EDCG416/668– Mathematics for Elementary Teachers I

Syllabus – Fall 2007

Instructor: Stan Dick, Ph. D.Office: W/4/185 in Suite W/4/181 (between the orange lockers)

Email:hone: 617-287-7647(during office hours only)

Office Hours: Tuesdays: 4 pm –6:30 pmand by appointment.

Class Time/Location: This course will meet from 4:00 - 6:30 pm, on Thursdays, from September6 through December 13, except November 22; in Wheatley Hall, 1st floor, room 43.

Course Description: This course for undergraduate and graduate elementary school teacher candidatesexamines content and methods for teaching mathematics to Elementary School students. The course may cover problem solving; the development of the numbers systems; the decimal system; the use of various manipulatives in teaching elementary mathematics; the standard algorithms for addition, subtraction, multiplication and division of integers, fractions and decimals, and their rationales; probability; statistics; geometry, and the relationship of elementary mathematics and various curricula to more advanced mathematics. The course is intended to help the prospective elementary school teacher to see the elementary school students’ mathematics education as an integral and fundamental part of their overall mathematical education.

Pre-requisites: The permission of the instructor, and an enthusiasm to learn mathematics.

TEXT/MATERIALS:

1. Mathematical Thinking Skills for Teachers, by Stan Dick. This text will be distributed to the class for the cost of printing the material.

REFERENCE MATERIALS:

1. National Council of Teachers of Mathematics, RestonVa; Principles and Standards forSchool Mathematics. The standards can be read on, or downloaded from, the NCTM website. Go to and go to the pages for Standards 2000 Project, Introduction, Principles for School Mathematics, Standards for School Mathematics, Standards for Grades Pre-K2, Standards for Grades 3-5, Standards for Grades 6B8, Standards for Grades 9B12.

2. Massachusetts Mathematics Curriculum Frameworks. Achieving Mathematical Power. Massachusetts Department of Education. A copy can be requested from the website.

Course Objectives: This course is designed to engage prospective teachers in understanding the deeper principles underlying elementary mathematics, and increase confidence and competence in doing and teaching elementary mathematics. Specifically, the course may develop or enhance the students= abilities to:

  1. gain a deep understanding of the mathematical content and procedures underlying elementary mathematics, and how that content relates to higher level mathematics, as well as other disciplines,
  2. increase problem solving skills, and the desire to explore, hypothesize, and try out new ideas, if problem solving is covered,
  3. understand and use manipulatives in teaching elementary mathematics,
  4. communicate effectively and use multiple representations of solutions and methods of teaching mathematics,
  5. create original questions and curricula in mathematics, and make connections to prior math knowledge and higher level mathematics,
  6. recognize and transfer math skills to other areas of mathematics as well as other disciplines,
  7. gain a big picture perspective of the role of the mathematics teacher by participating in mathematical inquiry and professional development, discussing current hot topics in mathematics education, and analyzing various curricula and standards, understand the intentions underlying various curricula,
  8. gain a better understanding of assessing the mathematical capability of elementary school students.
  9. gain a better understanding of how to adapt a mathematics lesson to include disabilities and learning preferences.

Homework - Homework is an essential component of this course. Homework problems from the notes and possibly other sources will be assigned during each class. Assigned homework exercises should be completed neatly and handed in for grading during the next class. Course notes sections should be read before they are covered in class, or, at the latest, before beginning related homework assignments. Students are expected to do at least three hours of work outside class for every class hour. Homework should be kept in a separate book or on loose leaf pages in a separate section of a notebook. Homework will be graded for effort and completeness, as well as correctness.

Group Work - We will form groups of about five students. Groups will work together to solve homework problems, present homework problems, do the final presentation, and generally help each other to learn the material.

Weekly Presentation of Homework - One group will present the homework problems to the class each Tuesday. The presenting group will rotate each week. Presenters should be prepared to answer questions from class members and the instructor.

