Math 121 Mathematics for the Elementary
Teacher Fall, 1998
Dr. Carolyn Cuff Office hours
MWF 10:30 – 11:00 (tentative)
Hoyt 154 x7291 T Th 2:15-3:00 and by appointment
OBJECTIVE: This course will cover some of the mathematical content
needed for elementary school teaching. The emphasis of the course will be on
problem solving, fundamental mathematical concepts, and applying mathematical
principles to nonroutine problems. The content of the course includes basic Set
Theory, Number Theory, Probability, Statistics, and Geometry. THIS IS NOT A
REMEDIAL COURSE BUT RATHER ONE THAT CHALLENGES THE PROSPECTIVE TEACHER TO
BECOME AN INDEPENDENT MATHEMATICS LEARNER.
Quality mathematics occurs by thinking
deeply about simple things.
TEXTS:
Joanna O. Masingila and Frank K. Lester, Mathematics
for Elementary Teachers via problem solving, text and student resource
manual
Sembera and Hovis MATH! A Four Letter
Word
REQUIREMENTS:
1. Class attendance - ALL students will attend ALL classes and be
prepared for every class. Students who are not prepared should not
inconvenience their classmates, professor and themselves by attending that
particular class. Unprepared students may be asked to leave that particular
class.
2. Preparation for class
Homework - Homework is the primary measure of your success in meeting
the objective of becoming an independent mathematics learner. This means the problems assigned are meant to
expand and reinforce material and investigations from class. All homework
problems are expected to be legibly completed with appropriate, concise and
comprehensive explanations of the solutions. Students should write in complete
and grammatically correct sentences. Homework is expected to take at
least three hours for each class. See
assessment details below.
Reading - There are three types
of reading; textbook, children’s literature, and MATH! A Four Letter Word.
Each of these readings, assessment procedure and due dates are explained in the
Readings Section
that follows.
3. Basic Skills Exam - These 30 minute exams are detailed in the Exam Section. Makeup exams
will only be scheduled for the reasons given on page 72 of the1998-99
Undergraduate Catalog.
4. Final
Project – Described below.
Textbook - The section listed in the Course Outline and Due
Dates should be read PRIOR to attending the class. After the content is
discussed, students are expected to reread the text.
Children’s Literature - On
reserve in McGill Library are children’s books that illustrate specific math
concepts in this course. Below is a partial description of the Reading Record
for Edu 32 Spring, 1997. You are expected to begin this Reading Record in this
class, recording the information Dr. Charlene Klassen Endrizzi requires, using
your own filing system or her prescribed system, and answering the question
posed in the Course Content and Due Dates section of this syllabus.
Ed. 32, Language Arts & Children’s
Literature
C. Klassen Endrizzi, Spring, 1997
Due April 4th
READING RECORD
Becoming familiar with hundreds of
children’s literature books is one objective for our course and your future as
a teacher. By April 4th, your goal is to read numerous excellent children’s
books. Obtain a 5x8 index card box. In your best printing, record information
about each book on a separate card. Information to record for every book read
includes: author, illustrator, date of publication, publisher, paragraph
summary, category/classification (genres or subject areas) and ideas for use in
the classroom. Use front of card to record this information. On the back side,
write a short personal response to each book (what you liked, didn’t like,
topics for discussion at the literature circle, etc.) Invite 10 students who
have read one of your books to write or draw their response to one of your
books on the back of your cards. Create four sections – 1 for picture books, 1
for chapter books, 1 for Math 18 (this course) books, and 1 for Science 31
books. On April 4th or 7th, you will have a thirty-minute
conference with Charlene and a small group of peers when you will discuss all
of the chapter books you read. Bring all chapter books you read to this
conference.
MATH! A Four Letter Word
- Reaction papers (NOT summary) are due as noted in the Course Content
and Due Dates.
Exams will be based on readings from
the text, in class activities and homework problems. Students should expect
short answer questions on the historical, social, and culture notes as well as
brief problems to solve. A sample exam will be given prior to the first in
class exam.
