Mathematics 141:  Mathematical Concepts for Elementary Education II
Fall 2011
Introduction

Professor:          Jeff Johannes                Section 1    MWF    1:30-2:20p    Sturges 113
Office:                South 326a
Telephone:          5403 (245-5403)
Office Hours:     Monday 11:30a - 12:20p, Wednesday 4-5p, Thursday 1-2p, 8-9p, Friday 2:30 - 3:30p,  and by appointment or visit.
IM:                    JohannesOhrs
Web-page:           http://www.geneseo.edu/~johannes

Course Materials
Mathematics for Elementary School Teachers Explorations, and Mathematics for Elementary School Teachers by Tom Bassarear

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, here are the common core state 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.

Your grade in this course will be based upon your performance on problem sets, weekly questions, reflection logs, 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                                                     A    90 - 100
10% - Weekly Questions                                            B    80 - 89.99
20% - Each of two In-Class Exams                            C    70 - 79.99
15% - Final Project                                                     D    60 - 69.99
25% - Comprehensive Final Exam                             E      0 - 59.99

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.

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 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.
In-class exams will take two days - the first day 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.  A complete, organised, well-presented compilation of all materials is due on the last day of class.  Your project will be checked for inclusion of all assigned topics and will be evaluated based on the clarity and accuracy of the explanations given as well as the overall presentation (neat, easy to find sections and entries, easy to read, well-written, & c).  Somewhere in this portfolio you must demonstrate appropriate uses of each of the manipulatives used 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.

While working on homework with one another is encouraged, all individual write-ups of solutions must be your own. You are expected to be able to explain any solution you give me if asked. 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 12 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 29    Introduction
31        8.8
September 2      8.8

7      8.1
9      8.4

12      8.5
14      8.7
16      8.9

19       8.10    WQ due
21       8.12
23       8.13

26      8.14
28      8.17
30      exam

October 3    exam
5      9.1
7      9.1

12      9.4    WQ due
14       9.4

17      9.6
19      9.7
21     9.9

24     10.5
26    10.7
28    10.11

31    10.12    WQ due
November 2    10.15
4    10.17

7    10.18
9    exam
11    exam

14      7.1
16      7.2
18      7.2

21   7.3 WQ due

28   7.12
30   7.13
December 2   overflow

5   7.15 WQ due
7   7.19
9

12         Review, Final Project Due

Friday, December 16 12N - 3p  Final Exam

Learning Outcomes
Upon successful completion of Math 141 - Math Concepts for Elementary Education II a student will be able to:

Probability and Statistics
•    Design and implement a simulation to estimate experimental probability
•    Calculate probabilities experimentally and theoretically.
•    Recognize which events are equally likely and which are not and calculate probabilities based on this knowledge.
•    Recognize events that are mutually exclusive and those that are not and calculate probabilities based on this knowledge
•    Use complementary events to solve probability problems
•    Use probability to solve problems and make decisions.
•    Model multistage experiments using tree diagrams
•    Model and compare experiments with and without replacements
•    Recognize and use dependent and independent events to solve probability problems.
•    Use geometric probability to solve problems
•    Create simulations to analyze problems in which experimentation is impossible or impractical.
•    Develop interesting and relevant probability experiments and games for children of varying abilities and backgrounds.
•    Use odds and expected value to solve problems and made education decisions.
•    Explain the connection between probability and odds.
•    Differentiate between permutations and combinations and solve problems using this knowledge.
•    Solve permutations and combination problems involving like objects.
•    Distinguish between and interpret pictographs, line plots, stem-and-leaf plots, histograms, bar graphs, circle graphs, box-and-whisker plots, and scatter-plots
•    Create stem-and-leaf plots, box-and-whisker plots and circle graphs
•    Compute mean, median, and mode and evaluate their usefulness in given circumstances.
•    Find outliers, range, and quartiles, variance, and standard deviation
•    Interpret standard deviation tables
•    Calculate how addition of data changes the mean
•    Evaluate how outliers effect mean
•    Evaluate abuses of statistics with regard to data collection and displays

Geometry and Measurement
•    Name the undefined terms of points, lines, and planes that are basic to geometry and state their properties.
•    Model, illustrate, and symbolize geometric terms and concepts
•    Differentiate between plane and solid geometry.
•    Use paper folding and construction tools to explore geometric properties of lines, angles, and polygons.
•    Use geoboards and other manipulatives to explore geometric concepts
•    Make conjectures based on observations and explorations and justify, prove, or defend the conjecture.
•    Recognize the difference between a justification and a proof.
•    Classify polygons according to their properties.
•    Explain the difference between measuring tools and construction tools.
•    Differentiate among acute, right, obtuse, and straight angles.
•    Compare and contrast polygons to create a hierarchy.
•    Use organized lists and sketches to ensure that all possible cases have been accounted for using the given in a problem.
•    Demonstrate, model, and illustrate geometric concepts for beginning learners.
•    Prove theorems and conjectures for more advanced learners.
•    Explore definitions and properties of perpendicular and parallel lines and use the knowledge to solve problems.
•    Verify that the sum of the measures of the interior angles of a triangle applies to all triangles whether they are acute, right or obtuse.
•    Prove that the sum of the measures of the interior angles of a triangle is 180 and that the sum of the interior angles of a convex polygon having n sides is (n-2)*180.
•    Prove that the sum of the measures of the exterior angles (one at each vertex) of a convex polygon is 360.
•    Using modeling rather than memorization to determine the sum of the measures of the interior angles of a convex polygon with n sides.
•    Solve problems that require combinations of geometric concepts.
•    Visualize three dimensions figures in order to count the number of faces, vertices, edges, and diagonals associated with these figures.
•    Define and differentiate between regular polygons and solids and those that are not regular.
•    Use knowledge of nets to determine characteristics of the unseen sides of a cube given a net of the cube.
•    Model nets for solids other than cubes.
•    Sketch and use networks to solve problems.
•    Recognize congruence and apply the knowledge to solve problems.
•    Verify that triangles are congruent using s.a.s., a.s.a., s.s.s
•    Verify that a.a.a is not sufficient to prove triangles congruent
•    Use construction tools to perform elementary constructions.
•    Use constructions to illustrate triangle congruences and similarities
•    Use a Mira and paper folding for constructions
•    Verify the Pythagorean theorem using construction and scissors
•    Recognize the converse of a theorem
•    Use the Pythagorean theorem and its converse
•    Find surface areas of geometric solids
•    Find volumes of geometric solids
•    Verify the conversion factor between Centigrade and Fahrenheit
•    Perform translations, reflections, and rotations by constructions, using dot paper and tracing paper
•    Perform compositions of transformations
•    Perform size transformations
•    Analyze figures to determine symmetries
•    Tessellate a page using a combination of transformations
•    Discover properties of altitudes and medians of triangles.
•    Prove or verify that constructions actually accomplish the required outcomes
•    Discover and list properties of  quadrilaterals
•    Discover, list, and use properties of similar triangles
•    Separate a line segment into n congruent parts by construction and by using lined paper
•    Use the Cartesian coordinate system to determine slopes of lines
•    Use the factor/label method for measurement conversions
•    Use dot paper to find areas
•    understand measurable attributes of objects
•    identify the units, systems, and processes of measurement
•    apply appropriate techniques, tools, and formulas to determine measurements
•    Use indirect measurement to solve problems
•    Justify area formulas for triangles, parallelograms, and trapezoids
•    Find areas of regular polygons