**Math 200 * Mathematical Concepts for Future
Teachers I* Fall 2012**

Course Syllabus

**Instructor: **Dr. Perla
Myers **Office: **Serra
Hall 133A

**Email: ** **pmyers@sandiego.edu** **Phone:** 260-7932

**Web Page: http://www.sandiego.edu/~pmyers**

**Meeting
Times:** Tuesdays and Thursdays: 10:45am-12:05pm

**Office Hours:** Monday 9-10:30pm, Tuesday 9-10am, Wednesday
1-3:30pm or by appointment.

**Mathematics Learning Center (MLC) Drop-in Hours****: **The MLC will be open starting Wednesday, September 12^{th}.
The MLC drop-in tutoring hours are free and available for all USD
students: Monday through Thursday, 11am-2pm and 7pm-9pm; Friday 11am –
2pm; Sunday 7pm-9pm.

**Prerequisites: **Math 115: College Algebra with a grade of C
or above.

**Required Supplies: ***Mathematics
for Elementary Teachers* by Baldridge and Parker packaged with five Singapore Primary
Mathematics books (3A, 4A, 5A, 6A Textbooks and 5A Workbook).

A
large three-ring binder with dividers and loose-leaf paper, graphing paper,
ruler, compass, protractor, a small shoebox, stapler, scissors, and colored
pens/pencils

**Computer Account**: I will send out notices via email, and post
assignments and place other relevant information on the course web page.

**Purpose of the Course:
**Math
200 is a **content course** for people intending to become elementary school teachers. It is designed to improve, broaden and deepen
your proficiency, appreciation and understanding of mathematics, to appreciate
that mathematics is universal and
understand issues that transcend culture and those that do not, and to help you acquire some specialized mathematical knowledge for
teaching. Issues such as “*the mathematics kids need to know*” and “*methods for teaching elementary school
mathematics*” will be addressed in the mathematics methods courses you will take
through the School of Leadership and Educational Sciences.

As future teachers you will be responsible for the mathematical education of children. One of the most important gifts you can give children is to help them grow as discoverers, inventors, and users of mathematics in order to better understand the world. Children can become powerful mathematical thinkers if the learning environment is structured so that children's work in mathematics more closely resembles the work of mathematicians in the field. Since doing mathematics often involves ill-defined situations and complex problems, young mathematicians must develop persistence and flexibility, build on one another's ideas, and communicate and justify their findings. In order for you to help children develop these life-long skills, you too must be a successful, confident problem-solver with a deep understanding of fundamental mathematics.

We will spend a lot of our class time working on problems and explaining problem-solving approaches to help you develop reasoning, problem-solving, and explanation abilities. You will practice explaining and interpreting other students’ explanations to determine their mathematical validity. The skills you gain while making sense others’ thought process and helping them grasp concepts will be essential when you become a teacher. An important part of learning to solve problems is the willingness to struggle with a problem even after you get stuck, and this is one of the first things you will face this semester. You may be surprised by how much you can do if you just keep working! The National Council of Teachers of Mathematics (NCTM) recommends:

*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… 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.*

One of the main purposes of
this course is to increase your problem-solving abilities. To this end, many of the problems you will
encounter are not at all similar to examples you will have seen, and some of
the individual homework and exam problems will probably take you longer than
you may be used to.

As you gain more knowledge and
experience, you will:

·
Become more confident in your ability to do mathematics with
understanding.

·
Become a persistent and successful mathematical problem solver.

**Learning Outcomes: **

By the end of the semester, you should be able to:

1.
Solve problems involving number and operations concepts effectively in
multiple ways.

2.
Explain the standard algorithms for addition multiplication, subtraction,
and division, as well as non-standard algorithms.

3.
Explain place value and different models for arithmetic effectively in
order to help others understand why a claim is true or false.

4.
Apply the arithmetic properties (commutative, associative, distributive,
identity, inverse) to justify procedures.

5.
Apply and explain the Fundamental Theorem of Arithmetic.

6.
Work with and explain fractions, rates, percentages, and ratios.

7.
Identify and work with numbers from different sets (rational, real, integers,
etc.)

8.
Identify, define, classify and draw models of numbers according to their
characteristics.

9.
Make and test conjectures. Identify invalid reasoning and provide
counterexamples to disprove statements that are not always true.

10. Write and explain complete proofs
of theorems and formulas involving number and operations concepts (recreate a proof, prove something different that uses
the same principles, and explain why certain specific steps of a proof make
sense and what their purpose is). Determine and explain when particular
theorems apply to a situation and apply them correctly.

