92.520 Mathematical Problem Solving
Focus on Mathematics
Development of this course was supported by Focus on Mathematics (http://focusonmath.org/), which is funded by the National Science Foundation under grant number 0314962.
UMass Online
The course is developed through UMass Online using WebCT. Registration for this course within Focus on Mathematics will be arranged through teachers' districts. Teachers in Focus on Math districts who get approval from their district leader are registered in a batch. UML students who take this course register in the usual way through ISIS. You will get login information just prior to the start of the semester. For general information on UMass Online or to log in once the semester starts, visit http://lowell.umassonline.net/.
Instructor
Kenneth Levasseur
Mathematical Sciences
UMass Lowell
Kenneth_Levasseur@uml.edu
Goals
The goals of this course for all students/teachers are:
1. Make students aware of the role of problem solving in mathematics and mathematics education. In particular they should become aware of how problem solving is integrated into state, national and international standards for mathematics education.
2. Help students investigate ways in which their own students' problem solving abilities can be enhanced using their curriculum. Although we will not look at curricula in depth, they should become capable of assessing the degree to which curricula address their state problem solving standards. The discussion will center around Teaching Mathematics through Problem Solving (NCTM: Reston VA, 2003), but will also draw on other resources that they will be encouraged to find.
3. Improve their own problem solving ability through working on problems. They will work on a variety of different problems, including at least one that they will work on for most of the semester.
4. Prepare to work with colleagues in order to replicate as much of this course as is feasible in their own district.
Prerequisites
There are no specific prerequisites for the course. A familiarity with the content of K-12 mathematics and an interest in delving deeply into that content is all that is really needed. It is expected that participants in the course will arrive with a variety of different mathematical backgrounds, but the goal of improving their problem solving ability is relative and so this course should be applicable for all "initial conditions."
Time Commitment
Course design is based on the assumption that students will spend at least six hours per week on three main activities. In a typical week, the six hours would break down in roughly the following way.
1. Three hours: completing worksheets from Ways to think about mathematics.
2. Two hours: reading and responding to selected chapters from Teaching Mathematics through Problem Solving.
3. One hour: working on a single long-term problem from a recent issue of a Mathematical Association of America journal.
Tentative outline of the course
Introductory Topics - getting started with an on-line course
Welcome
About the Instructor
Communications Tools
Communicating Mathematics
Course Requirements
Grading
Keeping in touch - changing your email address
Technical Support
Week 1 - Introductions, Overview and the MAA problems
Comments on Preliminary Problems
Introductions
Professional Development, "Ways to think..." and Facilitation
Teaching Mathematics through Problem Solving
MAA Problems
Featured Web Site: Mathematical Association of America
Chat Topic: the MAA problems
Week 2 - Consecutive Sums, Problem Posing
Problem Set 1-1: Problem Solving and Problem Posing (Consecutive Sums)
Mathematics as Sense Making
Selection of MAA problems
Chat topic: The first worksheet
Week 3 - Conjectures, Habits of Mind
Worksheet 1-2: You've got a Conjecture, Now what?
Habits of Mind
Featured Web Site: NCTM
Chat topic: Problematizing your Curriculum
Week 4 - Proofs, Technology
Types of Proof
Technology and Problem Solving
Featured Web Site: "Making Mathematics"
Chat topic: The role of Technology in Mathematics
Week 5 - Do it yourself, Sociomathematical Norms
Worksheet 1-3: Do it yourself
Social and Sociomathematical Norms
Chat Topic: Sociomathematical Norms
Week 6 - Classroom Applications, Control in Problem Solving
Worksheet 1-4: You know the answer? Prove it.
Selecting Quality Tasks
Chat Topic - Control Strategies in Problem Solving & the MAA problems
Week 7 - Statistics and Problem Solving
Worksheet 1-5: Discerning what is...
Progress reports on the MAA Problems
Teaching Statistics through Problem Solving
Chat topic: Facilitation - doing mathematics with colleagues
Week 8 - Pythagoras & Listening
Worksheet 4-1: What would Pythagoras do?
Modes of Listening
Proofs without Words
Chat Topic: Statistics
Week 9 - Puzzling out some Proofs, Low-SES Students
Worksheet 4-2: Puzzling out some proofs
Teaching Low-SES Students Mathematics through Problem Solving
Chat Topics: Proofs, Low SES students
Week 10 - Pythagoras' Second Cousins, Problem Posing
Worksheet 4-3: Pythagoras' second cousins
Problem Posing, the teacher's role
Problem Posing, the student's role
Chat Topic this week: Problem Posing
Week 11 - Pythagorean triples, Problematizing your own curriculum
Worksheet 4-4: Pythagorean triples (and cousins)
Problematizing Your Own Curriculum
This week's chat topic: Your Curriculum, is it Problematic?
Week 12 - Classroom cousins of Pythagoras, Assessment
Worksheet 4-5 - More classroom cousins
Assessment in a Problems-based classroom
Chat topic: Assessment
Week 13 - Wrap Up
Are you ready to Facilitate? - the Teacher's role
Final results on the MAA Problems
Final Chat Topic: Where do we go now?
Created by Mathematica (March 8, 2005)