SALEM STATE COLLEGE
DEPARTMENT OF MATHEMATICS
Fall 2008
Course: MSM 711
Linear Systems for Middle School Teachers
Instructor:
Dr.
Julie Belock
Office:
Sullivan Building, room 308C
Telephone:
(978) 542 - 6338
Email:
julie.belock@salemstate.edu
Website:
www.salemstate.edu/~jbelock
Course Description:
This course gives the
middle-school teacher a deeper understanding of systems of linear equations and
matrices. Topics include vectors, solving linear systems, operations on
matrices, inverses and determinants of matrices, and applications of matrices.
Particular emphasis will be placed on using matrices in transformational
geometry.
Prerequisite:
Prerequisites: MSM 701:
Patterns, Relations and Algebra for Middle School Teachers. Acceptance into the
Master of Arts in Teaching Middle School Mathematics program or permission of
the Master of Arts in Teaching Middle School Mathematics coordinator. Not
available for degree credit towards the MAT or MS
programs.
Required
Text:
Anton and Busby,
Contemporary Linear Algebra, John Wiley and Sons, Hoboken, NJ,
2003.
Suggested: TI-83 or TI-84
calculator
Course Goals: This course is intended to provide the
student with
1.
A deeper understanding of
the linear algebra topics taught at the middle school
level.
2.
Strategies for problem
solving and experiences in cooperative problem solving via in-class
activities.
3.
Tools for constructing
mathematical proofs.
4.
Concepts, theorems and
problem solving techniques from the field of linear
algebra.
5.
Means of connecting matrix
representations with geometric transformations.
6.
Practice using visual
reasoning as well as symbolic deductive modes of thought by incorporating
models, concrete materials, diagrams and sketches throughout the course.
Learning
Objectives: The student will be able
to:
1.
Approach problems from
multiple perspectives and help their students become better problem
solvers.
2.
Use mathematical language to
correctly state mathematical definitions and theorems.
3.
Use matrices to solve linear
systems.
4.
Perform matrix and vector
arithmetic.
5.
Demonstrate understanding of
matrix operations and apply them to solve problems.
6.
Prove theorems involving
matrix operations and applications to linear systems.
7.
Interpret linear
transformations geometrically.
8.
Represent geometric
transformations with matrices and vectors.
9.
Relate topics studied to
mathematics taught in middle school.
Course and Grading
Policies
Because of the engaged and
collaborative nature of the course, attendance at every meeting is essential.
Course grades will be determined as follows:
Graded problem sets
15%
Exam 1
20%
Exam 2
20%
Curriculum project
15%
Final exam
30%
Curriculum
project: As
part of the course, participants will be required to submit a 2 – 3 day lesson
plan drawing on a topic from linear algebra. Ideally the lesson will include some
application of matrices to real-world situations or to geometry. The written portion of this lesson plan
must include the specific goals of the lesson, standards addressed, materials
needed, instructions for carrying out the activity, instructions for recording
the activity data, and a list of questions for the student. Additionally the
lesson must include a set of notes to the teacher that would include helpful
hints, pitfalls to be avoided, and suggestions for assessing the activity.
Sample responses to the questions should also be included, as should a complete
bibliography.
Problems through Exam
I:
Problems are assigned on the
date listed, to be completed by the following class.
|
Date |
Sections /
Topic |
|
Problems |
|
9/9 |
1.1
Vectors and Matrices;
n-space 1.2
Dot Product and Orthogonality |
p.
13 |
1 – 27 odd, D3, D9,
P1 |
|
9/16 |
1.2
(continued) 1.3
(optional) 2.1 Introduction to
Systems of Linear Equations |
p.
25 p.
45 |
1, 3, 9, 11, 13, 17,
19, 21, 23, 27, 29, 32, 35. D2, D5, P7 1, 3, 5, 7,
15 |
|
9/23 |
2.1 Introduction to
Systems of Linear Equations 2.2 Solving Linear
Equations by Row Reduction |
p.
46 p.
59 |
17, 21, 23, 25, 27 –
30 1, 3, 5, 9 – 17 odd,
23 – 37 odd, 41, 43, 47, 49, P1 |
|
9/30 |
2.3 Applications of
Linear Systems 3.1 Operations on
Matrices |
p.
75 |
1, 3, 5 and
handout |
|
10/7 |
Exam 1 on Chapters 1 and 23.1 Operations on
Matrices (continued) |
p.
90 |
1, 3, 5 – 8, 29, 33,
D1 |