GEORGETOWN COLLEGE

Mathematics 204

Mathematics for Elementary Education II (3 hours credit)

Spring 2011

Dr. Christine Leverenz, ASC 102A, Phone: 8097

Dept. website:  http://spider.georgetowncollege.edu/mpc/

Course Description:  A continuation of Mathematics 203.  A detailed development of the mathematics taught in elementary school using a problem-solving approach.  Topics include further development of the real numbering system, informal geometry, probability and statistics.  For elementary education majors only.  Prerequisite:  Math 203

TextbookExploring Elementary Mathematics, Part II, Spring 2011 edition by C. Leverenz, available at The Store.  You will also need a TI Math Explorer calculator (no other calculator may be used for tests), unlined paper, and a measuring kit consisting of a centimeter and inch ruler, a safety compass, and a Safe-T-Pro Ruler.  No other measuring tools are acceptable.  You are expected to have these geometry aids with you for every class.  It may also be helpful to have colored pencils or markers, and sugar cubes (or other cube blocks).

I strongly suggest that you use a three-ring binder to organize all homework, notes, and handouts.

The MAT203 and 204 courses cover all elementary mathematics in the KY Program of Studies but at a much deeper level.  The approach used in this course depends on these four “big” ideas which form the basis for MAT203/204 and EDU315.

All mathematics makes sense because new concepts are logical expansions of previous knowledge.  For example, fraction operation lessons should build on knowledge of whole number operations.

Mathematics is active; the learner is constantly thinking, asking why, and working towards understanding.

Understanding of mathematics is demonstrated by knowing concepts and solving problems using differing viewpoints including pattern recognition and creation, reasoning using concrete examples and symbolic representation, and mental computation. Students demonstrate that they “understand” when they can apply ideas in new situations or new types of problems (in other words, aren’t just parroting back what the teacher has done).

Written and oral communication aids mathematical understanding.  Classroom dialogue is an essential part of children’s learning; they learn from talking about problems – both explaining their own thinking and listening to others (therefore a teacher challenge is getting the student to LISTEN to each other!)

LEARNING OBJECTIVES:  Students will

• demonstrate basic content knowledge of geometry, measurement, statistics, and probability through homework, the Basic Skills quiz, and exams;
• demonstrate analytical reasoning skills and problem solving skills in reasoning problems about these areas as demonstrated through in-class work and homework;
• apply oral and written communication skills when communicating on in-class work, on homework, and on tests and projects.

Requirements of the Course:

1. Daily work:  Class time is reserved for work that cannot easily be done individually including group problem solving, exploration of new ideas, oral presentations, and lecture.  Student participation is expected to be continuous and helpful.  Students are expected to speak only mathematics in class; students who make negative contributions will have points deducted from their daily work grade.

Students regularly put problems on the board, orally explain the solutions, monitor and assess board problems.  Homework policies are listed more completely at the end of this document.  Because class communication of mathematics is such an important skill, there is a grade penalty for absence from class.  Cell phone, MP3 players, iPods, and other electronic devices are not allowed during class because it interferes with concentration and communication.

All geometry homework assignments must use unlined paper.

2.  Projects:  Approximately 2 “larger” projects will be assigned throughout the semester.  These projects will be completed outside of class.  Explicit instructions will be distributed in class several weeks before the project is due.  The due dates are posted on Moodle.

3.  Basic Skills Quizzes:  These cover basic geometry skills:  measuring lengths, metric and English measurements, area and perimeter formulas and their use in simple cases, definitions of basic shapes.  The quiz will count 20 points and each question will be graded right or wrong.   A student must earn 90% (18 out of 20) on at least one basic skills quiz to make a grade of D or above in the course.  The first basic skills quiz will be given in class.  Those who need to retake the quiz will reschedule makeup quizzes outside of class; with very few exceptions, no more than 3 additional quizzes will be given to any one student.  Calculators will not be permitted on basic skills quizzes.  Basic skills quizzes should be finished before midterm.

4.  Tests:  Because teaching is primarily an individual endeavor and because I must certify that you know deeply the math you are to teach, the work shown on three hourly tests and a comprehensive final provide the bulk of your class grade.  If you cannot take an hourly test you must get word to me before the test is given.  The makeup will usually consist of that portion of the final exam covering the missed material.  The tentative test schedule is posted on Moodle.  No student may spend more than two hours on a test.

Course Outline:  The topics covered include geometry vocabulary, geometric properties that describe relationships between geometric figures, measurement of angles, lengths, areas, and volumes, statistical concepts, and probability.  We cover one section of the text per class period.

Evaluation

1.  Basic skills:  A Basic Skills grade of 90% must be earned to have a chance at a grade of D or above in the course.

2.  Homework and daily work:  The rubric for homework and daily work is given below.  3’s earn 100% so a grade of 4 on a problem is extra credit.

4pts- Above and beyond: uses exemplary methods, shows creativity, and goes beyond the requirements of the problem.

3pts- Complete: completes task with no more than a minor error, uses expected approaches, and communicates why an approach works.

2pts- On target:  completes task with minor errors or almost completes task, uses expected approaches, communicates what has been done rather than why.

1pt- Not there yet: makes significant errors or omissions, uses inappropriate approaches.

0pt- Problem not done.

3.  Projects:  The rubric for a project will be discussed when the assignment is made.  Together they count up to one test grade.

4.  Attendance:  Two unexcused absences or four excused absences will result in the final grade for the course being lowered to the next highest level.  Further absences, will result in the penalty being applied a second time.

