Math 110 Number Systems for Elementary School Teachers :
Fall 2006
Number Systems for Elementary School Teachers
Math 110
Section 006 12:40 – 1:40 Swart 101 MWF
Section 008 1:50 – 2:50 Swart 101 MWF
Course Description:
In this course we will do mathematics everyday, and we will discuss the mathematical work of teaching. This means that we will think about problems, conjecture, reason, and make arguments. We will learn to communicate our ideas using the language of mathematics, and we will learn to listen and to evaluate the mathematical thinking of others. The content of the course is focused on important mathematics of the elementary school curriculum as described in the National Council of Teachers of Mathematics (NCTM) Principles and Standards (2000): ideas about natural numbers, integers, rational and real numbers; number theory; operations; and the analysis of algorithms.
General Goals and Objectives for the Course:
Students in this course will:
· Create a variety of problem solving strategies;
· Use quantitative methods and symbol systems;
· Distinguish between, and effectively use, inductive and deductive reasoning;
· Learn to make mathematical arguments to justify solutions;
· Come to understand when a solution is correct and complete;
· Communicate mathematics orally and in writing using mathematical language;
· Learn to listen, evaluate and respond effectively to the ideas of peers;
· Build connections among, and work with, a variety of representations;
· Understand children’s models and the mathematical work of teaching;
· Gain an appreciation for the beauty and importance of mathematics.
Instructor: Mike Skowronski
Office: Swart 233
Office Phone: 424 – 7347 (when not in my office, call 424-1333 between 8:00 and 4:30 and leave a myoosickmessage)
E-mail: skowrons<at>uwosh.edu (best way to reach me)
Office Hours: MWF: 9:10 – 12:30
TR: by appointment
Texts and Other Required Materials:
- Number Systems: Course Materials for Math 110, edited by J. Szydlik.
- Elementary Mathematics for Teachers, by T. Parker and S. Baldridge, 2003
(along with the packaged Primary Mathematics materials from Singapore Math)
This is a content course. Content will include but will not be limited to material you may someday teach to your students. You will teach your students processes necessary for them to compete and function in a global society. You will be exposed to the process standards set forth by the NCTM, which are problem solving, reasoning and proof, communicating mathematically, connecting mathematics to other disciplines, and representing concepts using models and diagrams. Other content is intended to help you gain a greater appreciation of the mathematics you will be teaching to students someday.
Description of Specific Content:
- Problem Solving and the Language of Mathematics
- Place Value and Models for Arithmetic
- Analysis of Algorithms
- Prealgebra and a look at Algebraic Structure
- Factors, Primes, Divisibility, GCF, LCM, Fundamental Theorem of Arithmetic
- Models for Fractions
- Models for Integers
- Rational and Real Numbers
Format: We will spend most of our time working on problems in small groups and discussing problem solving ideas and solutions. You will sometimes need to write up the problem solving ideas and solutions and hand them in. However, you are always expected to think about the problems and to communicate your ideas with others. Just as your peers will have unique solutions, your future students will too. This format gives you the opportunity to hone the skills you will need as a teacher: listening and evaluating the thought processes of others; explaining your ideas to others both orally and in writing; and learning to help others understand mathematical ideas.
Evaluation
Homework: This includes individual problem write-ups, group problem write-ups, quizzes, and homework assignments.
Exams: All exams will be given in class. Exam dates will be announce approximately two weeks in advance.
Final Grade: Your final grade will be calculated in the following manner:
Homework, ETC.: 40%
Exam 1: 20%
Exam 2: 20%
Exam 3: 20%
Grading Scale:
A: 93-100%
AB: 87-92%
B: 83-86%
BC: 77-82%
C: 70-76%
D: 60-69%
F: Below 60%
Problem Write-up Guidelines
Problem write-ups should be typed or written in ink on paper (without confetti along the edge) and should include:
- An explanation of the problem: What is the question asking? (3 points)
- A description of your problem solving strategies: What did you try? Did you become “stuck”? If so what did you do? Include any relevant tables, data, or sketches. (6 points)
- The solution: What is the answer to the question? (8 points)
- An explanation of the solution: Why is your answer the correct one? Why does it make sense mathematically? Prove your answer is correct and there are no other solutions. (8 points)
Additional Information
- Students absent on the day of an exam due to participation in a university approved activity must make arrangements to take the exam early.
- Math tutors are available free of charge in Swart 113. There are tutors specifically for MATH 110.
- Mathematics is not a spectator sport. Therefore, you need to actively read and study the text. You may need to read the text several times before the concept becomes understandable. It may be helpful to form study groups and work together on problems. Remember too that being stuck is an honorable state. Sometimes if you are stuck it may help to throw the books down and take a break by listening to music, watching TV, or talking a walk or a drive.
- Wisconsin DPI Standards for Mathematics are your guidelines in the classroom. They can be found at http://www.dpi.state.wi.us/standards/matintro.html.