ACADEMIC HONESTY
This class is a hands-on activity based class. Group work is expected.
In this context, it is possible to misunderstand exactly what it means to be
responsible for "doing your own work." As such, I wish to define
specifically what I expect. Group study is a proper and effective way to
study if all of the participants have done their full share of the work.
Students may discuss problems together and reach conclusions together. But it
is a form of dishonesty for a student who has not attended class, read the
assignment, or thought about the problem on their own to try to use the ideas
developed by a group or claim credit for work to which one has not contributed.
It is also a form of dishonesty to encourage or allow such practices on the
part of others. Specifically the following will be considered dishonest:
a) copying work from a student who has taken
this course previously
b) copying some portion or all of the
required summaries from a classmate - these
are to be done "in your own words"
c) copying some or all of the required
mathematical concept. An easy check for this - if you can not restate
the concept in your own words, you do not understand the concept.
Violation of the above or of the usual
understanding of academic integrity will result in a zero for the assignment.
Notice of the action will be placed on file with the academic advisor and
office of the Vice President for Academic Affairs.
Backpack math - Details of this project can
be found in the Arithmetic Teacher Feb. 1993 issue on reserve in Mack
Library. To summarize this article, the backpack is meant to be a series of
interrelated activities sent home with different students throughout the year.
The student involves his/her family (brothers, sisters, parents, grandparents)
exploring the activities in the backpack. The backpacks must designed with the
following specifications a) aimed toward fifth grade (find a fifth grade text
and choose any topic), b) include 5 interrelated activities (these need not be
original but may not include activities done in this course), c) include a list
of readily available materials that would need to be collected for the backpack
use. Assessment criteria follow.
10% List
of materials is complete
5% Materials
are readily available and/or provided with the kit (for example, if you want 15
pieces of macaroni dyed blue you should include the recipe for dying macaroni!)
10% Grade
appropriate - don’t have 5th graders doing 1st grade material
50% (10%
for each activity) - Activity involves additional members of family, all
members of the family learn something, child has chance to explain his/her
thought process to older family member, children are doing meaningful
mathematics
25% Activities
are interrelated. Ideally, one activity should lead to the next. That is, the
ORDER that students do the activities should be prescribed for a mathematically
and/or pedagogically sound reason.
The project is due during the final
period. Each project will be graded by 2 other students and also by me. The
final grade will be the calculated by taking 50% of the grade I assign and 25%
of the grade each peer assigns. All feedback and the backpack can be picked up
from the Math Department secretary in January. Any not picked up by Feb. 1 will
be thrown away.
GRADING
Percentage of Final Grade
Homework 45%
Children’s Literature Review 9%
Basic Skills Exams 30%
MATH! A Four Letter Word Reaction Papers 6%
Final Project 10%
GRADING SCALE
> .920 A .790 - .799 C+
.900 - .919 A- .720 - .789 C
.890 - .899 B+ .700 - .719 C-
.820 - .889 B .600 - .699 D
.800 - .819 B- < .600 F
ABSENCE FROM CLASS IS NOT A REASON TO
FAIL TO TURN IN ANY ASSIGNMENT ON TIME. Students should make arrangements
to deliver assignments to my office (not the intercampus mail) by 12:30 p. m.
on the date due.
Homework is the major assessment tool
in this class. Of the two or three problems assigned with each class, one will
be graded extensively as follows; the other will be graded after a brief
reading.
