URI/School of Education in partnership with

Rhode Island Teacher Education Renewal (Project RITER)


Course Title:  MTH 420 Re-examining Mathematical Foundations for Teachers


Course Description (short):   Connects ideas covered in upper level math courses to topics taught in secondary school.  Designed for teachers.


Course Description (long): This summer course is designed to address the increasing demands on teachers to engage students in math and increase the percentage of students who graduate high school, ready for college.


In this course, designed for teachers, a connection is made between ideas covered in upper level math courses to topics taught in secondary and middle school.  In this way, teachers develop a deeper understanding of the topics they teach in their classes.


The course is project based.  Participants will look at standard topics in math, develop exercises for middle and high school students based on those topics, and draw the connection between the two. See "What Should Secondary School Mathematics Teachers Know?" by Johnny W. Lott.


Instructor:   Nancy Eaton, PhD, Professor and Chair,
                 Mathematics Department
                 Room 200, Lippitt Hall
                 Kingston, RI 02881
                 Cell:  (401) 218 – 7927


Location:   Pawtucket Administration Building, 286 Main Street, Pawtucket, RI 02861


Meeting Dates and Times:  July 8, 9, 10, 14, 15, 16, 17. (8AM - 2PM each day)


Course Web Page:  http://www.math.uri.edu/~eaton/Mth420Su09Syllabus.htm


Required Text:  Anthony Peressini, Zalman Usiskin, Elena Anne Marchisotto, and Dick Stanley Mathematics for High School Teachers: An Advanced Perspective, Prentice Hall 2003.

Also read The Opportunity Equation and How Do We Learn.


Course Goals: Standards are from the NCATE/NCTM Program Standards (2003) - Programs for Initial Preparation of Mathematics Teachers

    1. Address Standard 4 - Knowledge of Mathematical Connections. Recognize use, and make connections between and among mathematical ideas and in contexts outside mathematics to build mathematical understanding.
    2. Make connections between Standards given in the Grade Span Expectations (GSE's) and Grade Level Expectations (GLE's) to college level understanding of mathematics.
    3. In doing so, review and consider the content areas of Standard 9 - Number and Operation, Standard 10 -Different Perspectives on Algebra, and Standard 13 - Discrete Mathematics. These topics correspond to Chapters 2, 3, 5, 6, and 7 in the text.  
    4. Provide teachers with a deeper understanding of high school math and renew an appreciation of its structures and beauty.

Course Objectives:

    1. Demonstrate mathematical ideas that elicit consideration of a wide variety of mathematical topics and thus create connections across them.
    2. Use the GSE's and GLE's to prompt making connections between grade 7-12 level mathematics and 13-16 college level mathematics.
    3. Find similarities and differences between procedures used for operations involving integers, rational, real, and complex numbers.
    4. Consider algebraic operations and structures as a way to distinguish one number system from another.
    5. Investigate operations in other systems such as polynomials, matrices, and Galois fields to find similarities and contrasts to the number systems.
    6. Investigate the basics of Graph Theory as an example of a discrete mathematical structure.
    7. Learn applications of Graph Theory to a variety of real-world problems and connect this problem solving skill to the GSE's and GLE's
    8. Create a deeper understanding of middle school and high school level mathematics and see how that benefits students.
    9. Apply connections that have been made to the development of activities for students that ask questions that allow discovery of the same connections.

Course Actions:

    1. Presentations will be given to familiarize you with the concept of connections. Pi
    2. Together in groups and for homework, you will explore topics that will serve to review and advance your understanding of number systems, algebraic structures, and discrete mathematics. Due to time constraints of this course, we will limit our purview to these topics.
    3. The mechanism that we will use to explore the connections is described in the following steps. We will call these Mini cycles.
      • You will pick out a standard from the GLE's or GSE's or a topic from middle or high school level math that you feel is relevant to our course objectives and goals. 
      • With my help, you will create a list of specific ideas from our list of topics that possibly related to the standard or topic that you chose and then explore those connections.
      • As you explore, you will find topics that you will have to learn or review and together we will select relevant exercises from the text to work on. I will present general information on the topics that you have identified.
      • Bring those ideas back to a project or lesson that your students can do related to the standard or topic that you chose that illuminates many aspects and allows students to learn a topic from many perspectives. Use Depth of Knowledge Chart as a guide to developing lessons.
      • Advanced perspectives creates multiple viewpoints for your students.
    4. You will create Mini cycles, approximately one per day. For homework rewrite your notes so that you can keep a careful record of your work, Be prepared to present some of these informally in class.
    5. Keep a separate record of the exercises that you work on. For homework, carefully write out the solutions. Prepare to hand in a selection of these exercises at the end of the course and present some of them informally in class.
    6. Keep a journal of reflections that you will allow me to read. Include questions that you have so that we can go over them in class.
    7. Four groups will each formally present a cycle at the end of the course.
    8. In lieu of an exam, each of you will prepare a portfolio of your work, to be handed in on or before the week following our last class session. This portfolio will consist of a thoughtful presentation of each of the Mini cycles that you worked on.


Selection of webpages:

The Prime Number Pages http://primes.utm.edu/

Author’s Web Site for Mathematics for High School Teachers – An advanced Perspective http://mtl.math.uiuc.edu/math-hst/

Quantum Magazine, The Magazine of Math and Science http://www.nsta.org/quantum/

National Library of Virtual Manipulatives http://nlvm.usu.edu/en/nav/vLibrary.html

Pi through the ages http://www.gap-system.org/~history/HistTopics/Pi_through_the_ages.html

Recreational Math http://www.g4g4.com/recmath1.htm

Logic Mazes http://www.logicmazes.com/

An Applet about Pi http://upload.wikimedia.org/wikipedia/commons/2/2a/Pi-unrolled-720.gif

More Applets http://www.math.uri.edu/~bkaskosz/flashmo/

The final grade for the course will be based on the following:

10% - Informal Presentations of at least two exercises.

20% - Daily journal.

10% - One Informal presentation of mini cycle.

15% - One formal presentation of a mini cycle as part of a group.

25% - Portfolio of mini cycles due week after last class.

20% - Selection of 10 exercises that you have carefully written up.

A(92-100) A-(90,91) B+(87,88,89) B(82-86) B-(80,81) C+(77,78,79) C(72-76) C-(70,71) D+(65-69) D(60-64)

Special Considerations:


If you have a documented disability, which may require individual accommodations, please make an appointment with me prior to the class meeting. We will discuss how to meet your needs to ensure your full participation and fair assessment procedures.


Class Period Structure:


Go over questions from exercises that came up since last class.

Informal presentations of cycles from the day before.

I will present a cycle for your entertainment.

Form a new group and identify a standard from the GSE or GLE.

With your group work on a new cycle starting with that standard.

I will present material on the elements of college level mathematics that have arisen during your cycles.

Informal presentations of exercises from this day.

In the evening - carefully write up exercises and solutions from the day.

In the evening - carefully write up cycles.

Throughout the day and evening add questions and observations to your journal.