Mathematics 140
: Mathematical Concepts for Elementary Education I
Fall 2023
Introduction
Professor: Jeff
Johannes
Section 3 TR
11:00a-12:15p South 336
Office:
South 326a
Telephone: 5403
(245-5403)
Office Hours: Monday 5-6p in South 309, Tuesday
1-2p in South 309. Wednesday 12:30-1:20p in South 309, Thursday 8-9p
in South 336, Friday 2:30-3:30p in South 309, and by
appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page: http://www.geneseo.edu/~johannes
Course Materials
Lab Activity Manual by
Jonathan Duncan
Optional: A Problem Solving Approach To Mathematics For
Elementary School Teachers by Rick Billstein, Shlomo
Libeskind, Johnny W. Lott.
Occasional additional activities provided here
Required Supplementary Materials
Manipulatives
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, here is the New York State Standards for Mathematics.
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.
Learning Outcomes
Math 140 - Upon successful completion of Math 140
- Mathematical Concepts for Elementary Education I, a student will
be able to:
- Solve open-ended elementary school problems in areas such as
patterns, algebra, ratios, and percents,
- Justify the use of our numeration system by comparing it to
historical alternatives and other bases, and describe the
development of the system and its properties as it expands from
the set of natural numbers to the set of real numbers,
- Demonstrate the use of mathematical reasoning by justifying
and generalizing patterns and relationships,
- Display mastery of basic computational skills and recognize
the appropriate use of technology to enhance those skills,
- Demonstrate and justify standard and alternative algorithms
for addition, subtraction, multiplication and division of whole
numbers, integers, fractions, and decimals,
- Identify, explain, and evaluate the use of elementary
classroom manipulatives to model sets, operations, and
algorithms, and
- Use number-theory arguments to justify relationships involving
divisors, multiples and factoring.
Grading
Your grade in this course will be based upon your
performance on participation, weekly questions, three exams, and the
final project. The weight assigned to each is designated on
the left in the grade definition scale given on the right:
10% - Participation
10% - Weekly
Questions
20% - Each
of two In-Class Exams
15% - Final
Project
25% - Comprehensive
Final
Exam
In addition, you must pass several Basic Skills
Checks throughout the semester or your course grade will be
lowered by a half letter 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.
Opening Meeting
Students will earn two extra participation points
by visiting office hours during the first two weeks of classes, i.e.
no later than 12 September.
On Thursdays, 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 explain the concepts behind any calculations,
algorithms, etc. Material will come from activities and discussions
in class. 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.
In-class exams will have two parts - the first
part is devoted to a group exam, in which your group will complete
an activity much like those done in-class. You will submit one
well-written presentation of your findings from each group.
Individual exams will contain six
questions: four of the questions will be direct
problems. 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.
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.
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.
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.
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 with one another is encouraged, all
write-ups of weekly questions and final projects must be your own.
You are expected to be able to explain any solution you give me if
asked. Weekly questions and individual portions of exams will be
done individually. The Student Academic Dishonesty Policy and
Procedures will be followed should incidents of academic dishonesty
occur. Any work written, developed, or created, in whole or in
part, by generative artificial intelligence (AI) is considered
plagiarism and will not be tolerated. While the ever-changing
developments with AI will find their place in our workforces and
personal lives, in the realm of education and learning, this kind of
technology does not help us achieve our educational goals. The use
of AI prevents the opportunity to learn from our experiences and
from each other, to play with our creative freedoms, to
problem-solve, and to contribute our ideas in authentic ways.
Geneseo is a place for learning, and this class is specifically a
space for learning how to advance our thinking and professional
practice. AI cannot do that learning for us.
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.
Accessibility Accommodations
SUNY Geneseo is dedicated to providing an
equitable and inclusive educational experience for all students. The
Office of Accessibility (OAS) will coordinate reasonable
accommodations for persons with disabilities to ensure equal access
to academic programs, activities, and services at Geneseo.
Students with approved accommodations may submit a semester
request to
renew their academic accommodations. Please visit the OAS website
for information on the process for requesting
academic accommodations. Contact the OAS by email, phone, or in-person:
Office of Accessibility Services
Erwin Hall 22 585-245-5112
access@geneseo.edu
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 11 of plans to observe the holiday.
Military Obligations
Federal and New York State law requires
institutions of higher education to provide an excused leave of
absence from classes without penalty to students enrolled in the
National Guard or armed forces reserves who are called to active
duty. If you are called to active military duty and need to miss
classes, please let me know and consult as soon as possible with the
Dean of Students.
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 29 Introduction, curiosity, sale activity
31
1.3 discussion, video #42
September 5 History of number systems - research to
present: Tally, Egyptian, Greek, Roman, Babylonian, Mayan,
Hindu-Arabic, Chinese numbers
7
Basic Skills Check I discussion of other
bases; 2.1, 2.7, 2.8
12
2.2, 2.9
14
alternatives, 2.11 3.678
19
b 3.12
standard multiplication, b 3.13 lattice
multiplication
21
2.12m, 2.13m
26
b 3.15, 2.4, 2.12d, 2.13d
28
Basic Skills Check II b 3.19 , b 3.20 Weekly
Questions due
October 3 First Exam
5
3.6, 2.15 + checking mod 9
12
3.5, 3.3
17
NT3, NT4
19
3.8, 3.9
24
NT5, NT6
26
4.1
31
Basic Skills Check III 4.3 Weekly Questions due
November 2 4.5, 4.7
7 Second
Exam
9
4.9
14
b 5.13, b 5.14
16
4.11
21
Further
activities and discussions with decimals (RN9)
28
Relations between
decimals and fractions (RN10)
30 4.13 Weekly Questions due
December 5 4.14,
4.15
7
Review
11
Final Project due by 6p
Monday, December 18
8:00-11:00a final exam