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MATHEMATICS 185
Fall 2017
Texts: 1) Billstein, Libeskind, Lott: A Problem-Solving Approach to Mathematics for Elementary School Teachers (Addison-Wesley Publ.) 12th ed.
STUDENT HANDOPUT PACKET available from the instructor.
A scientific calculator is required for the course (containing exponential function and square root key)
Prerequisite: a grade of C in Math 180 or its equivalent
Course Supervisor: Shelley Ring. Phone: 650-5126 email: r HYPERLINK "mailto:ring@ccny.cuny.edu" ring@ccny.cuny.edu
Introduction
The course includes two major features that may be somewhat unfamiliar in a mathematics class: the use of both required writing exercises and mathematics activities. Both are described below. The purpose of the activities is to provide a concrete approach to the ideas that underlie elementary school mathematics. The goal of the writing exercises is to help you learn to express and reflect on these ideas. I hope that you will give me feedback on how well they both achieve those goals. Thanks!
Activities and Group Work
There are several justifications for group work:
1) Cooperative learning is used extensively in elementary school classrooms and you should have some experience with problem solving in a group setting.
2) English is a second language for many students. It is helpful for them to be provided with the opportunity to express these ideas first to a small group before addressing the instructor and the whole class. You will probably enjoy group work and the active involvement is often more effective (in the long run) than the passive learning situation of lecture. Students have commented that at times they find it easier to listen to and comprehend an explanation by a peer than by the instructor.
3) Group members are encouraged to exchange phone numbers. You are (of course) responsible for material missed due to absence and you should phone classmates for assignments and copy class notes from the day(s) that you were absent. It is helpful for students meet outside of class to do homework and study for exams.
During the semester, at four times keyed to the appropriate point in the syllabus, your instructor will choose a day when the class meets in R 7/219, and you will work in groups on one of the four Activities. There are copies of the Activity sheets in the Student Handout Packet. Read the material before the day of the Activity. Please be careful to return all of the materials with which you are provided, especially the pieces of the attribute set of Activity 1.
Writing Activities
You are all prospective elementary school teachers. In not too many years, you will be responsible for orchestrating the mathematics learning in your own classrooms. It is a very important that you have the opportunity to reflect on and clarify your own thinking about mathematics. As much as possible, you are encouraged to verbalize, during the class period, questions, concepts (and even misconceptions!) However, class time is severely limited. By providing continuing opportunities for you to write about mathematical ideas and reasoning, your teacher is strengthening your understanding as well as your ability to communicate.
185 Course Material
Sections are in Billstein. (12th edition)
Sections in text:
1-1, 1-2, (Problem Solving) and teach use of the calculator
2-2, 2-3 (Set Theory, especially logical connectors and their English equivalents. Do survey problems with Venn diagrams. Be sure to teach base twelve and binary. Do only addition and subtraction in other bases. Students will learn addition and subtraction in base four and six briefly in Activity 2.
3.1 (Numeration Systems)
4-1, 4-2, 4-3
Chapter 5 Review properties only
6-1, 6-2, 6-3, 6-4, Require understanding of the rules for the four operations. Again, this is a review. (Rational Numbers as Fractions.) 4
7-1, 7-2, 7-3, 7-4 (Exponents and Decimals) Also section 14-2 - the Pythagorean Theorem -only to illustrate real world occurrences of irrational numbers
8-1, 8-2, 8-3, 8.4 (Ratios and percents and algebraic thinking.)
9-1, 9-2, 9-3, 9-4 (Probability)
10-1, 10-2, 10-3, 10-4 (Statistics)
Four in-class Activities
Note: The syllabus should allow time for group work (say, fifteen minutes or so, once a week, within the regular class period) and student participation. In addition, there are the four full-period (one-hour) group activities that are part of the course. A copy of each activity is included in the course Student Handout Packet. The instructor should instruct the students to read and then review each activity in the packet before the actual class period of the activity. Each activity has questions to be answered by the students.
COURSE LEARNING OUTCOMES
DEPARTMENT: MATHEMATICS
.........................................................................
COURSE #: 18500
COURSE TITLE: Basic Ideas in Mathematics
CATEGORY: Required for prospective elementary education majors
TERM OFFERED: every term
PRE-REQUISITES: Math 18000
PRE/CO-REQUISITES:
HOURS/CREDITS: 4hrs. /wk., 3 credits
DATE EFFECTIVE: January 17, 2007
COURSE COORDINATOR: Rochelle RingCATALOG DESCRIPTION
Problem solving, sets, operations on sets, functions, numerical systems with different bases, topics in number theory, probability and geometry. Course involves writing exercises and collaborative work. This course is for potential education majors only.COURSE LEARNING OUTCOMES
Please describe below all learning outcomes of the course, and indicate the letter(s) of the corresponding Departmental Learning Outcome(s) (see list at bottom) in the column at right.
After taking this course the student should be able to:
Contributes to
Departmental Learning
Outcome(s):
1. apply a number of different strategies(Including simple algebra) to solve a variety of problems. a, b, c
2. use set theoretic concepts to reason and to describe relationships among various categories ofobjects and numbers. a, c, e1
3. solve problems using the concept of functions as rules, ordered pairs and graphs. a, b, c
4. develop a fluency with and an appreciation of our whole number numeration system, through a studyof historical numeration systems and bases other than ten. a,
5. use simple number-theoretic concepts (e.g., primes, divisibility) to solve problems to deepen theunderstanding of fraction and decimal operations learned in Math 180. a, e1
6. apply the concepts of least common multiple and greatest common divisor of two integers to operations on fractions. a, e1
7.model and solve real world problems involving fractions and decimals using set and number theoretic concepts. a, c, d
8. demonstrate a knowledge of the concept of irrational numbers and their approximations using a
calculator; in particular, their occurrence in geometry. a, c, d, e1
9. demonstrate a knowledge of the relationship, as well as the distinction, between theoretical and empirical probability. . a, c, e1
10. analyze games, compute probabilities of complementary and compound events and solvesimple counting problems. a, b, c, d, e1
11. interpret statistical graphs and numerical data as well as calculate and use measures
of central tendency and variation. a, b, c, d
12. explain orally or in written form the meaning of mathematical terms, operations and theoremsas well as solutions to problems that they will present in the future in their own classroom. a, e1,
Note: DLO d (use of technology) is limited to the use of the calculator
COURSE ASSESSMENT TOOLS
Please describe below all assessment tools that are used in the course.
You may also indicate the percentage that each assessment contributes to the final grade.
1. three one-hour exams (45%)
2. writing exercises (6%)
3. four one-hour activities (3%)
4. weekly quizzes (6%)
5. final exam (40%)
DEPARTMENTAL LEARNING OUTCOMES (to be filled out by departmental mentor)
The mathematics department, in its varied courses, aims to teach students to
a. perform numeric and symbolic computationsb. construct and apply symbolic and graphical representations of functionsc. model real-life problems mathematicallyd use technology appropriately to analyze mathematical problemse. state (e1) and apply (e2) mathematical definitions and theoremsf. prove fundamental theorems
g. construct and present (generally in writing, but, occasionally, orally) a rigorous mathematical argument.
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