Course
Information
Saint
Joseph’s University
Department of
Mathematics and Computer Science
MED 4185: Secondary Mathematics Curriculum
Fall 2006
Professor: Dr. Amy N. Myers Class
Location: Seminar Room BL 244s
Office: BL 242 Class
Meeting Times: 4:30 – 7:10 PM
Office
Hours: M 2:30 – 4:30, Tu 1 – 4, W 3 – 5 Phone: 1554
E-Mail: amyers@sju.edu
This course examines the ways in which high school students
acquire mathematical knowledge, considers the particular mathematical knowledge
they should have at each grade level (as articulated by the Principles and
Standards of School Mathematics), and applies this understanding to the
design of secondary mathematics curricula.
The course may also include one or more of the following: discussion of how mathematics curricula have
evolved over time in response to developments in cognitive science and other
factors; classroom barriers to mathematical proficiency in the form of gender,
cultural, and socio-economic biases; and a comparison of American secondary
mathematics curricula with those of countries that perform well on
international tests of student achievement.
We have a problem with mathematics
education in the
Although what and how we teach forms
only part of a solution, it is the aspect of mathematics education over which
we have the most control. Our best hope
for improving mathematics education comes from way we organize and present our
subject. In this course we focus on
organization (curriculum), while MED 4145 focuses on presentation (pedagogy).
Knowledge
of how students learn mathematics forms the basis for effective curriculum and
pedagogy. In this course we examine the
ways in which people acquire mathematical knowledge. We then consider the particular mathematical
knowledge high school students should obtain at each grade level, as well as
the principles that guide its sound organization and presentation. Finally we use our understanding of how
students learn mathematics and the knowledge they should acquire to evaluate,
improve, and develop mathematics curricula.
Studying
successful school mathematics programs provides a source of inspiration for the
design of curriculum and pedagogy.
Recent international studies of school mathematics achievement reveal
surprising differences in mathematics curriculum and pedagogy across
countries. In this course we consider
these differences and the directions they suggest for improvement.
Ineffective mathematics teaching and
curricula contribute to the problem of mathematics education. Some students encounter additional barriers
to mathematical proficiency in the form of gender, cultural, and socio-economic
biases in the classroom. Such biases arise from assumptions about students’
innate mathematical talent (or lack thereof).
This course examines the pervasive “myth of ability” and the effect of
teacher attitudes on student learning.
Course Objectives/Learning Outcomes
·
Articulate
the problem with mathematics educations, its sources, and the rationale for
addressing it.
·
Describe
the ways in which students obtain mathematical understanding, and apply this knowledge
to curriculum evaluation and design.
·
Use
the Principles and Standards to
design and evaluate mathematics curricula.
·
Know
how Americans students compare to those of other countries in terms of
mathematics achievement, and explain possible reasons for the difference.
·
Understand
the nature and effects of gender, cultural, and socio-economic biases in the
classroom.
Required
Texts
Supplemental
Grades for
this course are based on class participation, presentations, and written assignments,
with letter grades assigned as follows:
|
A |
student
demonstrates mastery of all course material, interprets it appropriately for
math education, presents this understanding clearly, and makes it relevant
for peers |
|
B |
student demonstrates
good understanding of most course material, usually interprets it
appropriately for math education, presents this understanding reasonably
clearly, and often makes it relevant for peers |
|
C |
student
demonstrates incomplete understanding of course material, occasionally
interprets it appropriately for math education, presents this understanding
somewhat clearly, and sometimes makes it relevant for peers |
|
F |
student
demonstrates inadequate understanding of course material, fails to interpret
it appropriately for math education, and makes unclear presentations which
are irrelevant to peers |
Absences
Due to the collaboration, the
reflective nature of the course, and the interrelated and cumulative sequence of
activities, students are required to be present at each class. Because some students of the class will have
a professional obligation, such as a “Back to School Night” for parent
conferences, two excused absences will not affect the student’s course grade. If a class must be missed, prior to the absence the student must
contact the professor for the details concerning a possible make-up assignment,
and make arrangements to deliver to the professor any assignments due during
that class. However, each ensuing
absence for any reason will result in a grade reduction. Four missed classes will result in a failing
grade for the course. If circumstances require extended absence, students
may withdraw from the course within the guidelines identified in the
Tardiness
Students are expected to arrive for class on time. A combination of three occasions involving
tardy arrivals or leaving class early will be counted as one class absence.