Extensive Reading
5 Complete understanding of the mathematical
concepts illustrated by the activity, well written solutions (this includes
grammar and spelling)
4 Almost complete understanding of the
mathematical concepts illustrated by the activity, well written solutions
3 Almost complete understanding of the
mathematical concepts illustrated by the activity, solutions have one or more
grammatical errors
2 Incomplete understanding of the
mathematical concepts illustrated by the activity, fairly well written
solutions
1 Incomplete understanding of the
mathematical concepts illustrated by the activity, poorly written solutions
0 Failure to turn in assignment
Brief Reading
1 More than one half of assignment is
correct and the material is presented well enough to be understood with a quick
reading
0 Less than half of the material is correct
or the material is poorly presented
Children’s Literature Review
2 Bibliography is complete and the question
is sufficiently answered
1 Bibliography is complete and the answer is
not sufficient
0 Bibliography is incomplete or is not
turned in
MATH! A Four Letter Word Reaction Papers
3 Obvious time and effort were put into the
reading and writing of the reaction paper
2 Some time and effort were put into the
reading and writing of the reaction paper
1 The paper was written at the last minute
and/or nothing in the book is referenced
0 Not turned in on time or not a reaction
paper
Final Project Assessment criteria has been
given above
COURSE OUTLINE AND DUE DATES FALL, 1998
Aug. 25 Introduction to Course, Introduction to Problem Solving
In class activities - Activity 1.2
Aug. 27 Problem Solving with Guess and Check, Visual Aids,
Solving a Simpler Problem
Reading and Prep - Chapter 0, Chapter 1.1,
1.2, 1.6
Due - Reaction Paper to Introduction and
Chapter 1 of MATH!
In class activities - Activity 1.1, 1.7
Homework – Activity 1.8, Exercise 30, Exercise 36
Sept. 1 Problem Solving and Patterns and Working Backwards
Reading and Prep - Section 1.3, 1.4
Due - Children’s Lit Connection - Ten
Black Dots How could this book be used in pre-kindergarten and kindergarten
to illustrate the concepts of patterns?
Reaction Paper to Chpt. 2 and 3 of MATH!
In class activities - Activity 1.3, 1.4
Homework – Exercise 37, 24, 25
Sept. 3 Problem Solving using algebra, the precision of
mathematical language
Reading and Prep – Section 1.5
In class activities – Activity 1.5, 1.6, 9.1
Homework – Activity 1.9, Exercise 38, 22
Sept. 8 Problem Solving with Patterns, nonlinear
relationships
Reading and Prep – Reread Chapter 1
Due – Exercise 40
Children’s Lit Connection - How Much is a
Million? How does this book illustrate problem solving with patterns?
In class activities – Activity 1.10
Homework – Exercise 31, 32, 33, 35
Sept. 10 Numeration systems and Place Value
Exam
Reading and Prep – Read Chapter 2 through
section 2.5
Due - Children’s Lit Connection - The
King’s Commissioners How does this book introduce place value?
In class activities – Activity 2.7, 2.8
Homework – Exercise 38, 50, 51, Activity 2.5
Sept. 15 Numeration systems and Place Value, continued
Reading and Prep – Section 2.6
In class activities – Activity 2.9, 2.10
Homework – Exercise 47, 44, 52, 51
Sept. 17 Problem Solving with Sets, Operations
Reading and Prep – Chapter 3
In class activities – Activity 3.1, 3.2
Due - Reaction Paper to Chpt. 4 and 5 of
MATH!
Homework – Activity 3.5, Activity 3.11,
Activity 3.12
Sept. 22 Number Theory Primes and Composites
Reading and Prep – Chapter 4 through section
4.3
Due - Choice for Final Project, if the final
project choice is not turned in at this time, no help will be offered towards
its completion
In class activities – Activity 4.1, 4.2, 4.3
Homework – Exercise 61, 62, 78, 79, 82
Sept. 24 Number Theory, Divisibility
Reading and Prep – Chapter 4.4-4.7
Due - Children’s Lit Connection - 12 Ways
to get to 11 How does this book illustrate basic number theory?
In class activities – Activity 4.7, 4.9
Homework – Activity 4.8, Exercise 79
Sept. 29 Number Theory, Modular Arithmetic
Reading and Prep – Chapter 4.8-4.9
Due - Children’s Lit Connection - The
Doorbell Rang How does this book illustrate largest common factor and least
common multiple concepts?
In class activities – Activity 4.10, 4.11,
4.12
Homework – Exercises 65, 66, 67, 68
Oct. 1 Number Theory, Representations of Number Theory Ideas
Reading and Prep – Review Chapter 4
Due - Children’s Lit Connection - Bridge
to Terabithia Several books have been written to explore the math and
children’s lit connection. Pick up the worksheet in the Mathematics Department
and complete it.
