Mathematics 140
: Mathematical Concepts for Elementary Education I
Fall 2007
Introduction
Professor: Jeff
Johannes
Section 2 MWF 12:30-1:20p
Sturges 105
Office:
South 326a
Telephone: 5403 (245-5403)
Office Hours: Monday 1:30 - 2:30p, Tuesday 1:45-
2:45p, Wednesday 4-5p, Thursday 8-9p, Friday 1:30 - 2:30p, by
appointment and
visit.
Email Address:
Johannes@Geneseo.edu
Web-page:
http://www.geneseo.edu/~johannes
Course Materials
Mathematics for
Elementary School Teachers Explorations by Tom Bassarear
Mathematics for
Elementary Teachers: A Conceptual Approach by Bennett and
Nelson
Occasional additional handouts provided
Required Supplementary Materials
Manipulative Kit, Scissors
Course Goals and Philosophy
The purpose of this course is to revisit the content
of the elementary mathematics curriculum with the focus on
understanding the underlying concepts and justifying the solutions of
problems dealing with this material. The focus is not on being able to
perform the computations (the how to do it), although that is a
necessity as well, but on demonstrating an ability to explain
why you can solve the problem that way or why the
algorithm works that way. You will need to be able communicate your
explanations
both verbally and in writing with strict attention to the mathematical
accuracy and clarity of your explanation. You will have the chance
to work with mathematical concepts in an active, exploratory manner
as recommended by the National Council of Teachers of Mathematics
(NCTM):
Knowing mathematics means being able to use it in
purposeful ways.
To learn mathematics, students must be engaged in exploring,
conjecturing, and thinking rather than only rote learning of rules and
procedures. Mathematics learning is not a spectator sport. When
students construct knowledge derived from meaningful experiences, they
are much more likely to retain and use what they have learned. This
fact underlies the teacher's new role in providing experiences that
help students make sense of
mathematics, to view and use it as a tool for reasoning and problem
solving.
If you feel a need to review elementary school
mathematics, this is your responsibility. For this purpose, I
recommend reading our textbook and consulting with me outside of
class. For a reference on the content of elementary school
mathematics,
I have provided a summary of the NCTM standards
.
It is also the purpose of this
course to improve your ability to engage in mathematical thinking
and reasoning, to increase your ability to use mathematical knowledge
to solve problems, and to learn mathematics through problem
solving.
The emphasis in this course is on learning numerical mathematical
concepts through solving problems. You will often work with other
students for the following reasons: Group problem solving is
often
broader, more creative, and more insightful than individual
effort.
While working on problems with others, students practice putting their
mathematical ideas and reasoning into words. This ability to
explain
mathematics is clearly essential for future teachers. While
working
in groups, students learn to depend on themselves and each other
(rather
than the instructor) for problem solutions. In groups, students
can
motivate each other to excel and accept more challenging
problems. Motivation to persevere with a difficult problem may be
increased.
Socialization skills are developed and practiced. Students are
exposed to a variety of thinking and problem-solving styles different
from their
own. Interaction with others may stimulate additional insights
and
discoveries. Conceptual understanding is deeper and
longer-lasting when ideas are shared and discussed.
Grading
Your grade in this course will be based upon your
performance on problem sets, weekly questions, reflection logs, three
exams, and the final project. A possible weight assigned to each
is designated on the left in the grade definition scale given on the
right:
20% - Problem
Sets
A 90 - 100
10% - Weekly
Questions
B 80 - 89.99
10% - Each
of two In-Class Exams
C 70 - 79.99
15% - Final
Project
D 60 - 69.99
15% - Comprehensive
Final Exam
E 0 - 59.99
10% - Reflection
Logs
10% - Participation
If you would like your grade to use a different
weighting scale, please inform me by Friday, September 9. In
addition, you must pass several Basic Skills Checks
throughout the
semester or your course grade will be lowered by a half
letter (e.g. from a B to a B-) for each incomplete check. Further
details are available below.
Participation
You are preparing to enter a profession where good
attendance is crucial and expected. It is important that you make
every attempt to attend class, since active involvement is an integral
part
of this course. Since much of the class is experiential, deriving
the
same benefits by merely examining someone's class notes or reading the
textbook would be impossible. Each class period you will be
working on activities with your group. If you are working in your
group you will receive
one participation point that day. If you also participate to the
class as a whole (answer a question, present a solution, ask an
insightful question or offer important relevant commentary) you will
receive two participation points for that day. If you are not
working in your group, you will receive no points for that day.
Working each day and never speaking in class will earn 80%.
Speaking every other day on which there is
an opportunity to speak will earn 95%. Scores between will be
scaled
linearly.
