Professor: Jeff
Johannes
Section 3 TR 10:00 - 11:15
South 336
Office:
South
326A
Telephone: 245-5403
Office Hours: Monday 1:30 - 2:20p, Tuesday 8:00 - 9:00p, Wednesday 4:00 - 5:00p,
Thursday 4:00 - 5:00p, Friday 3:00 - 4:00p (may cancel occasionally)
and by
appointment or visit
Email Address: Johannes@Geneseo.edu
IM:
JohannesOhrs
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?
- What is the easiest way to . . . ?
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
Tuesday, January 31.
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, March 29,
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 1.
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 1). 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 Trigonometry, complex, logs and exponentials
Week 10 review before MCE - discussion of any
secondary mathematics topics of interest, student directed.
Weeks 11-13 Transformations, Modeling and Statistics
Weeks 14 and 16 discussion of any
secondary mathematics topics of interest, student directed.
Sharing learning from final projects.
Date
|
Topic
|
Due
|
January 17
|
Introduction
|
|
19
|
Problem Solving
|
Grade
8 2009 book 2 and Grade
8 2009 book 3 (do all - show work)
|
24
|
Problem Solving
|
|
26
|
Problem Sovling
|
Complete
10 varied Integrated algebra sample tasks
|
31
|
Polynomials and
Number Systems -
Definitions and Arithmetic 2.8, 3.2, 6.2
|
Initial
Project
|
February 2
|
Inverses.
Rational
Expressions 6.3, 6.4, 6.6
|
Integrated algebra: August 2011 |
7
|
Primes,
divisibility, GCM, LCM,
mixed expressions
|
|
9
|
2.4, 2.5, 2.6, 2.7
|
Complete 10 varied
Geometry sample tasks
|
14
|
Rules of
Exponents.
Laurent polynomials and decimals
|
Problem Set
1
|
16
|
6.7, 6.8, 6.12-15
|
Geometry: August 2011 |
21
|
Polynomials and
Roots
|
|
23
|
3.2, 3.3, 3.4, 3.5, 3.6
|
Complete 10 varied
Algebra 2 / Trigonometry sample tasks
|
28
|
5.1-5
|
|
March 1
|
7.1-6
|
Algebra 2: June 2011
|
6
|
6.10, 7.9 |
Problem Set
2
|
8
|
|
Advanced
Algebra: June 1949 (select from this
index [might pop up for you])
|
20
|
|
|
22
|
|
Math
B: January 2010
|
27
|
Review for MCE
|
|
29
|
Review for MCE
|
MCE 7-9p (South 336)
|
April 3
|
Chapter 10
|
Problem Set
3
|
5
|
9.3-6
|
MCE retake 7-9p
(South 336) |
10
|
12.11-12
|
|
12
|
|
|
19
|
|
|
24
|
Irrationals 6.5, 7.7
|
|
26
|
Review
|
Problem Set
4
|
May 1
|
Review
|
Connections
Final Project
|
May 7, 8 -11a
|
Review
|
Questions about
secondary
mathematics
|