An
important aspect of this policy is plagiarism. This notion refers to the use of
another’s words or ideas without acknowledgement. It is the equivalent of theft. Some plagiarism is extreme and willful (i.e.,
buying or using the work of another).
Other forms of plagiarism may arise from carelessness or ignorance
(i.e., not using quotation marks or citations).
Plagiarism of any kind is not acceptable and will not be tolerated.
For
more information on plagiarism and how to avoid it visit http://www.sju.edu/libraries/drexel/plagiarism/index.htm.
If you have a documented disability
(learning, physical, psychological) for which you are or may be requesting
reasonable academic adjustments, you are encouraged to contact Services for
Students with Disabilities, 113 Science Center, 610-660-1620/1774 as early as
possible in the semester.
1.
2.
3.
Office
of Multicultural Life. This office seeks to enhance the self-image
of students from culturally underrepresented backgrounds by providing support
and presenting activities and programs that enable these students to become
culturally as well as academically rooted in the
4.
5.
Drexel
library. Visit http://www.sju.edu/libraries/drexel/,
or call 610-660-1900.
6.
7.
Office
of Instructional Technology.
This office is a customer-focused advocate of technologies that facilitate and
enrich the learning, teaching and research experiences of
Weekly
Schedule (subject
to change)
|
DATE |
CONTENT |
READINGS/ASSIGNMENTS |
Week 1
(8/29/06) |
Introduction Course overview
PowerPoint When is a Good Teaching Day a Bad Thing? Mathematics in Public Ma’s questions |
READ:
PREPARE: |
|
Week 2 (9/5/06) |
Before It’s Too Late discussion Microsoft Chairman Challenges Governors TIMSS discussion and student presentation The Nations Report Card discussion and
student presentation Brainstorm causes
for problem with math education Skemp discussion Curriculum Library
Visit Introduction to TIMSS 1999 Video Study |
READ:
PREPARE: |
|
Week 3 (9/12/06) |
Teaching Mathematics in Seven Countries discussion and
student presentations Skemp discussion |
READ:
PREPARE: |
|
Week 4 (9/19/06) |
The Case for Quantitative Literacy discussion MAA list of topics for
quantitative literacy The Learning Gap discussion Revise causes for problem
with math education How We Measure Up discussion Skemp discussion Lessons in Perspective discussion Using tips from Lessons in Perspective to design a
lesson Using Skemp Chapter
2 to design a lesson |
READ:
PREPARE: |
|
Week 5 (9/26/06) |
American and
Japanese classroom videos Revision of lesson
plans The Learning Gap discussion Revise causes for
problem with math education Student-led
discussion of Skemp Chapter 6 Create proofs
without words for theorems concerning the angles of polygons Student-led
discussion of Skemp Chapter 7 Why is dividing by
2/3 equivalent to multiplying by 3/2? Gender differences
discussion |
READ
PREPARE: |
|
Week 6 (10/3/06) |
Presentation of
lesson plans The Learning Gap discussion Japanese Lesson
Study video Gender differences
discussion Gender differences
findings |
READ: PREPARE:
|
|
Week 7 (10/10/06) |
Extra credit book
presentations A Coherent Curriculum discussion Proposed curriculum
changes articles Curriculum
Focal Points overview Principles and Standards overview Skemp discussion |
READ:
PREPARE:
|
|
Fall Break (10/17/06) |
No Class |
Fall Break |
|
Week 8 (10/24/06) |
Cognitive Science and Mathematics Education discussion Polya’s approach to
cognitive science Polya discussion Presentation of
examples |
READ:
PREPARE: |
|
Week 9 (10/31/06) |
New Knowledge about Errors discussion Some Classical Errors discussion Why Johnny Can’t
Add
discussion What was the new
math? Summaries of major components. The Original New Math discussion |
READ:
PREPARE: |
|
Week 10 (11/7/06) |
The history of
mathematics curriculum reform presentations The Math Wars discussion Interactive Mathematics Program What’s All the Fuss About Metacognition discussion |
READ:
PREPARE: |
|
Week 11 (11/14/06) |
Principles and Standards discussion Principles and Standards presentations Principles and Standards video Ten Myths About Math
Education Curriculum Focal Points discussion |
READ:
PREPARE: |
|
Week 12 (11/21/06) |
No Class |
Thanksgiving Break |
|
Week 13 (11/28/06) |
Discussion of
standards-based curricula, selection criteria,
and selection instruments Cognitive Science and Algebra Learning discussion Algebra for Everyone lesson plans |