Problem Sets
There will be several problem sets throughout the
semester. These will consist of problems from the text. The goal
of these assignments is to have you practice
solving problems and then being able to write clear, detailed, and
mathematically accurate solutions that explain what you did and why.
Simple numeric answers with some math computations (or work) shown will
not be sufficient. There will be an in-class discussion of the
difference between a "solution" and an "answer". Assignments are due at
the start of class and must be easy to read. Late assignments will not
be accepted.
These questions and papers will be graded on the
following scale
Question
(out of 4)
0 – missing question
1 – question copied
2 – partial question
3 – completed question (with some
solution)
4 – completed question correctly
and well-written
Assignments will be returned on the following class day.
Weekly Questions
On Wednesdays, I will assign a question relating to
the topic for the previous week. They will be due approximately
once a month as indicated on the schedule. The goal of these
assignments is for you to write substantial explanations of the main
concepts presented in class. They will eventually be incorporated
into your final project. Before the final project, they will be
collected for completeness and marked with suggestions.
Assignments are due at the start of class and must be easy to read.
Late assignments will not be accepted.
These questions and papers will be graded on the
following scale
Question
(out of 2)
0 – missing question
1 – question attempted, but
incomplete work
2 – question addressed
seriously
and in depth
In order to provide you with extensive comments,
there may be delays in returning these papers.
Exams
Two in-class exams will be given. Their focus is
largely conceptual and problem solving based. You should be able
to do and explain any of the assigned homework problems for the
material. You should be able to explain the concepts behind any
calculations, algorithms, etc. Material will come from lectures,
discussions in class, and the text. For example, you will need to be
able to explain clearly and with mathematical accuracy why we
can solve problems in certain ways or why various algorithms
or procedures work mathematically. You will also need to be able to use
and explain the use of the manipulatives relevant to the material.
Each exam will contain six questions: four of
the questions will be problems directly from the textbook. Two of
the questions will be more open ended and ask you to explain key
concepts from class. The exams will be graded as follows:
you will receive 40 points for attempting the exam. You may earn
up to 10 points on each of the questions. If you would like to
take the exam with less time constraints, you may choose to take it the
previous evening.
Make-ups for exams will be given only in extreme
cases with arrangements made with the instructor prior to
the exam or if there is a verifiable medical excuse or permission from
the Dean of Students. If you miss an exam and we have not made
arrangements prior to the missed exam, you must contact me before the
next class.
Final Project
This project will be a collection of
weekly question items that you will write up throughout the semester.
This collection
could one day be included in your professional portfolio to demonstrate
your level of mathematical understanding and preparation and your
ability to communicate mathematics in a clear and correct manner.
Details on this final project will be given out in class.
Reflection Logs
Your reflection log is a record of your thinking and
reactions to components of the course. These logs will be used
for various purposes including asking you to reflect on
challenges in
assignments or exams and asking you to reflect and react to
readings. Each courseday you will add an entry to your
log. Probably it should be at least a paragraph per day.
Each day will be out of 2 points. If you address the topic of the
day substantially you will receive 2 points. If you address it
less substantially you will receive 1 point.
Basic Skills Checks
As stated above, the goal of the course is a deeper
understanding of the content of the elementary school curriculum. At
the same time, there is a need to make sure that you can all do
the computations that you could one day teach. Therefore, throughout
the semester you will be given very short arithmetic quizzes which I
have called Basic Skills Checks. These quizzes will check your
computational competency (no calculators). They will be given prior to
each unit. If you do not pass each skills check (by demonstrating the
correct method for each question), your final course grade will be
lowered by one half letter for
each incomplete check. There will be the opportunity outside of class
to
retest in the event that you do not pass the skills check given in
class.
Feedback
Occasionally you will be given
anonymous feedback forms. Please use them to share any thoughts
or concerns for how the course is running. Remember, the sooner
you tell me your concerns, the more I can do about them. I have
also created a web-site
which accepts anonymous comments.
If we have not yet discussed this in class, please encourage me to
create a class code. This site may also be accessed via our course
page on a link entitled anonymous
feedback. Of
course, you are always welcome to approach me outside of class to
discuss these issues as well.
Math
Learning Center
This center is located in South Hall
332 and is open during the day and some evenings. Hours for the center
will be announced in class. The Math Learning Center provides free
tutoring on a walk-in basis.
Academic Dishonesty
While working on homework with one another is
encouraged, all write-ups of solutions must be your own. You are
expected to be able to explain any solution you give me if asked.
Quizzes and Exams will be done individually unless otherwise directed.
The
Student Academic Dishonesty Policy and Procedures will be followed
should incidents of academic dishonesty occur.
