**Math
300 * Mathematical Concepts for Future Teachers II * Spring 2016**

Course
Syllabus

**Instructor: **Dr. Perla Myers **Office: **Serra
Hall 133A/ Founders Hall 114

**Email: ** **pmyers@sandiego.edu** **Phone: **260-7932 (I check email more often)

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

**Meeting Times:** Mondays and Wednesdays:
2:30pm-3:50pm, Serra 128

**Office
Hours:** Monday 9:00am-11:00pm, or by appointment. To make an appointment
call (619) 260-4545.

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

Math
200: Mathematical Concepts for Future
Teachers I with a grade of C or above

**Required ***Elementary Geometry for Teachers* by Baldridge and Parker,

**Supplies:** *New
Elementary Mathematics 1*
(Syllabus D) by Sin Kwai Meng,

*Primary
Mathematics 3B, 4A, 5A, 5B, *and* 6B Textbooks *from Singapore
Mathematics,

A
stapler: Any assignment longer than one page must be stapled together.

A
large three-ring binder with dividers and loose-leaf paper (for a lot of
handouts),

graphing paper, ruler, compass,
protractor, small shoebox, scissors, & colored pencils.

**Email/Web:** I will communicate with you via
your USD email address often. I will post assignments and place other relevant
information on the course web page. Please check your email messages often.

**Purpose of the Course: **Math
300 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 and
to develop your own questions. To this end, many of the problems and
opportunities to pose questions you will encounter will not be 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 developer and
solver.

**Learning
Outcomes: **

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

1. Apply
correct terminology associated with geometry and measurement, and explain the
role of language and precision in mathematics in oral and written
communication.

2. Discuss
cultural differences in mathematical terminology.

3. Identify,
define, classify and draw geometric objects according to their characteristics.

4. Solve
problems involving geometric and measurement concepts effectively in multiple
ways.

5. Write and
explain complete proofs of theorems and formulas involving geometric and
measurement 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).

6. Explain
geometric and measurement concepts effectively in order to help others
understand why a claim is true or false.

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

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

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

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

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

12. Apply knowledge gained in class
to a real teaching experience with children.

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

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

15. Create and
classify your own questions. Make and test conjectures. Identify invalid
reasoning and provide counterexamples to disprove statements that are not
always true.

16. 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.

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

18. Use the software
available on an iPad to explain, learn and teach mathematics.

19. Use origami to aid
in learning and teaching geometry.

**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 your professor will
always be kind and respectful.

·
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 Wednesdays 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 that 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: Wednesday, February 24^{th},
Exam #2 (written part): Wednesday, April 6^{th}, Exam #2 (oral part):
TBA.

*** A
Cumulative final exam: **(May include written and oral parts.) Monday, May 16^{th},
2:00-4:00 p.m.

*** 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. Homework
assignments will usually be given on Tuesday and will be due by the beginning
of class the next Tuesday. Budget your time wisely, and start working on the
homework as soon as you receive it. You may ask 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 Component:**

*Correspondence with Elementary School Students:*** **Each group
of 2-3 future teachers will correspond with a group of 4^{th}/5^{th}
grade students about mathematics. You will describe and explain some of the
concepts you are learning in class and will hear about the mathematics the
children are learning. The purpose of this experience is for you to interact
with children mathematically and to become adept at working with technology to
share information. You need to create opportunities to explain mathematics and
to have the children explain mathematics to you. You will get more information
about this.

*Visit from Elementary School Children,
including your pen pals (Monday, April 25 ^{th--} more information soon*

· Our class will host some
elementary school students. Together we will develop the plan for the day. **For now, please keep the hours of 12-4
available for this event.** Our goals are to provide positive mathematics
experiences to the visitors, to engage students in mathematical thinking, to
help students discover the fun of doing mathematics, reinforcing their positive
attitudes, and to introduce the students to the university. More information
will be provided later.

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

(see
http://www.sandiego.edu/conduct/the_code/rules_of_conduct.php). 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

*MORE SPECIFIC OUTCOMES:*

**Understand and apply the concepts from Math 115 and 200.**

**Fractions**

**Definitions and Venn Diagrams (including polygons and polyhedra)**

·
Know how to
write complete mathematical definitions.

