Math 355: Math for Elementary & Middle School Teachers
Spring, 2001, 4 credits
Professor Larry Krajewski
Office: Murphy Center 526
Office Phone: 796-3658
Home Phone: 782-1648 [No calls between 10 p.m. and 7 a.m. please]
Hours: 10 MWF & by appointment
Prerequisite: C or better in Math 255 & passage of PPST
Text: Mathematics for Elementary School Teachers by Tom Basserear,
Houghton Mifflin, 1997
Final Exam 1:00 class: Friday, May 11, 7:40-9:40 a.m.
2:00 class: Monday, May 7, 9:50-11:50 a.m.
This course is designed to introduce the preservice K-9 teacher with ideas, techniques and approaches to teaching mathematics. Manipulatives, children's literature,
problem solving, diagnosis and remediation, assessment, equity issues, and the uses of the calculator are interwoven throughout the topics presented. The math content areas are rational numbers and geometry.
The Viterbo University Teacher Education Program has adopted a Teacher As Reflective Decision Maker Model. Each course is designed to contribute to the
development of one or more of the knowledge bases in professional education.
This course contributes to the development of the knowledge bases: Knowledge of the Learner, Curriculum Design, Planning and Evaluation, and Instructional and
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.
You may qualify for free tutoring in the Learning Center.
Lecture, class discussion, small group work, student presentations.
Todd Wehr Library The following books are on reserve:
Selected Bibliography for Gender Equity in Mathematics and
Technology Resources Published in 1990-1996 ,Women & Mathematics
Various books on problem solving
Upon successful completion of this course, the student will be able to:
explore, conjecture, reason logically and use a variety of mathematics methods effectively to solve nonroutine problems.
establish classroom environments so that his or her students can explore, conjecture, reason logically and use a variety of mathematics methods effectively to solve
nonroutine problems and develop a lifelong appreciation of math in their lives;
design and use several forms of assessment, such as portfolios, journals, open-ended problems, tests, and projects
become familiar with educational research on effective teaching of mathematics.
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.
Six summaries of articles in professonal journals on the following topics (include a copy of the article in your summary; article must be at least two
Geometry <due February 1>
Assessment <due February 15>
Technology <due February 29>
Measurement <due March 22>
Fractions <due April 11>
Equity and mathematics <due May 2>
The purpose of this assignment is to acquaint you with some resources outside of the textbook and to introduce you to some ideas or activities that
you may want to share with the class when we are investigating the appropriate topic.
Please follow these guidelines:
Include a copy of the article with your summary.
Use the reporting form included in your packet.
Articles must be at least two pages long in the original citation.
Articles taken from the internet must be complete (No missing pictures, diagrams, or equations.)
A problem notebook with assigned problems from the text and class.
You must work out the solutions. Merely copying answers from the solutions manual is not appropriate.
Completion of a minimum of 12 hours of field experience working with an elementary student on mathematics
A journal of your sessions with an elementary student. [NOTE: you MUST MEET WITH YOUR STUDENT AND FULFILL THIS
REQUIREMENT IN ORDER TO PASS THIS COURSE.]
Two math activities, one on geometry and one on fractions
Three in-class exams
Problem notebook & Math Activities 6
Student journal 10
Investigations (4) 16
Tests (3) 60
Learning Journal 5
A. Spatial Reasoning
B. Van Hiele levels
C. Two dimensional geometry
D. Three dimensional geometry
E. Translations, Reflections and Rotations
III. Extending the number system
B. Rational numbers and fractions
1. Models for rational numbers
2. Comparing rational numbers
3. Renaming rational numbers
4. Addition and subtraction
5. Multiplication and division
D. Proportions and ratios
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.
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.
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 320 - 796- 3085 ) within ten days to discuss your accommodation needs.
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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.
The Culture of Education