Interdisciplinary 301:  Topics in Secondary Mathematics
Spring 2010
Introduction
Professor:        Jeff Johannes                                    Section 3  TR 10:00 - 11:15 South 336  
Office:            South 326A                    
Telephone:      245-5403
Office Hours:    Monday 2-3p, Tuesday 5-6p, Wednesday 4-5p, Thursday 8-9p, Friday 12N-1p, and by appointment or visit
Email Address: Johannes@Geneseo.edu
Web-page:        http://www.geneseo.edu/~johannes

Optional Book
    Mathematics for High School Teachers:  An Advanced Perspective, Usiskin, Peressini, Marchisotto, Stanley

Purposes
    This course, which is intended for the mathematics major who is enrolled in the secondary education program, provides a bridge and establishes connections between the college level mathematics required of the mathematics major and the mathematics of the secondary school curriculum.

Overview
    In this course we will attempt to address some of the following entirely reasonable questions:
We will not attempt to answer the following questions which are possibly reasonable but irrelevant to our pursuit in this course:
   
Grading
    Your grade in this course will be based on four large components:  an opening problem solving project, problem sets, work on past regents exams which will culminate in a mathematics competency exam, and a final project of preparing review materials for a topic in secondary mathematics.  Each of these components will determine 1/5 of your grade.  Additionally1/10 will be determined by writing connections to other mathematics courses, and 1/10 will be determined by your attendance and lively participation in class. 

Initial Project
    This project will constitute solutions to an individually selected subset of eight nonroutine problems from a collection distributed at the beginning of the semester.  It will also include the creation and solution of two such individual problems by you.  It is due on Tuesday, February 2. 

Problem Sets
    There will be several problem sets throughout the semester.  These will consist of problems from class and 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". You are encouraged to consult with me outside of class on any questions toward completing the homework.  You are also encouraged to work together on homework assignments, but each must write up their own well-written solutions.  A good rule for this is it is encouraged to speak to each other about the problem, but you should not read each other's solutions.  A violation of this policy will result in a zero for the entire assignment and reporting to the Dean of Students for a violation of academic integrity.  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 or plagiarised 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.

Regents Exams
    You will complete a sequence of New York State Regent's Exams from prior years.  Read the entire exam.  Complete all of and only the writing questions (unless instructed otherwise).  Do not hand in the objective questions.  The exams are due on Thursdays.  This work will culminate in a Mathematics Competency Exam composed of questions from Regent's Exams (both objective and writing questions will be included) which will occur Thursday, April 1, 7-9p.  Failure to complete at least 80% of the exam currectly will limit your course grade in 301 to no higher than a D.  At least one retesting time may be scheduled individually in the instance of failure to pass. 

Final Project
    The final project will be the preparation of review materials for a topic not addressed in 301 class.  Topics will be selected from the topic list for the New York State Mathematics CST.  Review materials will include an original summary of the topic (with justifications of all methods) with references for more information.  Furthermore, there will be a selection of non-trivial problems on the topic with solutions.  The final project is due on the last day of class, May 4.

Connections
    As this course is the capstone of your undergraduate preparation, it is a valuable opportunity to reflect upon the work that you previously completed.  Throughout this course we will be exploring secondary school mathematics from a more advanced perspective.  In order to establish the connections between your courses and your future teaching, please keep note of the occurrences you see of the material in your courses tying into the school curriculum as discussed in this class.  Here is an example:
In Algebra (330) we studied the abstract ring of fractions we proved several facts about them, and worked over rings more general than the integers.  This abstraction helped me to more clearly understand when we studied fractions in other bases.  The properties that we studied in this class (301) are special cases of the properties we saw in 330, much like our work in other bases generalised what our students will see when working with normal fractions.  Its all just different settings of the same properties.
We have this class (301) for 14 weeks.  Write up such an observation for each week of the class.  It is due on the last day of class (May 4).  This assignment will be graded out of 28, two for each week.

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.  If you are present and involved in class 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 involved, 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.  If the entire class participates regularly, I will cease to record participation.

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. 

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 February 1 of plans to observe the holiday.  

Schedule  (This schedule is subject to change, but I hope to hold mostly to this outline.) 
 
Weeks 1-2 Problem Solving
Weeks 3-6 Polynomials and Number Systems
    Definition
    Arithmetic (addition / subtraction / multiplication / division)
    Inverses?
    Rational Expressions
    Primes, divisibility, GCD, LCM, mixed expressions
    rules of exponents
    laurent polynomials / decimals
    polynomials and complex numbers
    roots:  prove complexes in pairs
       descartes rule of signs
       rational root test
       synthetic division
       symmetric polynomials
       binomial coefficients
Weeks 7-9 Student choice topic #1
Week 10 review before MCE - discussion of any secondary mathematics topics of interest, student directed.
Weeks 11-13 Student choice topic #2
Weeks 14 and 16 discussion of any secondary mathematics topics of interest, student directed.  Sharing learning from final projects. 
   
Date
 Topic
 Due
January 19
 Introduction
21
 Problem Solving
 Math A:  June 2007 (select from this index)
26
 Problem Solving
28
 Problem Sovling
 Grade 8 2007 book 2 and Grade 8 2007 book 3 (do all - show work)
February 2
 Polynomials and Number Systems - Definitions and Arithmetic
 Initial Project
4
 Inverses.  Rational Expressions
 Course 2:  June 1997 (select from this index)
9
 Primes, divisibility, GCM, LCM, mixed expressions
11
Complete 10 varied Integrated algebra sample tasks
16
 Rules of Exponents.  Laurent polynomials and decimals
 Problem Set 1
18
Course 3:  June 1997 (select from this index)
23
 Polynomials and Roots
25
Complete 10 varied Geometry sample tasks
March 2

March 4
Complete 10 varied Algebra 2 / Trigonometry sample tasks
9
 Problem Set 2
11
Advanced Algebra:  January 1951 (select from this index)
23

25
Math B:  January 2007 (select from this index)
30
 Review for MCE
April 1
 Review for MCE
 MCE 7-9p (South 336)
April 6
Problem Set 3
8
MCE retake 7-9p (South 336)
13

15

22

27

29
 Review
 Problem Set 4
May 4
 Review
 Connections
Final Project
May 7, 12 - 3p
 Review
 Questions about secondary mathematics