11. Perform mental arithmetic effectively.

12. Identify when it is appropriate
to introduce a variable.

13. Identify and explain the validity of others’
statements and explanations and compare them.

14. Select and apply representations (verbal, symbolic,
visual, material, manipulative, technological) and examine correspondences and
equivalences among representations.

15. Clearly
communicate complete solutions to problems verbally and in writing. This involves
using complete sentences to explain individual steps in the solutions, correct
notation and proper units.

16. Explain,
interpret and correctly apply definitions.
Provide examples and non-examples to illustrate definitions.

17. Summarize and apply information
based on the reading of mathematical information and develop your own questions
to guide your reading.

18. Apply methodologies for mathematical concept
development used in other countries.

19. Incorporate ideas, techniques and styles for teaching
mathematics from other countries.

20. Apply correct terminology
associated with numbers and operations and explain the role of language and
precision in mathematics in oral and written communication.

21. Discuss cultural differences in
mathematical terminology.

22. Apply knowledge gained in class to real teaching
experiences with children.

**Course Expectations:**

*What I expect from you:*

You are expected to conduct
yourself maturely and respectfully in the classroom so that the classroom
atmosphere will remain supportive and positive:

- You will act in a
professional and ethical manner as befits the teaching profession. The effort, detail, and thoughtfulness
you put into your work should reflect the standards of performance you
will be expected to meet as a teacher.
- You will come to class
ready to expand your knowledge of mathematics.
- Your attitude towards your fellow classmates and professors
will always be kind and respectful, in and out of the classroom.
- You will work hard and
take initiative in your learning as well as other's learning. You will work actively with your peers,
sharing, taking and giving, listening and explaining, questioning and
answering. You will be genuinely
curious about others’ ideas, and take the responsibility for being
prepared for participation in class discussions and group work, and for
assisting your peers in coming to an understanding of mathematics. You should expect the same from your
classmates.
- You will arrive to class on time and stay in the
classroom until the end of class. If you will need to arrive late or leave
class early, you should let me know before class starts. You will take
care of any pressing personal needs you may have before coming to class.

·
You will come
ready to ask questions, explore, make mistakes, reflect and grow while helping
others grow.

·
You will not
settle for answers, rules and formulas—you will work until the rules and
formulas are fully understood, and the answers are justified and connected to
other ideas.

- You will stay
organized, keep up with the work, and get help if you feel lost. The usual rule of thumb for college
courses is a minimum of two hours of study out of class for every hour in
class.

This will be a difficult course
and most of you will find it challenging.
We will face the challenge together with a positive attitude. Although
there may be times when you feel overwhelmed at the quantity or difficulty of
the work, keeping a positive attitude is essential to your success and the
success of those around you.

*Expect to
spend at least 6 hours per week studying for this challenging college-level
course.*

IF YOU
FEEL THAT YOUR MATHEMATICS BACKGROUND NEEDS STRENGTHENING, BUDGET SEVERAL MORE
HOURS PER WEEK TO FILL IN THE GAPS.

*What you can expect from me:*

·
** Respect and
Encouragement**. I respect your decision to pursue a degree in
education in order to take on such an important role in our society—that of
teaching our future generations. I
assume you are in this class because you want to be, just as I am. We share a common desire to grow as teachers
and learners. You can expect our time
together to be productive.

·
I want you to
succeed! I will provide the learning
environment and opportunities for you to improve, broaden and deepen your
understanding and appreciation of mathematics.
I will provide the support necessary for you to succeed in this course,
both in and out of class. I am available
during my office hours and by appointment, as well as via email.

**Attendance Policy: **I expect that you are
committed to learning and will attend every class on time and ready for a
prompt start. The time in class is
crucial for achieving the goals of the course.

The learning community we create in class will benefit from the sharing of ideas, questions and mistakes.

*For those students
that miss no more than one class (excused or unexcused) the final exam score
may replace the single lowest exam grade.*

**Grading:** Your grade
will be determined by 2 exams (35%), quizzes (10%), cumulative final exam
(30%), homework (10%), community service learning (10%) & class
participation (5%).

*** Weekly quizzes: **You will have a short quiz
most Thursdays in the beginning of class. There will be no make-ups for quizzes
you miss, but your lowest quiz score will not be counted in your quiz
grade. These quizzes are designed to
give you an idea of areas where you need more work and, therefore, you may make
up quizzes for some credit after they are graded.