·
Draw a
mathematical Venn diagram that represents relationships between sets.

·
Understand the difference between Venn diagrams as used in mathematics
and “Venn”-like diagrams sometimes used in other subjects.

·
Write
definitions for sets of objects, determine what shapes satisfy a certain
definition, and find non-examples for a definition. Create lists of characteristics satisfied by a set of objects—be able to
determine which characteristics are necessary, sufficient, and redundant.

· Draw examples and non-examples of
the different objects we have explored using compass, protractor, straightedge
and set square.

· Determine properties of shapes.

· Classify and give general and
specific names for objects. Know the names and how to pronounce them.

· Visualize a polyhedron from its
net and draw the net of a polyhedron.

**Measurement **

· Explain: What is measurement?

· Describe the process involved in
measuring.

· Explain how units are used? What
are some advantages of standard units? Nonstandard units?

· Know the following: 1 inch = 2.54
cm, 1 foot = 12 inches, 1 mile =5280 feet, 1 yard = 3 feet, 1 ton = 2000 pounds
(lbs), 1 metric ton = 1000 kilograms, 1 kg = 2.2 lbs., 125 liters = 33 gallons,
1 gallon = 4 quarts, 1 quart = 2 pints, 1 pint = 2 cups, 1 lb = 16 ounces, 1
liter = 1000 cubic centimeters, the metric system prefixes (milli, centi, deci,
deca, hecto, kilo), how each inch and centimeter are subdivided in a ruler.

· Describe the systems of
measurement used in the U.S.

· Select
appropriate units of measurement and convert between different units.

· Understand error and accuracy in
measurement.

**Angles and
Angle Facts:**

· Draw angles and measure angles
using a protractor and straight edge.

· Know how to write complete
unknown angle proofs using the format explained in the book (elementary proof format).

· Know and prove the angle facts.

**Teaching
issues and Reasoning**

·
Understand
the teaching sequence for the topics we have discussed.

·
Understand
possible misconceptions/mistakes in the topics we have discussed.

·
Look at
someone’s work to understand it, determine its validity. If it is correct, justify it, and if it is
incorrect determine how it can be corrected.

·
Know how to
write complete teacher solutions using the Singapore model method and the angle
facts we have learned.

·
Use
inductive reasoning and deductive reasoning and determine when each type of
reasoning is used.

·
Specify when
inductive reasoning and when deductive reasoning are used.

·
Identify the
validity of a given statement.

·
Prove that a
statement is false (not always true) by using a counterexample.

**Transformations,
Symmetry and Tessellations**

·
Find all
reflection and rotational symmetries of an object.

·
Draw objects
with certain symmetries.

·
Perform
translations, rotations, reflections and recognize the kind of transformation
performed on an object.

· Know what it means for an object
to tessellate the plane and determine if certain sets of objects tessellate the
plane.

· Prove that there are only three
regular polygons that tessellate the plane.

· Create certain types of
tessellations.

**Congruent
Triangles**

· Prove and use information about
congruent triangles.

· Apply the congruence tests: SSS,
ASA, SAS, Right-hypotenuse-leg test to prove facts about polygons.

· Explain why some possible tests
(AAA, ASS) do not guarantee congruence.

**Know how to
solve problems using different representations:**

·
Model method

·
Algebraic
representation

·
Know how to
write word problems and perform and justify operations with fractions.

**Scaling**

· Determine if two shapes are
similar.

· Know different strategies for
finding dimensions of similar shapes, and explain why they work—that is,
explain how the scale factor is used in each strategy and be able to show
pictures that illustrate the concepts.

· Determine how lengths, areas and
volumes of similar shapes are related.

· Describe the results of
enlarging/reducing using a copier.

**Areas and
perimeters: **

· Estimate areas and perimeters of
irregularly-shaped objects.

· Know area formulas and prove them
for a rectangle, square, parallelogram, triangle, trapezoid and circle.

· Figure out how to use known area
formulas to find out the areas of shapes whose area formulas we do not know.

· State and prove the Pythagorean
Theorem using area arguments.