In class activities – Activity 4.15, 4.16
Homework – Activity 4.13, 73, 76, 77
Oct. 6 Probability and Statistics,
Probability of an Event
Exam
Reading and Prep – Chapter 5 through section
5.1
In class activities – Activity 5.1, 5.2, 5.3
Homework – Exercises 25, 26, 27, 28, 29
Oct. 8 Probability and Statistics, Fair
Games and Basic Notions
Reading and Prep – Chapter 5.2 and 5.3
In class activities – Activity 5.4, and 5.5
Homework – Exercises 39, 41, 28
Oct. 13 Probability and Statistics, Basic Counting Principles
Reading and Prep – Chapter 5.4
Due - Children’s Lit Connection - Each
Orange had 8 Slices How does this book illustrate the multiplication rule?
In class activities – Activity 5.6
Homework – Exercises 30, 32, 37, 40, 45
Oct. 15 Probability and Statistics, Basic Statistics, Central Tendency and
Variation
Reading and Prep – Chapter 5.5, 5.6, 5.7
Due - Children’s Lit Connection - Anno’s
Mysterious Multiplying Jar Permutations and combinations use factorials.
Read the last part of the book to find out about factorials. How does this book
illustrate factorials?
In class activities – Activity 5.7, 5.8
Homework – Exercises 9-15 (all one exercise)
Oct. 22 Probability and Statistics, Measures of Variation
continued
Reading and Prep – Chapter 5.8, 5.9, 5.10
Due - Outline (brief) of final project, if
not turned in at this time, no help will be offered towards its completion
In class activities – Activity 5.9, 5.10
Homework – Exercises 48-53 (all one exercise), 47
Oct. 27 Probability and Statistics, Sampling
Reading and Prep – Reread Chapter 5
In class activities – Activity 5.11
Homework – Analyze the data collected in class
Oct. 29 Fraction Models and Operations, Models of Fractions
Reading and Prep – Chapter 6 through 6.4
In class activities – Activity 6.1, 6.2, 6.3
Homework – Activity 6.4, 6.7
Nov. 3 Fraction Models and Operations, Linear Models continued
Reading and Prep – Chapter 6.5
In class activities – Activity 6.8, 6.9
Homework – Exercises 20, 23, 27
Nov. 5 Fraction Models and Operations
Reading and Prep – Reread Chapter 6
In class activities – Activity 6.13, 6.14
Homework – Activity 6.15, 6.16
Nov. 10 Real Numbers: Rationals and Irrationals
Exam
Reading and Prep – Chapter 7
In class activities – Activity 7.9, 7.13,
7.14
Homework – Exercise 24, 47
Nov. 12 Geometry, Ideas of definitions and proof, lines and angles
Reading and prep – Chapter 9
In class activities – Activity 9.2, 9.4, 9.5
Homework – Activity 9.6, 9.8, 9.9
Nov. 17 Measurement, Length, Perimeter and Area
Reading and Prep – Chapter 10 through
section 10.1
In class activities – Activity 10.1, 10.2,
10.4
Homework - Activity 10.3, Exercise 54, 68
Nov. 19 Measurement, Investigating proof via Pythagoras
Reading and Prep – Chapter 10.2, 10.3
Due - Children’s Lit Connection - Counting
on Frank How does this book illustrate nonstandard measurement?
In class activity – Activity 10.5, 10.6
Homework – Exercise 59, 69, 70, 66
Nov. 24 Measurement, Analytic and Transformational Geometry
Reading and Prep – Chapter 10.4
In class activity – Activity 10.14, 10.15,
10.16
Homework – As assigned in class
Dec. 1 Measurement, Tessellations
Reading and Prep – Chapter 10.5
In class activity – Activity 10.17
Homework – Exercise 63, 64
Dec. 3 Measurement, Tessellations continued
Reading and Prep – Chapter 10.5
In class activities – Activity 10.18
Final as scheduled Backpack Math peer grading and exam