Prerequisite Courses: Intermediate Algebra (Math 111) & Math 106
Materials: Scissors, colored pencils, notebook, Computer floppy
disk
In April: Protractor and Compass.
General
Learning Outcomes
*Show a more positive attitude toward learning and using mathematics
*Show a decrease in anxiety toward learning and using mathematics
* Students develop
fundamental algebra and arithmetic skills, as well an ability
to communicate these skills in their future teaching profession.
* Critical Thinking
and problem solving skills are developed to the point where students
can solve meaningful and relevant applied problems as individuals
and as groups.
* Graphing calculator
skills are developed so that students are comfortable using mathematics
with technology.
Specific Learning Objectives
First Semester Objectives, MET 106
I) Sets, Whole Numbers,
Numeration, Calculator Skills, The Language of Mathematics
A) Writing mathematics correctly
B) Set concepts, especially as related to whole numbers ( membership,
distinctness, equality, subsets, one-to-one correspondences,
intersection, union, null set, roster and set-builder notation.
C) Whole number numeration systems ( Egyptian, Babylonian, Roman,
Mayan, Hindu- Arabic)
D) Place value and Expanded notations.
E) Spelling and pronouncing whole numbers, and the "illion"
system.
II) Field Properties, Properties
of Equality.
A) Field Properties of "+" and "x" on the
set of Real Numbers ( closure, commutativity, associativity, identity
elements, inverses, multiplication properites of 0 and 1, and
distributive properties.
B) Properties of Equality ( additive, multiplicative, substitution,
reflexive, symmetric, transitive)
III) Algorithms in Bases
other than Ten
A) Introduction to a variety of algorithms
B) Counting in bases other than ten, especially two, five, eight,
twelve and sixteen.
C) Elementary "+" and "x" facts in other bases.
D) Using elementary facts to perform more complicated calculations
in other bases using a variety of algorithms.
IV) Prime Factorization
A) Methods of finding prime factorizations of Natural Numbers.
B) Divisibility
C) Greatest Common Divisior and Least Common Multiple
D) The role of Prime Factorization in reducing fractions and in
adding fractions.
V) Teaching Fractions,
Decimals and Percents
A) Fractions and the set of Rational Numbers
B) Relations between fractions, decimals and percents
C) Visual and manipulatives
D) Calculators
VI) Irrational Numbers
A) Proof of the existence of the set H ( irrationals) based on
the square root of 2
B) The Golden Ratio, Pi, and other great irrational moments.
Second Semester Objectives, MET 206
I) Statistics
A) Forms of data, meaning of data
B) Organizing data
C) Analyzing and using data by written algorithms
and by technology
D) Perspectives on data in society and in education
II) Probability
A) History and meaning of probability
B) Representation of probabilities
C) Calculating probabilities
D) Perspectives on probabilities in society
and in education
III) Measurement
A) History and meaning of measurement- English
and International Systems
B) Dimensional Analysis in both systems, many
applied units and situations.
C) Practice with real-world measure and units
of measure
D) Perspectives on measurement in society and
in education
III) Geometry
A) Eratosthenes measures the Earth, introduction
to uses, history and basic geometry
B) Basic two and three-dimensional areas and
volumes and applications
C) Other geometric topics- toplolgy, tessalations,
fractals
D) Perspectives on geometry in society and
in education
Class Policies
Missing Class for illness, travel, etc.
You are responsible for making up the points for a missed class. If you miss a class for any reason, you will not get the ten points for the class for that day. ( The exception here is the snow day. See " Bad Weather Policy " below) . To make up points for a missed class, you need to visit the instructor's office briefly before or after class or during office hours. If you feel you had an excusable reason for missing class explain what you feel you can to the instructor. You will be asked to show that you have covered the work done for that day, including getting lecture notes (and the day's quiz questions if applicable) and doing the assigned work in the text or other activity. This may be presented in class or in the instructor's office up to two weeks after the missed class. Your grade will be then be made up by having your "0" for the day changed to the appropriate score. This could be up to the full "10" if the absence is regarded as unavoidable and the work is made up. It may also be fewer points depending on the reason for absence and the quality of the makeup work. for example "sleeping in" does not usually qualify for a full class makeup. This policy is important for students interested in getting the best possible grade, since the daily grade accounts for 30% of the course grade. Each daily score is thus about 1% of your final grade. You do get to drop your lowest daily score, so this proceedure could be skipped at least once with no consequence to your grade.
Whenever possible, tell the instructor in advance if you know you are going to miss a class. He can inform your study group and prepare make up work for you. You will likely be able to make up more points this way too. Use the email address given on the homepage or leave a message on the office phone.
Food and Drink: Food is not allowed in NMC classes, so if food follows you into class, be courteous and leave no trace of it on the table or anywhere. Always recycle what you are able to. There are bins in the building for deposit cans that benefit the student government.
Cheating: You are on your honor not to cheat on any of your
college activities. If cheating is occuring and you are aware
of it, you may mention the fact that it has occured to the instructor
without any associated names. Any paper or exam in which cheating
has been shown to occur will receive a grade of 0 %
Class
Web Page
There is a class web
page for Math 106 & 206, and you are expected to visit it
as often as possible. For each unit of study there are enrichment
assignments and opportunities for extra credit. If you do not
have internet at home, use your time at NMC to get on our computers
to visit the web page. Links to class topics are usually provided.
Assignments are posted there, as well as in the regular class
room. If you're on the internet now, you are reading it!