**Volumes**

· Estimate volumes of
irregularly-shaped objects.

· State volume formulas and prove
them **(No need to memorize the formulas
for the test—understand the concepts)**

*A complete
solution write-up includes:*

· A restatement of the problem in
an unambiguous way in your own words.

· An explanation of the reasoning
behind the solution, so that one could apply it to a similar problem.

· Complete paragraphs (with
complete sentences) detailing the solution in a logical, clear and concise
manner.

Thorough, logical, and organized
step by step reasoning including all possible scenarios; A statement of the
answer with analysis of why it makes sense.

· Examples, diagrams and graphs
(that are accurate) when needed.

· Correct spelling, grammar and
punctuation.

· An ending that restates the
solution clearly and ties back to the original problem.

Someone outside the class should understand and follow your
explanation/description. It may be
necessary to re-write the explanation/description so that it is presented in an
organized way and so that it satisfies all the characteristics above.

·
*Identify, use and understand the
terminology:*

Fraction, whole unit, fractional unit,
numerator, denominator, geometry,
point, line, plane, segment, ray, surface, collinear, non-collinear,
straightedge, congruent segments,
(mathematical) Venn diagram, set, intersection, mutually exclusive, endpoints,
triangle inequality, measurement, standard units, non-standard units,
the metric system, customary system of measurement, weight, capacity, unit,
notation, unit conversions, inch, foot, mile, yard, kilo, centi, milli, deci,
deca, etc., metric system, measurement model, angle (two definitions), volume,
gram, ounce, pound, ton, metric ton, milliliter, liter, cup, pint, quart,
gallon, congruent, degree, radian, full
turn, acute angle, right angle, obtuse angle, straight angle, reflex angle,
protractor, adjacent angles, bisector, congruent angles, supplementary
angles, complementary angles, measure of an angle, vertical angles, circle,
radius (radii), diameter, compass, set square, triangle, tangent line, tangent
circle, intersection points, quadrilateral, vertex (vertices), exterior angle,
interior angle, parallel lines,
perpendicular lines, bar diagrams, teacher’s solution, curve, length,
distance, set, subset, disjoint sets, universe, parallel postulate, polygon, right triangle, acute triangle, obtuse
triangle, scalene triangle, isosceles triangle, equilateral triangle, square,
rectangle, rhombus, kite, parallelogram, trapezoid, side, pentagon, hexagon,
heptagon, octagon, nonagon, decagon, dodecagon, n-gon, regular polygon,
diagonals of a polygon, convex, concave, equilateral, equiangular, line of
reflection, center of rotation, symmetry, reflection symmetry, rotational
symmetry, n-fold rotational symmetry, rotational symmetry of order n, center of
symmetry, converse, auxiliary lines, counterexample, corresponding
angles, interior angles along a transversal, alternate interior angles,
alternate exterior angles, closed
polygonal path, inductive reasoning, deductive reasoning, proof, theorem,
congruent triangles, SSS, ASA, SAS, Right-Hypotenuse-Leg Test, transformation,
congruence transformation, isometry, rigid motion, rotation, reflection,
translation, image, tessellation, regular tessellation, semi-regular tessellation,
area, area units, square unit, unit square, region, composite region,
perimeter, altitude, height, base, Pythagorean Theorem, hypotenuse, legs,
Pythagorean triples, irrational number, square root, special triangles, pi,
chord, circumference, central angle, arc, sector, special triangles,
similarity, similar, proportional,
implied units, scaling, scale factor, constant of proportionality, similarity
transformation, enlargement, reduction, area scaling principle, circle, pi,
diameter, radius, chord, circumference, central angle, arc, sector, unit cube,
cubic unit, cuboid, prism, pyramid, lateral face, lateral edge, apex, cylinder,
right prism/cylinder, oblique prism/cylinder, cone, sphere, equator, great
circle, polyhedron, naming of prisms/pyramids—according to the number of sides
of the base (pentagonal prism, hexagonal prism, rectangular prism, etc.),
naming of polyhedra—according to the number of faces (hexahedron, dodecahedron,
octahedron, icosahedron, tetrahedron, etc.), regular polyhedron, Platonic
solid, face, vertex.