5.  Tests and course grading scale:  The grading scale for the course and for tests is

92 – 100 A

87 – 92 A/B

82 – 87 B

77 – 82 B/C

70 – 77 C

60 – 70 D

The projects and hourly tests count 55% of the final grade; the final exam counts 25% of the final grade; homework counts 20% of the final grade.   Contributions, both positive and negative, to class discussion, board problems, group work, and others’ understanding of mathematics will be carefully considered when making final grade decisions, particularly in borderline cases.

Attendance:  Class attendance is required; no allowance in grades will be made for cuts.  If illness, college business, or some other legitimate excuse prevents you from attending it is up to you to inform me of this.  I expect you to be prepared for class on the day that you return.  TA assignments are not legitimate excuses for missing class.  Attendance is required to submit work.

Office Hours: Please come to my office to get individual questions answered.  Office hours are posted on Moodle.  If you call my office and I don’t answer please leave a message; when speaking with someone in my office I don’t answer the phone.  If you miss class for an unexcused reason please do not come to my office for help on that material since it is not fair to the rest of the class to give one-on-one special teaching to those who do not see fit to attend class.

Homework Specifics:  It is expected that the student will spend a minimum of 3 hours per class meeting on homework.

1.  For all assignments, a yes/no or number answer must be accompanied by at least a one-sentence explanation of the logic behind the answer.  No explanation, no credit.

2.  Homework problems will be review, new material, problem solving, reading, computer work, and writing.  Most assignments also have one problem that is an introduction to the next day’s work.  There are very few drill and practice exercises; almost all problems are designed for you to think through familiar material in new ways or to solve unfamiliar problems.  Much of the problem solving is from a magazine for elementary teachers, “Teaching Children Mathematics” and is designed for use in an elementary classroom.  You are expected to finish the in-class work and use this work as background for the homework.  Look up unfamiliar vocabulary in a dictionary or online!

3.  Homework OK’s                                      Homework No-no’s

unlined paper for geometry drawings        Cramped papers – leave space between problems.

Any paper including straggly edges.          Multiple columns on one page.

Pen or pencil                                               No work or reasoning.

Problems out of order.

Continuing problems on another page.

Cross outs.

4.  Board problem assignments and any changes to homework assignments will be posted on Moodle.

5.  The first 5 or 6 lines or first 1.5 inches of paper should be left blank until the end of the assignment.  In this section please tell me if you if you are particularly proud of a problem.  Also, you may ask a specific and mathematical question about a particular problem.  This gives you an extra venue for communication, particularly if you could not make office hours one day.

6.  If you want my feedback on homework you must leave me room to write – about 5 lines for a longer problem.  If I don’t have room to write I won’t be happy when writing comments.

7.  It is fine for students to collaborate on homework as long as it is true collaboration on all problems – everyone is contributing equally to the solution.  All such collaboration on homework must be acknowledged, e.g.: I worked with or received help from (Source Name) on this problem. Such acknowledgments will not count against the paper.  Allowing people to copy your work and/or copying someone else's work is not ethical behavior and will be penalized when discovered. See the pages in the Student Handbook under Honor Code for the penalties associated with cheating.

8.  Homework will be spot-checked, meaning that I will select a few problems to grade carefully; the rest of your homework score will be determined by my overall impression of completeness, correctness, and signs of effort.

9.  Collected homework must be submitted by the author.  Collected homework is due one-hour after class is over.  Please do not work on homework during class; this practice affects how we are prepared to do the next night’s homework.

Basic skills quiz: sample

1.  Fill in the conversions.  (I will choose 5 of these.)

1 ft = ________ in               1 yd = ________ ft              1 mi = ________ ft        1 yd = _________ in

1 km = ________ m           1 m = _________ cm         1 m = ________ mm          1 cm = ________ mm

2.  Measure the line segment (the longer one to the right.)  Note:  I allow 1 number above or below my answers to be correct; not all rulers are exactly the same.

3. I will choose one of the following.  The number and the type of units may change.

a. Explain what 5 cm means.  The 5 represents____________________  and the cm represents _______________.

b. Explain what 5 cm2 means.  The 5 represents____________________  and the cm2 represents _______________.

c. Explain what 5 cm3 means.  The 5 represents____________________  and the cm3 represents _______________.

4. (I will choose 2 out of the following 8 types of problems for one quiz.  Each one counts 3 points – 1 pt for the formula, 1 pt for the computation, 1 pt for the units.  On any problem the figure may be sketched as in part c and d.)  If the measurements are given as fractions use fraction computations and if the measurements are given as decimals use decimal computations.

Use p 22/7 or 3.14 as appropriate.  No calculators for these computations.

a. The formula for the area of a circle is __________________.  If a circle has radius = 1/3 cm then the area is ___________.

b. The formula for the circumference of a circle is ______________.  If a circle has radius = 2.1 cm. then the circumference is _____________.

c. The formula for the area of a rectangle is ________________.  The area of this rectangle is _________.

d. The formula for the perimeter of a rectangle is _____________.  The perimeter of this rectangle is _____________.

e. The formula for the area of a triangle is _______________.  If a triangle has base 3m and height 5m then the area is ___________.

f. The formula for the perimeter of a triangle is _____________.  If a triangle has sides of 3/2 m., 5/3 m., 1/3 m., then the perimeter is _____________.

g. The formula for the area of a square is _______________.  If a square has a side of 6.1 yd. then the area is _____________.

h. The formula for the perimeter of a square is ___________.  If a square has a side of 1.5 in. then the perimeter is ______________.

5.  Give a word definition of each of the following geometry terms.  (I will choose 4.)  Word definitions must describe the figure exactly, not include any other figure, and use geometric language.

Terms:

scalene triangle,

isosceles triangle,

equilateral triangle,

obtuse triangle,

acute triangle,

right triangle,

trapezoid,

parallelogram,

rhombus,

rectangle,

square,

polygon,

circle