Attendance
You need to be
in class almost every day to do well in this course. If you cannot
attend class because of illness or other another difficult situation,
contact the instructor about the absence. Use the phone or email.
Class credit lost to absence might be made up if explanations
are given prior to absence and arrangements are made with the
instructor. Attendance is a significant part of the grade
formula.
Study Groups
Research and experience have shown that most students work and learn better if they interact in the classroom in meaningful discussion of the academic material. Study groups are helping transform education- and industry as well.
You may choose or be assigned to a study group. This group will collaborate on class lab activities, homework and, in some cases, on exams.
Group members are encouraged to support each other in every possible way in order to get each other through the semester. Choose a group name. Exchange phone numbers. If you feel you are in the wrong group, contact the instructor.Homework & Preparation for Class
There will be homework
on a daily basis. As with most college courses, plan on
about two hours out of class for every classroom hour, averaged
over the week. Homework should include any questions on
previously assigned work and preparation for the upcoming class.
Daily Grade
Toward the end of most class sessions, there will be a short quiz that includes the current material and often will pertain to previous material too. Some quizzes will be done as a group, others individually. Written homework can serve as a quiz grade too. On days that no written work is collected, you will receive a grade based on your group's participation in the activity. A grade will be written for each day of class, 10 being the best and zero indicating an absence. These will be averaged and will form a significant fraction of the overall course grade. You may drop your lowest daily grade.
Thus, if you arrive on
time and participate actively, staying on task you are assured
of at least 5 or 6 points out of 10 each day. If you show
some knowledge of the day's lesson on the quiz, you are up to
about 8. If you are careful with your quiz (help is usually allowed
and encouraged) you can earn 10 out of 10 each day.
Conversely, if you
are not present for much of the class on a regular basis (arrive
late, or leave early) you will not be earning the full participation
grade on a daily basis. The class is structured around collaborative
learning. An advantage of this is that tests are not all individual
and not the only basis for a grade. The other side of this is
that you are both a teacher and a student within your group and
you need to use all the class time actively.
| Daily Grade Rubric | Based On: | Points Awarded: |
| 0 to 10 Points Per Day | Attendance, Participation in Activity, Group effectiveness and time on task. | 0 to 5 |
| Daily Quiz, graded homework, sample of daily work | 0 to 5 |
If you miss a class, you will get a score of zero unless you make it up. See the section above under class policy for makeups for a missed class. This is very important for earning a good grade in a class which grades on attendance as this one does.
There will be about 4 exams and a Final Exam. You must be present for an exam, unless you have worked out a re-take with the instructor in advance. Any missed exam that has not been discussed with the instructor will result in a grade of 0 %.
Some exams include both an individual and a collaborative component.
These will include:
*Doing the exam together
as a learning team
*Discussing the exam
as a team and then writing the exam individually.
* Doing part of exam
out of class as a group, and part individually in class.
Final Exam
The Final Exam will be comprehensive and will be taken individually. It is hoped that by taking the other exams with some collaboration, that your ability to perform well on exams will be improved. This theory tested on the final exam, which is all individual effort. The Final exam normally counts as 15% of the final grade. Your score on the final should be reasonably close to your test average.
Part of your actual class
grade will come from your own assessment of your efforts. You
will grade yourself with a number grade (e.g. "3.5")
at the middle and at the end of the semester based on these criteria:
* Your own
attitude and effort toward the class
* Your contribution
to your study group.
Your contribution
to the group would be based on being present during the entire
class scheduled time, being on-task during class, teaching or
learning from group members in a constructive way, building group
morale, encouraging group progress.
For example, a 0.0
point group member arrives late, leaves early, is not prepared
for the day's activity, talks about many things except the mathematics,
and discourages others from learning.
The 4.0 student is
on time, on task and ready for each day's activity, and makes
the study group a productive and happier place to study.
Your course grade is calculated by this weighted system. Your grade may be viewed any day on the internet by social security number.
| Daily Grade | 30% Drop lowest score |
| Exams | 50% |
| Final Exam | 15% |
| Self Assessment | 5% |
Your weighted score related to the course grade:
|
|
|
| 100 > X > 94% | 4.0 |
| 93 > X > 87% | 3.5 |
| 86 > X > 82% | 3.0 |
| 81 > X > 76% | 2.5 |
| 75 > X > 71% | 2.0 |
| 70 > X > 66% | 1.5 |
| 65 > X > 60% | 1.0 |
| X < 60% | 0.0 |
Bad Weather Policy
If Traverse City Schools
(or your local schools) are closed for the day, your grade in
the class will not be directly affected by missing your
math class.
You decide if it is
worth the risk or inconvenience.
You may make
up the quiz or we may not have it. Your grade may be indirectly
affected if we end up meeting and if you don't do any studying.
Whenever you are absent,
check the class Web Page for assignments and extra credit . Email
is a good way to inform the instructor of your absence.
Helpful Links
on the Internet:
http://www-history.mcs.st-and.ac.uk/~history/HistoryTopics.html
Math
in the Movies
Generating
Pythagorean Triples
TI-83
Graphing Calculator
The
Prime Machine
The
Largest Known Primes
A
Teacher's Home Page
Carlson's
Fractal Gallery
Mathematics
on the Web
The
Joy of Pi
Sacred
Geometry Discovery
Tom
Gettys - Platonic Solids
Virtual
Reality Polyhedra
WhoWasThere
History
Topics
Kids Web - Astronomy and Space
History of Mathematics
The Nine Planets
Science News Online - The Weekly Newsmagazine of Science
MSTE: WebDice
The Fibonacci Numbers and the Golden section