*** Two exams: **The
first exam will be a written exam. The
second exam will consist of two parts, a written part, and an oral part. The
exams are tentatively scheduled: Exam #1: Thursday, October 11^{th},
Exam #2 (written part): Tuesday, November 20^{th}, Exam #2 (oral part):
TBA.

*** A Cumulative final exam **(may include written/oral parts): Tuesday, Dec. 18^{th},

*** Homework and Writing Assignments:**

*1) ** Reading Questions*: The elementary school curriculum is in constant
flux, and teachers are expected to adjust to the new methods. Thus, you will be required to learn new
mathematics on your own. Searching for
information and reading to learn mathematics (or any other technical material)
are skills that take practice. The
reading questions provide opportunities to develop these important skills.

*2) **Practice/Exploration
questions/Projects: *Questions from the book and additional questions from other resources
will help you practice your math skills and your problem-solving
abilities. Budget your time wisely, and
start working on the homework as soon as you receive it. You may ask homework questions during office
hours and via email.

*Late homework
will only be accepted with your attached “late voucher” up to one class after
the due date. *

**** Community Service Learning Components:**

*Pen
pal letters:*** **Each pair
of future teachers will correspond with two or three children in 5^{th}
or 6^{th} grade about mathematics weekly. You will describe and explain some of the
concepts you are learning in class and will read about the mathematics the
children are learning. The purpose of
this experience is for you to interact with children mathematically. You need to create opportunities to explain
mathematics and to have the children explain mathematics to you. Each letter should include at least:

·
A pleasant
greeting and some getting acquainted conversation (example: sharing some
weekend activities, your favorite books, your pastimes, your family background,
and asking the children about theirs).

·
Careful/thoughtful
responses to the children’s questions and problems (you may write notes to the
individual children within your letter).

·
A
description/explanation of one of the concepts you are learning in class:
“Talk” to the children about the concepts.
You can also ask questions about these topics, or ask them what they
think they are.

·
A worthwhile
mathematical problem for the children related to the concepts we are learning
in class and questions about the mathematics the young students are learning in
order to find out about the children’s understanding.

·
You may also
include puzzles, drawings, math games, etc.

*Family Math Night (scheduled for Wednesday, November
28^{th}*

Our
class (and a couple other classes) will hold a Family Math Night for Elementary
School families. Each pair of students will develop a "worthwhile
mathematical task" appropriate for elementary school children and their
parents. Our goals for the school are to
provide positive mathematics experiences for the families, to engage children
and their parents in mathematical thinking, to give children an opportunity to
see that their parents value mathematics and to help students discover the fun
of doing mathematics, reinforcing their positive attitudes. More information will be provided later.

*Benefits
of the Community Service Learning components for you:*

·
Making
connections between the mathematics you are learning and that which is taught
in elementary school.

·
Reinforcing your
understanding by creating an activity and writing about your learning and
composing explanations/solutions to children’s questions.

·
Practice
formulating explanations appropriate for school-age children.

·
Satisfaction
of becoming children’s role model, helping them reinforce their understanding and become more successful in
mathematics.

·
You may include
these activities in a job application, résumé, school application, etc.

*Your
commitment: *

·
Communicate with
your pen-pals each week throughout the semester. Turn in your letter on time, as the children
look forward to receiving them.

·
Learn about the
children’s mathematical thinking and share your insights with the class.

·
Develop a 25-30
minute worthwhile mathematical task appropriate for 4^{th}-5^{th})
**using the concepts we have learned in
class (or will learn in class)**. A
worthwhile mathematical task:

·
is accessible to everyone at the start, is extendible,
involves students speculating, explaining, justifying, etc, encourages
collaboration, and is engaging. Be sure
to satisfy all the characteristics of a worthwhile mathematical task. Your activity should be a “why” activity; not
just a “how” activity.

·
Be ready to share
your activity with several groups of children.

·
Provide **handouts** so children can remember, continue and extend the activity at home.

·
Turn in the
letters and a reflection paper at the end of the semester.

**Academic Integrity Policy: **Cheating and
Plagiarism are serious offenses and will be treated
severely

(see http://sa.sandiego.edu/studentcode.html#rulesofconduct). Although I encourage you to work with others, the work you turn in should be your own. Always cite your sources and your collaborators.

“Those who can, do. Those who understand, teach.” --Lee Shulman