M 360M/396C, Fall 05
Assignment for Thursday, October 6
1. Do the exercise Fold-A-Form (passed out in class) for class
discussion.
2. Read (slowly, pondering as you read) the Reasoning and Proof
Overview ((pp. 56 - 60; document Reasoning and Proof in UT E-Reserves)
of the Principles and Standards.
(If you have read this section
before, be sure to read it again -- it's got a lot in it, so you can
undoubtedly get something new from it even if you've read it before.)
Pay special attention to the following points:
- Important vocabulary:
conjecture, converse, inductive reasoning, deductive reasoning.
- As you read, think about the role of
reasoning and proof in your own mathematical learning. Did your
learning in primary, middle, and secondary school meeet the standards
outlined here? If not, how might you teach your students so that their
mathematical learning does meet these standards?
- Think as you read about how reasoning and
proof are used in problem solving.
- Bottom of p. 56/top of p. 57: Try doing the "magic
trick" and figuring out why it works yourself before reading the
discussion of how it works.
- p. 58 , first paragraph: Note how the
sophistication of students' justifications should grow as the students
progress through the grades.
- p. 58, second paragraph. What related
conjecture involving prime numbers can you formulate? Can you verify
it? Is the converse of the conjecture discussed here true? Why or
why not?
- p. 59, top: Reflect on your own proficiency in
the various types of reasoning listed here.
(If you're looking for a journal topic: Your thoughts on the reading
would make a good one.)
3. Continue working on any class activities not yet discussed in class.
4. Continue working on any problems not yet discussed, paying
special
attention to:
•
Analyzing/understanding the problems
• Reasoning
5. M 396C only: Hand in journals.
Note: The first exam will be
Thursday, October 27 (usual class time and place.)