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

 

Course Description

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.

 

Course Rationale

          We have a problem with mathematics education in the United States.  Too many students graduate from high school lacking the mathematical and quantitative skills necessary for success in higher education, the workforce, and daily decision making.  This happens despite national awareness of the problem and years of attempts to correct it.  In this course we consider the extent of the problem, and discuss possible causes and solutions.

          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

  • The Learning Gap, Harold W. Stevenson and James W. Stigler
  • Principles and Standards for School Mathematics, NCTM
  • The Psychology of Learning Mathematics, Richard R. Skemp
  • A packet of required reading materials can be purchased from the Saint Joseph’s University Press.   
  • Other required readings are linked to the course website.  

 

Supplemental Readings

   

Course Requirements

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

                                       

Attendance Policy

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 Saint Joseph’s University graduate catalog.

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.

 

Academic Honesty Policy

          Saint Joseph’s University has adopted and enforces an official academic honesty policy.  Please review this policy in the course catalog at http://www.sju.edu/academics/catalogs/.

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.

 

Accommodations

          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.

 

Student Resources

Writing Center.  Located in Bellarmine 129, this center offers writing tutoring at several locations, including the dorms and the Learning Resource Center.  You can stop in or call 610-660-1341 for an appointment.  You can also drop by the Writing Center without an appointment.  If you do not have a scheduled appointment, tutors will work with you on a first-come, first-served basis.  For more information visit http://www.sju.edu/writing-center. 

 

1.     Learning Resource Center.  Offering tutorial services, study skills workshops, ESL tutoring, etc., in Science Center 302, this center also provides on-line learning resources such as computer assisted learning, study strategies, and the On-Line Writing Lab (OWL).  The latter offers a 24-hour response to students’ paper drafts.  For more information email LRC@sju.edu, call (610) 660-1775/1778, or visit http://www.sju.edu/LEARNING.

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 Saint Joseph’s University.  For more information call Shoshanna Edwards-Alexander at (610) 660-1140, or visit http://www.sju.edu/student_life/multicultural_life/.

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 Saint Joseph’s students and faculty.  Visit http://it.sju.edu/,  or call 610-660-1770. 

 

 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:

  • Classrooms, Teachers, and Gender Differences
  • The Learning Gap Chapters 4 – 6
  • Skemp Chapters 6 and 7

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

Proofs Without Words

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

Gender outline

 

READ

  • Teachers’ Beliefs and Gender Differences
  • The Learning Gap Chapters 7 – 10
  • Skemp Chapters 14, 16, 17, and 18

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

RadioTimes:  Homework

 

READ:

  • Cognitive Science and Mathematics Education
  • Polya Introduction, Parts I and II
  • An Example of Using Polya’s Strategy

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:

  • New Knowledge about Errors (pages 165 – 176)
  • Some Classical Errors
  • Why Johnny Can’t Add Chapters 1 – 3
  • (Optional) Why Johnny Can’t Add Chapters 4 – 11
  • The Original New Math

PREPARE:

 

Week 9

(10/31/06)

New Knowledge about Errors discussion

Some Classical Errors discussion

Common Misconceptions

Why Johnny Can’t Add discussion

What was the new math?  Summaries of major components.

The Original New Math discussion

“New Math” by Tom Lehrer

READ:

PREPARE:

 

Week 10

(11/7/06)

The history of mathematics curriculum reform presentations

The Math Wars discussion

Mathematically Correct

Interactive Mathematics Program

What’s All the Fuss About Metacognition discussion

When Good Teaching Leads to Bad Results

Principles and Standards overview

READ:

  • Cognitive Science and Algebra Learning

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

NCTM Navigations

NCTM Illuminations

Cognitive Science and Algebra Learning discussion

Algebra for Everyone lesson plans