Disability Accommodations
SUNY Geneseo will make reasonable accommodations for
persons with documented physical, emotional or learning
disabilities. Students should consult with the Director in the
Office of Disability Services (Tabitha Buggie-Hunt, 105D Erwin,
tbuggieh@geneseo.edu) and their individual faculty regarding any needed
accommodations as early as possible in the semester.
Religious Holidays
It is my policy to give students who miss class
because of observance of religious holidays the
opportunity to make up missed work. You are responsible for
notifying
me no later than September 7 of plans to observe a holiday.
Postscript
This is a course in the mathematics
department. This is your mathematics content course. In
this course, you will develop a mathematical background necessary in
order to teach elementary school students. You will deepen your
understanding of gradeschool mathematics topics and connections.
You will not be learning how to teach mathematics to children, that is
the purpose of
your methods course in the school of education. As a
mathematician, I am trained to teach you mathematics, and I will do
that. I am not trained to teach you how to educate, and that is
not the goal of this course. Please keep this in mind.
We will be undertaking a great
amount of interactive group work in this course. You may
view these as games. If you come in eager to play, then you
will be more likely to be successful and perhaps occasionally enjoy
the games. If you come in saying "I don't want to play this
stupid
game," we will all be annoyed and frustrated, and the course as a whole
will be less successful. Please play nicely.
Out of necessity, I am more formal in class and more
personal out of class. If you ever want
additional help, please come to see me either during my office hours,
at an appointed time, or by just stopping by (I am frequently in my
office aside from the times that I will certainly be there). It
is important that you seek help when you start needing it, rather than
when you have reached desperation. Please be responsible.
Teaching is one profession where you have direct
impact on hundreds of lives. It is truly
an incredible responsibility. It is vitally important that
teachers set high expectations for themselves and their students.
Daily preparation of interesting, instructive lessons for twenty-five
or more active children of varying aptitudes is extremely
challenging.
I am dedicated to helping you prepare for this exciting career, and
will try to help you reach your full potential. Best wishes for a
challenging and fulfilling semester.
Schedule (This schedule is subject to change, but I
hope to hold mostly to this outline.) Two numbers separated by a
period refer to explorations that we will be studying that day in
class.
August 27 Introduction
29
1.1
31
1.4, Reflection Logs due
September 5 1.3 discussion, 2.1
7
History of number systems:
read text §2.3. Present pp. 103-110, Problem Set 1 due
10
Chinese numbers and discussion
of other bases; 2.9 part 1 base 6
12
Basic Skills Check I, Rest of 2.9
14
Mental mathematics discussion in
the context of 3.2, 3.5, 3.9, 3.17, Reflection Logs due
17
3.3
19
3.6, Problem Set 2 due
21
Addition and subtraction in
other bases
24
3.8, Weekly Questions due
26
3.10
28
First Exam
October 1
3.12
3
3.13
5
3.14, Reflection Logs due
10
3.15
12
Basic Skills Check II, 3.18,
Problem Set 3 due
15
3.19
17
3.20
19
4.2, Reflection Logs due
22
4.3
24
4.5, Weekly Questions due
26
Integers with reference to 5.1-4
29
5.7, Problem Set 4 due
31
5.8
November 2 Second Exam
5
Basic Skills Check III, 5.8
7
5.9
9
5.10, Reflection Logs due
12
5.13
14
5.14
16
5.16
19
Further activities and
discussions with decimals (RN9), Problem Set 5 due
26
Relations between decimals and
fractions (RN10)
28
overrun space
30
6.4, Reflection Logs due
3
6.4, Weekly Questions due
5
6.5
7
overrun space
10
Review, Final Project due
December 17 12N - 3p
final exam
Problem Sets:
1 - 1.1 p. 13 Technology Connection
1.2 12, Writing and Discussion 3
2.1 40
2 - 3.1 6, 10, 12, 24, 37
mentals: explain 5 computations you find
most interesting from 3.2: 23-28, 3.3: 17-24, 3.4:
27-28.
Explain your method for mentally computing the result. Be
sure to include at least one each of addition, subtraction,
multiplication and division.
3 - 3.2 4, 6, 8, Making Connections 1
3.3 10, 42, 50, 56, 58, Writing and Discussion
1
3.4 Writing and Discussion 3
4 - 3.4 10, 16 (discuss/explain), 20, 42
4.1 12, 32
4.2 30
5.1 12
5 - 5.2 8, 12, 30, 52, Writing and Discussion 4
5.3 18, 38, 54
6.1 18, Writing and Discussion 1
practice problems for final - 6.2 4, 22, 30, Writing and Discussion 4
6.3 34, 42, Writing and Discussion 1, 4
6.4 2