathematics that is at the secondary level.
The Web Page evolves. New material is added each time I offer the course and some 'favorite' problems fade into memory.
Saturday, May 16, 2009
Introduction
Problems to explore
Divide a Square into a Set of Acute Triangles
Bisectors Problem in 120 degree Obtuse Triangle
Arithmetic Mean -- Geometric Mean Inequality
Folding a sheet of paper into equal areas
Construct Equilateral Triangle with vertices on three given parallel lines
Discussion of instructional issues (to be a part of each session)
Note: This sort of reflection may be interspersed in our problem discussions and examples. We will attend to
Strategies for conducting classes.
Selection of Problems
Preparation of Problem Material, Use of material from outside the web page
Using Problems I may not have solved recently
Student engagement in Problem Solving
The role of the student produced 'resources'
Student activities
Student ownership
Portfolio Assessment
Longer view -- something to carry with them from the course
Adapting to large classes
Sunday May 17, 2009
Introduction to the writing of George Polya; excerpts from a video of Polya
Follow-up from Previous Problems
Problems to explore
Discussion of instructional issues
Monday May 18, 2009
Follow-up of Previous Problems
Video Excerpts from one of my classes
Problems to Explore
Discussion of instructional issues
Tuesday May 19, 2009
Follow-up of Previous Problems
Problems to Explore
Volume of Holes Left by Tree Spade
Ratio on a line segment -- Something Golden
Half the Area of a Triangle: A Line Parallel to a Side
Half the Area of a Triangle: A line Through a Point on the Side
Discussion of instructional issues
Wednesday May 20, 2009
Follow-up of Previous Problems
Problems to Explore
Square Inscribed along a base of any Triangle
Discussion of instructional issues
Wrap-up and summary