EDCG416/668 – Mathematics for Elementary Teachers I
Syllabus – Fall 2007
Instructor: Stan Dick, Ph. D.
Email: ssdick@comcast.net
Office: W/4/185 in Suite W/4/181 (between the
orange lockers)
Phone: 617-287-7647
(during office hours only)
Office Hours: Tuesdays: 4 pm – 6:30 pm and by appointment.
Class Time/Location: This course will meet from 4:00 - 6:30 pm, on Thursdays, from
September 6 through December 13, except November 22; in Wheatley Hall, 1st floor,
room 43.
Course Description: This course for undergraduate and graduate elementary school
teacher candidates examines 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, Reston Va; Principles and Standards
for School Mathematics. The standards can be read on, or downloaded from, the NCTM
website. Go to http://standards.nctm.org/document/index.htm 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,
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2.
3.
4.
5.
6.
7.
8.
9.
increase problem solving skills, and the desire to explore, hypothesize, and try
out new ideas, if problem solving is covered,
understand and use manipulatives in teaching elementary mathematics,
communicate effectively and use multiple representations of solutions and
methods of teaching mathematics,
create original questions and curricula in mathematics, and make connections to
prior math knowledge and higher level mathematics,
recognize and transfer math skills to other areas of mathematics as well as other
disciplines,
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,
gain a better understanding of assessing the mathematical capability of
elementary school students.
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
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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 presentation due 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 22 General Outline of Project and Major Concepts Due
November 29 Detailed Project Plan Due
December 6
Draft of Final Presentation Report Due
December 13 Final Presentation and Final Report, and Handouts for Class Due
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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:
Presentations
Homework
Final Presentation
Class Participation
Final Exam
Total
25%
25%
20%
10%
20%
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
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disabilities. If you have a disability and need accommodations in order to complete
course requirements, please contact the Ross Center (617-287-7430). The Ross Center
is located in the Campus Center, 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 ⅓ x ½ = 1 6 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 1 6 of a whole egg crate, so ⅓ of ½ of an egg crate is 1 6 of an egg crate, or
⅓ x ½ = 16 .
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 ⅓ x ½ using egg crates, it would not be right to say
something like:
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is ½ of an egg crate and
is ⅓ of an egg crate, and since ⅓ x ½ = 1 6 , the
answer is
Since this is 1 6 of an egg crate. The manipulatives are the concrete
items by which 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 1 6 , it would be OK to use egg crates and say that
since
is the unit, and therefore,
is half and
is
1
6
, that there
are three of
in
therefore there are three 1 6 ’s in ½ so ½  1 6 is 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 ereserved materials, go to http://www.umb.edu/ , 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.
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