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

Course Syllabus


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

Email:                                         Phone: 260-7932 (I check email more often)   

Web Page:               

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.



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 24th, Exam #2 (written part): Wednesday, April 6th, Exam #2 (oral part): TBA.


* A Cumulative final exam: (May include written and oral parts.) Monday, May 16th, 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 4th/5th 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 25th-- 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 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


Understand and apply the concepts from Math 115 and 200.




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.



·      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.



·      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.



·      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.