Math 355 Syllabus
Spring, 2007
Course: Math 355, Mathematics for Elementary and Middle School Teachers, 4 credits
Instructor: Dr. Larry Krajewski
MC 525
e-mail: llkrajewski@viterbo.edu
Phone: 796-3658 [office], 782-1648 [home] (call before 10 p.m. please)
Office Hours: 12MW, 9 TTh & by appointment
Prerequisites: Grade of C or better in Math 255
Text: Mathematics for Elementary Teachers, 3rd ed., by Tom Bassarear, Houghton Mifflin, 2005.
Activity Packet
Description
This course is designed to introduce the preservice K-9 teacher with ideas, techniques and approaches to teaching mathematics. Emphasis is on problem solving and problem posing, use of manipulatives and children’s literature, and understanding children’s thinking. The math content areas are the geometry and rational numbers.
The Viterbo University Teacher Education Program has adopted a Teacher As Reflective Decision Maker Model and the Wisconsin Standards For Teacher Development and Licensure, also known as INTASC (Interstate New Teacher Assessment and Support Consortium) Standards. Each course is designed to contribute to the development of one or more of the INTASC Standards. (These standards can be found at http://www.dpi.state.wi.us/dpi/standards/index.html)
Franciscan values, Viterbo core abilities and the liberal studies are the basis of the Viterbo education experience. Focus of every professional education course is on the learning of the PK-12 pupil. Viterbo education courses infuse constructivist practices, use of technology, PK-12 collaboration, awareness of diversity, traditional and authentic assessment, teacher work sample components, and real-world experiences into the preparation of the preservice teacher.
Wisconsin Standards for Teacher Development and Licensure (INTASC)
Standards 1,2,3,4,6,8,9
Wisconsin Model Academic Standards
A, B, F
Wisconsin Content Guidelines
1,2,3,4,5,6,7,8,9,10
Viterbo Core Abilities
Thinking, Communication, Cultural Sensitivity
Resources: You may qualify for free tutoring in the Learning Center.
The following materials are on reserve in the Todd Wehr Library:
- Sample solutions to investigations
- Selected Bibliography on Gender Equity in Mathematics
- Various books on problem solving
Methodology: Lecture, class discussion, small group work, student presentations.
Goals (INTASC 1)
To help students:
1. learn to value mathematics;
2. learn to reason mathematically;
3. learn to communicate mathematically;
4. become confident in their mathematical ability; and
5. become problem solvers and posers.
Objectives
Problem Solving (INTASC 1,2,3)
Upon successful completion of this course, the student will be able to:
- build new mathematical knowledge through problem solving
- solve problems that arise in mathematics
- apply and adapt a variety of appropriate strategies to solve problems
- monitor and reflect on the process of mathematical problem solving
Reasoning and Proof (INTASC 1,4)
Upon successful completion of this course, the student will be able to:
- recognize reasoning and proof as fundamental aspects of mathematics
- make and investigate mathematical conjecture
- develop and evaluate mathematical arguments and proofs
- select and use various types of reasoning and methods of proof
Communication (INTASC 6)
Upon successful completion of this course, the student will be able to:
- organize and consolidate his or her mathematical thinking through communication
- communicate his or her mathematical thinking coherently and clearly to peers, teachers, and others
- analyze and evaluate the mathematical thinking and strategies of others
- use the language of mathematics to express mathematical ideas precisely
- create and use representations to organize, record, and communicate mathematical ideas
Connections (INTASC 1,4)
Upon successful completion of this course, the student will be able to:
Student Responsibilities:
One cannot benefit from or contribute to a class discussion or activity unless one is physically present (this a necessary condition, not a sufficient one). Attendance is required. Call me (796-3658) if you will not be in class. A valid excuse is necessary to miss class. Unexcused absences may lower your grade for the course.
Assigned readings of the texts and handouts need to be done if meaningful discussion can occur.
As teachers you should appreciate the importance of class participation. Your active participation makes the course go. Math is not a spectator sport. Assigned problems and textbook exercises are ways for you to develop problem solving skills and reflect on your learning. Do the problems when they are assigned.
Content
I. Geometry
A. Spatial Reasoning
B. Van Hiele levels
C. Two-dimensional geometry
D. Three-dimensional geometry
E. Translations, reflections and rotations
F. Symmetry
II. Measurement
A. Length
B. Area
C. Volume
III. Rational Numbers
A. Models
B. Ordering
C. Renaming
D. Addition and subtraction
E. Multiplication and division
F. Decimals
Requirements
- Two math activities, one on geometry and one on fractions (see handout)
- Three investigations
- Learning journal from class
- Three exams
- Four summaries of articles in professional journals on the following topics:
Geometry , Assessment, Fractions, and Equity
[Some good sources are Arithmetic Teacher, Teaching Children Mathematics, Mathematics
Teaching in the Middle School, AIMS, and School Science and Mathematics.] (see handout)
- Completion of a minimum of 12 hours of field experience working with an elementary student on mathematics (see handout)
- A clinical journal of your sessions with your elementary student [NOTE: YOU MUST MEET WITH YOUR STUDENT AND FULFILL THIS REQUIREMENT IN ORDER TO PASS THIS COURSE.]