Final Presentation–Students, in their groups, will make a presentation to the class on the last regular class meeting of the semester. The presentation should take about 20 minutes or 5 minutes per group member, whichever is longer. The purpose of the presentation is to show content mastery of some portion of the course, show skill in developing a lesson plan and presenting a lesson, show understanding of and sensitivity to teaching all children, show understanding of assessment, and to review or re-teach the chosen material to the remainder of the class. Presentations usually cover material already covered in class (but might include new, related material), and should be in the form of a lesson for our graduate class (not an elementary school class). Each lesson presented should include 1) a manipulatives component, 2) an assessment of the material covered in the lesson (but the assessment will be in the report and will not be executed), 3) a discussion about how the specific lesson provided could be adapted to include three students with special needs or particular learning preferences such as the students described in the appended lesson plan format, and 4) an activity that involves the class, including a handout for each member of the class. All group members should share equally in the planning and delivery of the final presentation.

At the start of the presentation, the group should provide to the instructor, a binder containing the lesson plan for the presentation, and any other materials relevant to producing the lesson, or at least references to where these materials can be obtained.

On November 22, three weeks before the presentation (see schedule) each group must submit to the instructor, in writing, a preferred presentation topic and a list of sub-topics that will be covered in the final presentation. Topics may have to be changed or modified in some cases if there is too much duplication or the topic is not broad enough or is too broad, or in some way inappropriate. Twenty minutes at the end of the class will be reserved for group work on the final presentation outline due on May 2.

On November 29, two weeks before the presentation date an outline of the presentation must be handed in. The outline will include a summary of the presentation including:

1)a description of the activities and mathematical concepts that will be presented,

2) a delineation of who will present each of the activities,

3) a discussion of what manipulatives will be used in the presentation and how they will be used, and

4) an estimate of the presentation time (which should be about 20 to 25 minutes).

Presentation outlines will be reviewed and modified (if necessary) by the instructor by the next class. One half hour at the end of the class will be reserved for group work on the description of the final presentationdue on May 9.

On December 6, one week before the final presentation a detailed description of the presentation is due, including a sample of what will be covered, and a draft lesson plan. Presentation descriptions will be reviewed and modifications will be suggested during the class if necessary. Forty five minutes at the end of the class will be reserved for group work on the final presentation, due the next week.

On December 13, a final presentation report is due to the instructor at the beginning of the presentation. It will include all items mentioned above as well as a detailed portfolio covering the presentation. The report should be one, unified seamless group report, not a collection of reports from individual class members. Presenters should be prepared to answer questions from class members and the instructor.

The mark on the final presentation will be based on the difficulty of the material presented, the perceived understanding of the material, the quality of the lesson plan, the quality and completeness of the final report, and the quality of the presentation. A rubric for the final presentation is attached.

Final Presentation Schedule (all items due in writing)

November 22General Outline of Project and Major Concepts Due

November 29Detailed Project Plan Due

December 6Draft of Final Presentation Report Due

December 13Final Presentation and Final Report, and Handouts for Class Due

Final Exam: There will be a three-hour comprehensive final exam, covering the course material in the period from December 17–December 21, 2007. The questions on the final exam are generally similar to the homework questions. However, in the instructor’s experience, students’ grades on the final exam are generally lower than the grades on homework and presentations. For this reason students should make a special effort to cover the course material broadly and deeply, when studying for the final exam.The exact date and time of the final exam will be provided on the UMB website later in the semester.

Class Participation: The class participation grade is based on the contribution the student makes to the class and his or her group. Specifically this grade is based on such items as promptness of arrival to class, amount of support provided to student’s group, and participation in class discussions.

Please notify me of any conflicts concerning the final exam date immediately after the date is announced.

Formula for Grading: The overall grade in the course will be determined by the formula below, except as further elaborated upon below:

Presentations25%

Homework25%

Final Presentation20%

Class Participation10%

Final Exam20%

Total 100%

Letter Grade Ranges: A: 93 to 100; A– : 90 to 93– , B +: 87 to 90 – , B: 83 to 87– , B– : 80 to 83– , C + : 77 to 80 – , C: 73 to 77– , F: below 73.

Please consult the instructor before dropping this course.

