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.
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.

### 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.

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.

### Weekly Questions

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.

### 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.

### 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.

#### 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.

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 accommodationsContact 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