- Assistance in a Family Math Night at Viking Elementary in Holmen on the night of March 15th
Evaluation
Points
Tests (200 points each) 600
Investigations 200
Clinical journal 80
Learning journal 60
Readings 40
Math Activities
20
total 1000
A Note to You
This is a course for prospective elementary and middle school teachers about how children learn mathematics and how to create positive, developmentally- appropriate mathematics instruction. Since we have all gone to elementary school, we have learned and "know" the mathematics which will be addressed in this course; in fact, we may know it so well that we have forgotten what it was like to ever not know it. Or, because of inadequate past instruction, we may feel we "know" certain mathematical topics but have never really understood them, or we may even dislike the subject. If this is the case, consider this course an opportunity to break the cycle of negative, disempowering mathematics teaching. Mathematics can be an intellectual adventure, a powerful tool, and a creative experience for children. As a teacher, you can make it so.
Some of you may have had mathematics courses that were based on the transmission, or absorption, view of teaching and learning. In this view, students passively "absorb" mathematical structures invented by others and recorded in texts or known by authoritative adults. Teaching consists of transmitting sets of established facts, skills, and concepts to students. I do not accept this view. I am a constructivist. Constructivists believe that knowledge is actively created or invented by the person, not passively received from the environment. No one true reality exists, only individual interpretations of the world. These interpretations are shaped by experience and social interactions. Thus, learning mathematics should be thought of as a process, of adapting to and organizing one's quantitative world, not discovering preexisting ideas imposed by others. It is one way to make sense of the world.
Consequently, I have three goals when I teach. The first is to help you develop mathematical structures that are more complex, abstract, and powerful than the ones you currently possess so that you will be capable of solving a wide variety of meaningful problems. The second is to help you become autonomous and self- motivated in your mathematical activities. You will not "get" mathematics from me but from your own explorations, thinking, reflecting, and participation in discussions. As independent students you will see your responsibility is to make sense of, and communicate about, mathematics. Charles Schultz, creator of "Peanuts", compared people to multispeed bikes and noted that "most of us have gears we do not use." Hopefully you will see mathematics as an open-ended, creative activity and not a rigid collection of recipes. And the last is to help you become a skeptical student who looks for evidence, example, counterexample and proof, not simply because school exercises demand it, but because of an internalized compulsion to know and to understand.
I want to help you learn to do something different from and better than what you have experienced as pupils in previous mathematics classes A mathematics methods class is about mathematics, about children as learners of mathematics, about how mathematics can be learned and taught, and about how classrooms can be environments for learning mathematics. It's a class where the students learn about learning mathematics while they themselves are learning mathematics.
As a teacher I have come to realize that when I teach mathematics I teach not only the underlying mathematical structures but I am also teaching my students how to develop their cognition, how to see the world through a set of quantitative lenses which I believe provide a powerful way of making sense of the world, how to reflect on those lenses to create more and more powerful lenses and how to appreciate the role these lenses play in the development of their understanding.
So I ask your help in establishing a mathematical community where one uses logic and mathematical evidence as verification rather than the teacher, where mathematical reasoning replaces the memorization of procedures, and where conjecturing, inventing, and problem solving are encouraged and supported.
You may find this experience frustrating at times. Persevere! Eventually I hope you will own personally the mathematical ideas you once knew unthinkingly or only peripherally (and sometimes anxiously). I want you to become competent and confident using mathematical ideas and techniques. I want you to be ready to learn how to get other persons actively involved in problem solving. To nurture a mathematical idea in the mind of a child might be easier if it first thrived in the mind of the child's teacher.
In training a child to activity of thought, above all things we must beware of what I will call "inert ideas" - that is to say, ideas that are merely received into the mind without being utilized, or tested, or thrown into fresh combinations . . . Education with inert ideas is not only useless: it is, above all things, harmful. Except at rare intervals of intellectual ferment, education in the past has been radically infected with inert ideas . . . Let us now ask how in our system of education we are to guard against this mental dryrot. We enunciate two educational commandments, "Do not teach too many subjects," and again, "What you teach, teach thoroughly." . . . Let the main ideas which are introduced into a child's education be few and important, and let them be thrown into every combination possible. The child should make them his own, and should understand their application here and now in the circumstances of his actual life. From the very beginning of his education, the child should experience the joy of discovery. (Alfred North Whitehead, The Aims of Education)
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Americans with Disabilities Act If you are a person with a disability and require any auxiliary or other accommodations for this class, please see me and Wayne Wojciechowski, the Americans With Disabilities Act Coordinator (MC 335 <796- 3085>) within ten days to discuss your accommodation needs.
It is somewhat surprising and discouraging how little attention has been paid to the intimate nature of teaching and school learning in the debates on education that have raged over the past decade. These debates have been so focused on performance and standards that they have mostly overlooked the means by which teachers and pupils alike go about their business in real-life classrooms - how teachers teach and how pupils learn.