for EMAT 4600/6600: Problem
Solving in Mathematics
James W. Wilson
105 Aderhold Hall, (Office in Rm 110-F)
Internet Address: http://jwilson.coe.uga.edu
E-mail address: firstname.lastname@example.org
I maintain an open door policy for office hours. I come to the office
early each morning and if I am not tied up in a meeting or talking to
another student I am available to you.
Prerequisites for EMAT 4600/6600: MATH 2210 or permission
of the instructor.
Comment for Middle School Teachers: Middle school teachers
have in the past been recommended for this course. It appears not to be
a "good fit." Please talk with me and other students in the
class before you panic and flee. We will work with you to make the course
a positive experience.
This course will concentrate on solving, or attempting solve, mathematics
problems. How can one implement problems solving goals and activities
in mathematics instruction without first becoming a problem solver?
The emphasis is on exploration of various mathematics contexts to learn
mathematics, to pose problems and problem extensions, to solve problems,
and to communicate mathematical demonstrations.
The problems will come from many sources and contexts. The primary ground
rule is that the problem situations can be investigated with pre-calculus
mathematics. We will use problem contexts to pose problems, explore mathematical
relationships, examine the use of resources -- media, technology, references,
or colleagues -- to engage in mathematics problem solving. Inquiry, investigation,
exploration will be significant descriptors of what we want to accomplish.
Contextual Teaching and
This course and others will
be part of the University of Georgia implementation of the concepts
of Contextual Teaching and Learning (CTL). From the USOE Web Site on
CTL, we have the following description:
Contextual teaching and learning
is a conception of teaching and learning that helps teachers relate
subject matter content to real world situations and motivates students
to make connections between knowledge and its applications to their
lives as family members, citizens, and workers and engage in the hard
work that learning requires. Contextual teaching and learning strategies:
- emphasize problem-solving;
- recognize the need for
teaching and learning to occur in a variety of contexts such as home,
community, and work sites;
- teach students to monitor
and direct their own learning so they become self-regulated learners;
- anchor teaching in students
- encourage students to
learn from each other and together; and
- employ authentic assessment.
See the following links for
exemplifary problems can be used in contextual teaching and learning:
There is no textbook.
Course assignments and materials (especially problems sets) are mostly available
on this Web Site
Material will also be given
via handouts, via class demonstrations, and via use of references.
Occasionally, a problem or problem context will come up during the class
discussions, either from class members or when the discussion jogs my
memory of a repressed problem. Obviously, students are encouraged to locate
appropriate problems from other materials of interest to them.
Using the Web Site, handouts, references, and ingenuity, each student
will define and accumulate a mathematics problem resource. The
resource may be a Web Site created by the student, or it may be a loose-leaf
notebook, or it may be some combination of media or other organization.
The substance of the resource is the student's organization of problem
material, solutions, comments, and instructional notes.
I will help you create a Web
Site if you want it. However, a resource (notebook) can be assembled without
any use of technology or the Internet except to have access to the problems.
To explore problem solving in mathematics as
. . . a curricular
. . . an instructional strategy
. . . the essential core of mathematics
. . . a process for doing mathematics
To develop a "can do" approach to mathematics problems
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
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.
You are expected to attend class. (Why is it necessary in 2001 for faculty
to have to make such a statement?) If you have to miss for reasons other
than illness, see me prior to the absence. If you are ill, your first
priority is your health and the health of others. See me afterward and
we will work with you.
Absences without good reason is grounds for withdrawal from the course.
Grades and Requirements
Grading is a necessary part of what we do and it is my intention to base
grades on performance in meeting the requirements of the course. This
performance includes the following:
-- working with others
-- class discussions
3. The "resource"
- Problems with solutions,
comments for use in class, modifications of problems, extensions
- Some organization to
the resource that makes sense
- A CTL section
4. Final assignment.
This will be in lieu of
a final examination and in large part will draw heavily from material
you and I select from your resource.
These items do not have the security inherent in criteria on some set
of examinations. I do not believe the usual "tests" are appropriate.
Rather, with some discussion to understand what we are about, "tests"
might, for example, be replaced by an open assignment for exploration.
Most of our sessions in will be in Room 111/113. This room is equipped
with a demonstration computer that I plan to use quite a bit. Computers
in Room 228 and elsewhere will be available for our use. (Note: It is
possible that you could avoid any use of a computer or a TI-81 calculator
during this course, but why would you want to?)