Summer 2005 Assignments
View the "Guidelines for Written Work."
The
Prescribed Format for Lesson Plans
Go Directly to:
Assignment #1 - Due on Thursday, June 23
(1) Get your computer account activated. (You should change your initial password.) Access your Groupwise e-mail account and send an e-mail message to your instructor. If you have another e-mail account that you prefer to use, go through the steps to have your SU Groupwise e-mail forwarded to that preferred account.
(2) Log in on the campus computer system and do the following:
Use Netscape or Internet Explorer to access your instructor's web page. Find the home page for this course.
Follow the appropriate links and read the "Tentative Course Syllabus," and "Guidelines for Written Work,"
Explore some of the links for this course at http://faculty.salisbury.edu/~dccathcart/MathReasoning/ReasoningLinks.html
(3) Read A.D. Garner's Chapter
1 "A Cautionary Note," on pp. 10-17
in Discrete Mathematics Across the Curriculum, K-12 [NCTM, 1991].
(4) Work through Burrell et. al.'s Chapter 20 "Recursive Thinking:
A Method for Problem Solving," on pp. 166-170 in [NCTM, 1991]. Write up a
discussion of the relationship between the problem discussed in the chapter and
the problem about triangular numbers that we discussed in class session #1
on Tuesday, June 21.
(5) Carefully review Polya's
four-step problem solving process. Look at the link http://faculty.salisbury.edu/~dccathcart/MathReasoning/Polya.html.
(6) Write up an illustration of Polya's four-step process
in addressing the "Counting Triangles Problem" stated at http://faculty.salisbury.edu/~dccathcart/MathReasoning/ClassSessions/session_2.pdf.
(7) Read the article "Twenty Questions about Mathematical Reasoning" The article is found by following one of the "Links for this Course."
http://www.stolaf.edu/people/steen/Papers/reason.html. Jot down a few brief remarks or questions in reaction to Steen's article.
Assignment #2 - Due on Monday, June 27
(1.) Describe a problem solving lesson, or two, appropriate for middle school
students that you plan to create. Your lesson may be based on a problem similar to the
"Counting Triangles Problem" we have been considering. However, you may
choose any appropriate topic - perhaps one suggested by a reading or something
you found on a web site. You should design
your lesson plan using the format
prescribed for this course. When you address the "Appropriate Content
Standards Connections" follow the links to Maryland
State Content Standards for Mathematics and Maryland
Learning Outcomes and plan to relate your lesson to some Maryland standards
or prescribed learning outcomes. Alternatively, you may relate your
lesson to some NCTM Standards.
(2.) Read Chapter 3 "Strengthening a K-8 Mathematics Program
with Discrete Mathematics" in [NCTM, 1991]. Write up a one or two
paragraph reaction to the chapter. You may comment on terms or concepts
that are not meaningful to you. You may comment on any topics that
you would like to see explored or developed more fully.
(3.) Read Chapter 4 "Graph Chasing Across the Curriculum: Path Circuits,
and Applications" in [NCTM, 1991]. Identify an activity based on the
content of the chapter and appropriate for middle school students that you would
like to investigate further.
Go to http://standards.nctm.org/document/chapter6/rep.htm
and review the NCTM's Representation Standard for grades 6-8. Comment
on how the activities suggested in Chapter 4 relate to that standard.
(4) Vsit the web site
http://www.utm.edu/departments/math/graph/ and start working through the three
tutorials - "Introduction to Graph Theory," "Euler Circuits and Paths," and
"Coloring Problems."
Assignment #3 - Due on Wednesday, June 29
(1) Write up a lesson plan for a lesson, or lessons, you started working on in Assignment #2.)
(2) Read pp. 87-the first paragraph on p.90 of Chapter 11 "Graph
Theory in the High School Curriculum" in [NCTM , 1991].
(3) Visit the web site http://www.mazeworks.com/hanoi/index.htm and consider the Tower of Hanoi Puzzle. Look for a relationship between the number of disks and the minimum number of moves to complete the prescribed task. Once you have figured out either a recursive relationship or an explicit direct computational relationship (functional equation, closed form solution), write up a solution to the following problem in a way that illustrates application of Polya's four-step problem solving process:
Suppose one starts
with a tower of 32 disks in the Tower of Hanoi Puzzle and moves one disk
each second. If one
accomplishes the task of moving the tower of disks in the minimum number
of moves how long will it
take to complete the task?
(4) So far we have considered the following chapters in [NCTM, 1991]: Chapter 2, Chapter 3, Chapter 4, part of Chapter 11, and Chapter 20. Read the following chapters in [NCTM, 1991] and respond as requested.
Read Chapter 1 "Discrete Mathematics: The Math for Our Time." Consider the list of topics proposed for a high school course on pp. 7-8. Identify those topics that you think might be introduced at some level of abstraction in the middle school. Also, identify those words in the list that have no meaning to you.
Consider the survey problem on p. 21 in Chapter 3. Employ a Venn diagram in addressing the three questions.
Read Chapter 6 "Discrete Mathematics in the Traditional Middle School Curriculum," and then propose a problem appropriate for pre-algebra middle school children similar a problem we considered in class or similar to one of the two problems introduced in the chapter. Suggest how middle school children might "think like mathematicians" in approaching and solving your problem.
Read the the following sections in Chapter 9 "Discrete Mathematics: An Exciting and Necessary Addition to the Secondary School Curriculum." Consider the section on "Graph Theory" on pp. 69-70. Consider the section on "Difference Equations" on pp. 71-72. Identify those concepts you would like explained further.
(5) Work through the on-line logic text "Introduction to Logic" by Warner and Costenoble. Work a few of the exercises for each section you complete. The text can be found at http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/logic/logicintro.html.
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