301 Introduction

Interdisciplinary 301: Topics in Secondary Mathematics
Spring 2025
Introduction

Professor:     Jeff Johannes                                    Section 3 TR 12:30 - 1:45p South 328
Office:         South 326A
Telephone:      245-5403
Office Hours:   Monday 5:00 - 6:00p South 328, Tuesday 4:00 - 5:00p Fraser 114, Wednesday 12:00N - 1:00p Newton 213, Thursday 8:00 - 9:00p South 336, Friday 11:00a - 12:00N Welles 133, and by appointment or visit.
Email Address: Johannes@Geneseo.edu
Web-page:    http://www.geneseo.edu/~johannes

Textook

The Mathematics that Every Secondary School Math Teacher Needs to Know, Sultan and Artzt

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:

What do I need to know in order to teach students and to promote understanding and empowerment in my students, rather than repetition and mindless manipulation?
What do my undergraduate mathematics classes have to do with high school mathematics?
What are the reasons and justifications behind high school mathematics?
What mathematics do I as a teacher need to know that is different from that which my students need to know?
What mathematics do I need to know in order to complete my certification?
What are the answers to all the 'why' questions that good students will ask me?

We will not attempt to answer the following questions which are possibly reasonable but irrelevant to our pursuit in this course:

How do I get the kid in the fifth row to stop talking long enough to learn something?
Where will I be student teaching?
How much will I get paid?
What is a sesquilinear function?

Learning Outcomes

Upon successful completion of INTD 301 students will be able to

create and solve sophisticated multi-step problems in various topics from the secondary curriculum.
construct multiple representations for selected topics from arithmetic, algebra, geometry, trigonometry, probability, and statistics.
make connections between concepts in different areas of mathematics and between the mathematics of undergraduate courses and the mathematics of the secondary curriculum.
recognise current and historical types of mathematics assessment in New York state and be prepared to implement curricular programs that address these needs and those of their students.

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 Thursday, February 6.

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 others' 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. 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 4, 7-9p. Failure to complete at least 80% of the exam correctly will limit your course grade in 301 to no higher than a D. At least one retesting time will be offered in the instance of failure to pass.

Solutions and Plagiarism

There are plenty of places that one can find all kinds of solutions to problems in this class. Reading them and not referencing them in your work is plagiarism, and will be reported as an academic integrity violation. Reading them and referencing them is not quite plagiarism, but does undermine the intent of the problems. Therefore, if you reference solutions you will receive 0 points, but you will *not* be reported for an academic integrity. Simply - please do not read any solutions for problems in this class.

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.

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 Vector Analysis (350) we worked extensively with differential forms. For them, anticommutativity was very important, and prohibited us from ever seeing dx^2. In 301 this week, we've been using commutativity regularly. It's interesting that sometimes having it is helpful and sometimes not is helpful. Knowing places where we have anticommutativity helps me to appreciate the role of commutativity.

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. 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.

Opening Meeting

Students will earn two extra points on the first problem set by visiting office hours during the first two weeks of classes, i.e. no later than 4 February.

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. More information on the process for requesting academic accommodations is on the OAS website. If you have questions, please 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 February 4 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 Trigonometry, logarithm, exponential, and complex numbers.
Week 10 review before MCE - discussion of any secondary mathematics topics of interest, student directed.
Weeks 11-15 discussion of any secondary mathematics topics of interest, student directed. Sharing learning from final projects.

Date	Topic	Due
January 21	Introduction - Stories with Holes
23	Calendar Problems - Strategies	Grade 7-8 NYS Samples 2024
28	Problem Solving	Algebra I: June 2024
30	Polynomials and Number Systems - Definitions and Arithmetic 2.8, 3.2, 8.2
February 4	Inverses. Rational Expressions 8.3, 8.4, 8.6	Complete 10 varied Integrated algebra sample tasks
6	Primes, divisibility, GCM, LCM, mixed expressions	Initial Project
11	2.4, 2.5, 2.6, 2.7	Geometry: June 2024
13		CST Topics for end course and final project
18	Rules of Exponents. Laurent polynomials and decimals	Complete 10 varied Geometry sample tasks
20	8.7, 8.8, 8.12-15	Problem Set 1
27	Polynomials and Roots	Algebra 2: June 2024
March 4	3.2, 3.3, 3.4, 3.5, 3.6
6	Trigonometry	Complete 10 varied Algebra 2 / Trigonometry sample tasks
11	More trigonometry	Problem Set 2
13	Logarithms	Complete 10 varied Common Core Illustrations (ask me how)
25	Complex
27	More complex	Advanced Algebra: January 1954
April 1	Review for MCE
3	Review for MCE	MCE 7-9p (South 336)
8	MCE Topics
10	MCE Topics
15	Probability
17		MCE retake 7-9p (South 336)
22	Coordinate geometry
24
29	Irrationals
May 1	What do you say? / Calculus?	Problem Set 3.5
6	Review - Problem Solving reflection	Connections Final Project
Monday, May 12, 8a-3p	Pre-student teaching festival.	Questions about secondary mathematics