Math 130/131/132
Fall 2004 - Fall 2005
Concepts and Processes I , II, and III
Section 1: M, W, R
Section 2: M, W, R 11:30 12:45; ACW 203; Holden
Section 3: M, W, F
Instructors:
Debra Borkovitz ACW 210 x2230 dborkovitz@wheelock.edu
Office Hours: Wednesday 10:00 11:00 or by appointment or drop by. Good times to find me are Mon, Thu 2-4 and
Friday mornings.
Peter Holden ACW 202 x2124 pholden@wheelock.edu
Office hours: Mon, Thurs 10-11:15
Ivy Schram ACW 208 x2325 ischram@wheelock.edu
Office hours:
Course Description: Provides an opportunity for students deepen their understanding of Number and Operations; Algebraic Thinking; Geometry and Measurement; and Probability and Data Analysis. Emphasizes problem-solving strategies, justifying reasoning, mathematical communication, representation, and making mathematical connections. Intended primarily for prospective teachers. Three-semester sequence; the first two semesters meet for three periods per week. All semesters require an additional study group led by a peer tutor. (First two semesters satisfy the College Requirement in Mathematics). Introductory.
Text/Materials: Bassarear, Tom, Mathematics for Elementary
School Teachers, 3/e,
Technology: A scientific calculator is required, and you should bring it to class with you. Graphing calculators are recommended, but not required (if you don’t use a graphing calculator, a calculator that can represent fractions -- such as the TI-30 or TI-32 -- is recommended.)
We will also be using the spreadsheet software Excel and other software throughout the course. No experience is assumed. Since we will often be using computers in class, you should always bring a disk with you.
Course Goals:
1) Problem Solving: Someone once said that good mathematics students are the ones who "know what to do when they don't know what to do." In this course we will learn various strategies for approaching mathematics problems, including what to do when you're stuck or when you're not sure how to start.
2) Communication: Mathematics has its own language, which often uses ordinary words in very specific ways. In this course you will have ample opportunity to communicate your mathematical ideas both orally and in writing and to improve your ability to read mathematics. Being required to communicate mathematics might be a new experience for you, but you will receive support and direction in improving this important and complicated skill.
3) Reasoning: How do you know whether your answer is correct in a math class? Do you usually wait for a teacher to tell you? If you do, what will you do when there is no teacher around? In this class you will learn to justify your thinking with answers that can “convince a skeptic.”
4) Representation: Sometimes “a picture is worth a thousand words” in mathematics too. Representation is about capturing a mathematical concept. Besides pictures, representations can include graphs, equations, charts, physical objects, and even numbers themselves. Finding a good representation is often a key to problem solving (for example, think about how much easier it is to multiply 24 x 19 than it is to multiply XXIIII and XIX), and using several different representations for the same concept or problem can enhance understanding.
5)
Mathematical Connections: Mathematics makes much more sense and is much
more interesting when you can see the connections between different topics both within mathematics and between math and
other subjects. When you understand the
relationships between different concepts, you don’t need to memorize.
Tentative Outline of Topics:
First Semester, Math 130:
Topic I: Introduction to Problem Solving, Reasoning, and Communication,
(Chs 1 and 2)
Challenging new problems, introduces the important processes and the style of the course. Introduces algebraic thinking, which will be a theme throughout the course.
Topic II: Whole number operations (Ch 3)
Understanding addition, subtraction, multiplication, and division in multiple ways.
Topic III: Number Theory (Ch 4)
Includes factors, multiples, prime and composite numbers, and divisibility rules.
First semester assignment: Reflective Letter, begin portfolio.
Second Semester: Math 131
Topic IV: Extending the Number System (Ch 5)
Fractions and decimals: representations, ordering, mental math, operations, place value, etc.
Topic V: Proportional Reasoning (Ch 6)
Continuation of algebraic thinking, includes percents.
Topic VI Probability (Ch 7)
Includes simulation and games.
Second Semester Assignment: Reflective Letter, continue portfolio
Third Semester: Math 132
Topic VII: Data Analysis (Ch 7)
Using graphs, tables, and equations to make sense of real world data. Surveys.
Topic VIII: Geometry and Measurement (Chs 8-10)
Properties, transformations, and geometric problem solving and reasoning.
Final assignment: Complete Math Portfolio.
Teaching Assistants / Study Groups: We are fortunate to have many students working as teaching assistants for the course. The teaching assistants will lead study groups, and might be available for individual or group help outside of the study groups.
The study groups will provide an opportunity for you to discuss your homework with your TA and other students in the class and to get more individualized help with the material. Study groups are an important part of the course, and attendance is mandatory.
Expectations: You are expected to do the following:
1) Think. You are capable of thinking intelligently about mathematics (no matter what your previous experience has been). This class is not about memorization, and it is not about imitation.
2) Attend class, be on time, and participate. Attendance will be taken, and absences and lateness will negatively affect your grade. Class will start on time. If you are late (which you should not be), please enter the class in a quiet, non-disruptive way.
3) Work cooperatively with other students in class.
4) Take the initiative in getting help when you need it. Help can come from another student in the class, a TA, a peer tutor, or the professor.
5) Seriously attempt all assigned homework, and turn in your assignments on time. If you miss class it is your responsibility to find out any announcements or assignments before the next class meeting. Homework must be handed in on time.
Homework:
Homework is critical for your success in this course. You can expect an average of about eight hours per week of out of class work, although this will vary from week to week and from student to student. You are strongly encouraged to work with other students when doing your homework, and your study group will provide a consistent opportunity for you to do so. Your instructor will give you additional information about homework policies for your section.
Notebooks:
On the first day of class, you will be given a bound quad ruled notebook, which you will use for reflection on your mathematical understanding and on other aspects of the course. More specific instructions will be provided by your instructor.
Baseline Proficiencies: To pass the course, you will need to pass several baseline proficiencies that address material that all future teachers should know. More details will be provided in a few weeks.
Assessment/Evaluation: You will receive ample feedback about your progress in the course. Your instructor will give you further details on how your work will be assessed and how your grade will be computed
Cheating: Cheating is, of course, unacceptable, and will be reported to the Scholastic Review Board. However, in a course like this, where students often work together, it can sometimes be a little confusing to figure out where to draw the line. If you work with other students on a homework assignment, you should write up your final paper afterward when you are by yourself. You can (and are encouraged to) talk to other people in the class, and to the TA's, but you also need to make sure that you understand and can explain the group's results all by yourself.
Disability Support Services: If you have a disability and need
accommodations, please notify your instructor as soon as possible. You are also encouraged to contact the
coordinator of Disability Services, at extension 2304. To receive academic accommodations at
*************** Everything on this syllabus is subject to change **************
Copyright 2005, Debra K. Borkovitz. You may copy or edit this material for non-profit, educational use only.
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