Spring 2003 Assignments
View the "Guidelines for Written Work."
Each assignment you submit must be enclosed in a cover sheet employing a prescribed format. Information on "The Prescribed Format for Assignment Cover Sheets" can be found by following one of the following links.
The
Prescribed Format for Assignment Cover Sheets (Internet Explorer)
The
Prescribed Format for Assignment Cover Sheets (Netscape)
The
Prescribed Format for Lesson Plans
Go Directly to:
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:
a. Use Netscape or Internet Explorer to access your instructor's web
page. Find the home
page for this course.
b. Follow the appropriate links and read the "Tentative
Course Syllabus," "Guidelines
for Written Work,"
and the "Instructors'
Policies."
c. Explore some of the links for this course at http://faculty.salisbury.edu/~dccathcart/MathReasoning/ReasoningLinks.html
3) Read A.D. Garner's chapter "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, January 28.
Assignment #2 - Due on Tuesday, February 11
1. Carefully review Polya's
four-step problem solving process. Look at the link
http://faculty.salisbury.edu/~dccathcart/MathReasoning/Polya.html.
(2.) 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.
Assignment #3 - Due on Tuesday, February 18
(1.) Create a problem solving lesson appropriate for middle school
students. Your lesson should be based on a problem similar to the
"Counting Triangles Problem" we have been considering. Your geometric
design need not be based on triangles. You may decide it would be
better to work with squares or some other geometric shape. Design
your lesson plan using the format
prescribed for this course. In addressing the "Appropriate Content
Standards Connections" follow the links to
Maryland
State Content Standards for Mathematics and Maryland
Learning Outcomes and 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. If you will want to have your own version of Logo on your
home computer, visit the site Welcome
to MSW Logo and learn about available resources. If you have
a Mac computer, then you should visit Brian
Harvey's web site for a Mac version of Logo.
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the home page for this course.
Assignment #4 - Due on Tuesday, February 25
1. Read Chapter 4 "Graph Chasing Across the Curriculum: Path Circuits,
and Applications" in [NCTM, 1991]. Identify an activity you will
develop based on the content of the chapter and appropriate for middle
school students. Start working on a lesson plan for that activity.
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 activites suggested in Chapter 4 relate to that standard.
2. Work through the activites in the workshop handout "Problem
Solving with Discrete Mathematics." Try to complete the summary tables
on page 7 of that handout.
3. Try to continue working through the materials titled "Getting
Started with Logo."
Assignment #5 - Due on Tuesday, March 11
1. Write up a lesson plan for a lesson, or series of lessons,
based on a topic introduced in Chapter 4 "Graph Chasing Across the Curriculum:
Path Circuits, and Applications" in [NCTM, 1991]. (You started working
on this plan in Assignment #4.)
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. Try to work through the activities in "Getting Started with
Logo." If you progress to Lesson 10 you will be introduced to recursion
in Logo. You may find it necessary to use "CTRL/G" to stop program
execution rather than "CTRL/Break."
5. Continue the task of organizing your porfolio.
6. Provide peer reactions to some lesson plans.
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Assignment #6 - Due on Tuesday, April 8
1. So far we have considered the following chapters in [NCTM,
1991]: Chapter 2 (Assignment 1), Chapter 3 (Assignment 3), Chapter
4 (Assignment 4), part of Chapter 11 (Assignment 5), and Chapter 20 (Assignment
1). Read the following chapters in [NCTM, 1991] and respond as
requested.
a. 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.
b. Consider the survey problem on p. 21 in Chapter 3.
Employ a Venn diagram in addressing the three questions.
c. During class session five we considered a problem where we
were to determine the number of cats, dogs, and birds in a pet store given
the number of legs and heads the relationship between the number of dogs
and the number of cats. Read Chapter 6 "Discrete Mathematics in the
Traditional Middle School Curriculum," and then propose a problem appropriate
for pre-algebra middle school children similar to the 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.
d. 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.
e. Read pp. 87-first paragraph on p. 90 in Chapter 11 "Graph
Theory in the High School Curriculum." Research Euler's solution
to the Koingsberg
bridges problem and apply that method to the problem
of walking through all the doorways introduced in class in February
26. Both problems can be found on the course web site at http://faculty.salisbury.edu/~dccathcart/MathReasoning/ClassSessions/GraphProbs.pdf.
You might visit the web site at
http://www.utm.edu/departments/math/graph/
for a brief tutorial on graph theory including Euler circuits and paths.
2. Please keep working through the material on Logo.
3. Develop another lesson appropriate for middle school children
on a discrete math topic. Choose a topic related to graph theory,
counting, Venn Diagrams, or pattern recognition employing recursive thinking.
Use the prescribed lesson plan format provided for you at http://faculty.salisbury.edu/~dccathcart/MathReasoning/LessonPlanFormat.html.
4. Visit the NCTM web site and consider the NCTM's
"Reasoning and Proof Standard for Grades 6–8."
Assignment #7 - Due on Tuesday, April 15
1. Do visit the web site http://www.utm.edu/departments/math/graph/
and work through the three tutorials -
"Introduction to Graph Theory," "Euler Circuits and Paths," and "Coloring
Problems."
2. Read "Formulating Algorithms" on pp. 93-94 in Chapter 11 of
[NCTM, 1991]. Relate that topic to the tutorial on "Coloring Problems"
you completed and our discussion of algorithms.
3. Develop a lesson related to an aspect of graph theory that
is appropriate for middle school students. Use the prescribed
lesson plan format.
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Assignment #8 - Due on Tuesday, April 22
1. Revisit the NCTM web site specifying the standards
for reasoning and proof for grades 6-8.
That site is at http://standards.nctm.org/document/chapter6/reas.htm.
2. Revist the site where under the "Maryland State Content Standards
for Mathematics" it is specifed what students should be able to do under
the category of "Reasoning."
Those standards are stated at http://mdk12.org/mspp/standards/math/reasoning.html
3. Revisit the site where under Maryland Learning Outcomes the
"Math
Process" outcomes for K-8 are specified. Those outcomes are specified
at http://www.mdk12.org/mspp/mspap/whats-tested/learneroutcomes/math_process/k-8/outcomes.html
4. Strart working through the on-line logic text "Introduction
to Logic" by Warner and Costenoble. In particular, try to complete
at least the first four sections. 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.
5. Read Chapter 1 "The Truth of It All" in the Solow text [S,
2002].
Assignment #9 - Due on Tuesday, April 29
1. Continue working through the on-line logic text. Finish as
many sections as you can and work some of the exercises.
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/logic/logicintro.html.
2. Read through pp. 9-15 of the Solow text [S, 2002].
3. Try to do Exercise 2.23 on page 22 of [S, 2002].
Assignment #10 - Due on Tuesday, May 6
1. Continue working through the on-line logic text. Finish as
many sections as you can and work some of the exercises.
http://people.hofstra.edu/faculty/Stefan_Waner/RealWorld/logic/logicintro.html.
2, Read through Chapter 3 of the Solow text [S, 2002].
3. Try to work Exercise 3.1.a., 3.1.c., 3.7(a,b, c), and 3.10.