Attendance: Attendance at class meetings is critical in this course and is mandatory. The course moves at a rapid pace due to the large amount of material to be covered in a short period of time, and it may be difficult to catch up if you fall behind. In addition, notification of changes to this syllabus, to due dates and homework assignments or any other components of the course may be provided verbally during class meetings, or by email. The first absence will be excused. Students will lose 2% of their grade if they are absent twice, will lose 4% if they are absent three times, and will not get credit for the course if they are absent 4 times or more.

Send Me an Email: Send me an email before the next class from the account you use most. The subject of the email should be EDCG416/668. I will use this address to send important communications to you during the semester, including assignments, exam coverages, etc. It is your responsibility to send this email, keep me apprised of any changes, and tell me if you are not receiving emails.

Accommodations: Section 504 of the Americans with Disabilities Act of 1990 offers guidelines for curriculum modifications and adaptations for students with documented disabilities. If you have a disability and need accommodations in order to complete course requirements, please contact the RossCenter (617-287-7430). The RossCenter is located in the CampusCenter, 2nd floor, Room 2010. The student must present these recommendations and discuss them with each professor within a reasonable period, preferably by the end of the Drop/Add period.

Academic Honesty: Students are required to adhere to the Code of Student Conduct, including requirements for academic honesty, which are delineated in the UMass Boston Graduate Studies Bulletin, undergraduate Catalog, and relevant program student handbook(s). For purposes of this course, homework may be worked on jointly by the students, but each students should do the final draft of the homework problems independently, and the homework handed in for grading should be his or her own work, and should be written by the student handing it in.

Incomplete (INC) Grade: Except as mentioned above under Final Exam, the INC grade is only given in cases of extreme illness or other serious and well documented problems. The INC grade is given only if the student is passing the course except for an assignment or exam that has been excused, but not yet completed. It is never given if the student is failing the course, or as a mechanism to better a student’s grade.

Every effort will be made to abide by this syllabus. However changes to this syllabus may be made, at the discretion of the instructor, verbally during any class, or by email to the address provided by the student, and will be considered official and binding.

Note: While this order is not always observed in my text, one would teach a concept using manipulatives before using number concepts and rules. For example, we could use egg crates to show that ⅓x½ =by showing that one-third of one-half of an egg crate is one-sixth of an egg crate. We would show this as follows:



Let’s assume represents a whole egg crate, and our unit in this



case. Thenis ½ of an egg crate, and  is ⅓ of the ½ of the egg crate,

but is of a whole egg crate, so ⅓ of ½ of an egg crate isof an egg crate, or

⅓x½ =.

By doing enough problems like this, we might notice that we could have gotten the answer by multiplying the numerators of ⅓ and ½ to get 1, the numerator of the answer, and, and multiplying the denominators of ⅓ and ½ to get 6, the denominator of the answer.

But if asked to demonstrate ⅓x ½ using egg crates, it would not be right to say something like:



 is ½ of an egg crate andis ⅓ of an egg crate, and since ⅓x½ =, the

answer is.Since this is of an egg crate. The manipulatives are the concrete items bywhich we show things about numbers, which are in themselves very abstract.

Note: When doing problems in the text you must use only methods developed so far. For example, if asked to divide ½ by , it would be OK to use egg crates and say that since



 is the unit, and therefore, is half and is , thatthere



are three of  in, therefore there are three ’s in ½ so ½is 3. It would not be correct to use the rule that says “when dividing by a fraction we can multiply by the reciprocal of the fraction” if we have not yet proven that rule.■

E-Reserve Instructions: Some course materials, including the syllabus, may be put on e-reserve by your instructor. These materials can be accessed online using a browser. To access e-reserved materials, go to , highlight Academics, click Healy Library, under Electronic Resources click E-Reserves, click Electronic Reserves and Reserves Pages. On the page you are brought to, set the leftmost window to ‘Instructor’, the second window to ‘contains’, and type ‘Dick’ into the rightmost window. Then click Search, and choose the item you wish to read or print. When asked for a password use “elementary” without the quotes.

EDCG416_668 Syllabus Fall 2007 - 1