Mathematics 141 :
Mathematical Concepts for Elementary Education II
Spring 2023
Introduction
Professor: Jeff
Johannes
Section 5 TR
11:00a-12:15p
Math Learning Centre
- South 332 (sometimes, including exams, in Fraser 116)
Office:
South 326a
Telephone: 5403
(245-5403)
Office Hours: Monday 5-6p Fraser 116, Tuesday 8-9p South
336, Wednesday 2-3p Fraser 104, Thursday 4-5p Fraser 116, Friday
12-1p Fraser 116, 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
Occasional additional handouts provided
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 are 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
Upon successful completion of Math 141 - Mathematical Concepts for
Elementary Education II , a student will be able to:
- Solve open-ended elementary school problems in using
visualization and statistical reasoning,
- Demonstrate the use of mathematical reasoning by justifying
and generalizing patterns and relationships,
- Identify, explain, and evaluate the use of elementary
classroom manipulatives to model geometry, probability and
statistics,
- Explain relationships among measurable attributes of objects
and determine measurements,
- Analyze characteristic and properties of two- and
three-dimensional geometric shapes and develop mathematical
arguments about geometric relationships,
- Apply transformations and use symmetry to analyze mathematical
situations,
- Explain and apply basic concepts of probability, and
- Formulate questions that can be addressed with data and
collect, organize, and display relevant data to answer them.
Upon successful completion of the R/
requirement, students will be able to
- convert a problem into a setting using symbolic notation;
- connect and find relationships among symbolic quantities;
- construct an appropriate symbolic framework;
- carry out algorithmic and logical procedures to resolution;
- draw valid conclusions from numeric/symbolic evidence.
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% - In-Class Exam
15% - Final
Project
25% - Comprehensive Final Exam
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, submit a report if the entire
group works remotely, 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 6 February.
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, 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.
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.
Feedback
I have 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.
Occasionally I will ask you to give feedback about particular
details in the course using this website.
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.
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.
Accommodations
SUNY Geneseo is dedicated to providing an
equitable and inclusive educational experience for all students. The
Office of Accessibility will coordinate accommodations, auxiliary
aids, and/or services designed to ensure full participation and
equal access to all academic programs, activities, and services at
SUNY Geneseo. Students with letters of accommodation should submit a
letter and discuss needs at the beginning of the semester. Please
contact the Office of Accessibility Services for questions related
to access and accommodations. Erwin Hall 22 (585) 245-5112 access@geneseo.edu
www.geneseo.edu/accessibility-office.
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 February 7 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 from the
manual linked above. I will put needed supplies in [brackets].
January 24 Introductions, snowflakes
[paper, scissors]
January 26 B8.8 + video#20 [paper,
scissors]
January 31 7.1, 7.2 - Please use this
map for the dining hall question. [notebook or stack of paper,
rulers]
February 2 B10.6, B10.7
[dot paper in the role of geoboards]
February 7 7.3, start 7.4 [colour tiles, dot paper]
February 9 7.4, 7.5 [dot paper]
February 14 7.6, 7.7 [string, ruler, scissors, templates for
circles and cones]
February 16 7.8, 7.9 Weekly Questions due [blocks, any
cyclinder (can, water bottle, …)]
February 21 First Exam (Fraser 116)
February 23 15
[graph paper]
February 28 Diversity Summit
March 2 7.13, B9.6 [only the activities
themselves]
March 7 7.18, 6.5 [protractor (not a compass - please don't
confuse them), ruler]
March 9
6.14 and extension [compass and ruler]
March 21
7.19, 7.20 [pattern blocks, dot
paper]
March 23 B8.9,
6.2 [only activities and my
directions]
March 28
7.22 [only activities] Weekly Questions due
March 30
6.4 [pattern blocks,
protractor maybe]
April 4 Second Exam (Fraser 116)
April 6 6.8 [only activity]
April 11
6.3 [only activity]
April 13
6.10 [blocks; isometric dot
paper]
April 18 8.10 [spinners, dice, items from a bag]
April 20 8.11 [items from a bag]
April 25 8.3 [only activity]
April 27 B7.15, 8.5 [items from a
bag]
May 2 8.7 [only activity] Weekly questions due
May 4
8.8 [websites or coins]
May 9 Review (Fraser 116)
May 12 Final Project due by 5p
Thursday, May 18 12:00N - 3:00p Final Exam (Fraser 116)