Intermath | Rockdale Modeling in Algebra Workshop Syllabus, Spring 2003
InterMath- Algebra

 

Instructor:
        A. Kursat Erbas

Office Address:

        614 Aderhold Hall

        University of Georgia

        Athens, GA 30602

Telephone: (706) 542-4177

 Fax: (706) 542-4551

 e-mail: aerbas@coe.uga.edu

 

Office Hours: Upon request.

 

Important Information:

InterMath Website

http://www.intermath-uga.gatech.edu/

 

How to get into your folder by Microsoft Front Page?

From menu bar select: "File"-->"Open Web"

Web Name: http://www.intermath-uga.gatech.edu/tweb

User Name:im-rockdale2

Password: (given by the instructor)

Select folder “rockdale2” ŕ your folder name

How to get into your folder by InterMath Web-based FTP?

URL: http://www.intermath-uga.gatech.edu/ftp

User Name:im-rockdale2

Password: (given by the instructor)

Select folder “rockdale2” ŕ your folder name

How to get into your folder by WS_FTP?

 

        ProfileName: intermath-tweb

        Hostname/Address: www.intermath-uga.gatech.edu

        Host Type: Automatic Detect

        User ID: ceismctech\im-rockdale2

        Password: (given by the instructor)

        Select folder “rockdale2” ŕ your folder name

Click Here to go to participants list

 

Course Policies:

Attendance: Attendance is absolutely essential to success in this class.  You are expected to attend every class; please notify the instructor if you know you are going to be absent.

 

Spending Time outside of Class: You can not expect to accomplish what you should from this course without spending time with the material outside of class. The usual expectation of 2 hours of study outside of class for every hour in class is a minimum. Please communicate with me as soon as possible if you are having trouble managing time - I want to help you get the most out of this course that you can.

 

This course will concentrate on using various software applications to solve mathematics problems, to organize pedagogical demonstrations, and to set up problem explorations. All materials for the course are maintained by an Internet Web page site and students will create and use web documents in the course.

The emphasis is on exploration of various mathematics contexts to learn mathematics, to pose problems and problem extensions, to solve problems, and to communicate mathematical demonstrations.

The following technologies will be used:

Graphing Calculator 3.0 (from http://www.pacifict.com)
Geometers Sketchpad (from http://www.keypress.com)
Spreadsheets (recommend Microsoft Excel)
Hand Held Calculators such as TI-81, TI-82, or TI-83 (TI: Texas Instruments)

Web Page Browser (recommend Netscape 7.0 or Internet Explorer)
Web Page Authoring Tool (recommend Microsoft FrontPage or Microsoft Word or Netscape 7.0 Composer)
Time on computers -- in the workshop and at home or school

2. GOALS ADDRESSED

Participants will:

  • Expand and strengthen their mathematical knowledge and capabilities, specifically in the domain of algebra by investigating challenging algebra problems
  • Engage in problem solving by identifying patterns, forming conjectures, and developing proofs through the use of technology
  • Use mathematics-specific technologies such as dynamic geometry software, graphing programs, spreadsheets, and the Internet to explore algebra investigations
  • Write and post online solution processes to the investigations using web page development software
  • Develop middle school mathematics instructional activities and strategies that incorporate technology-enhanced mathematical investigations
  • Develop a network of peer educators available for continued support during and following the workshop

3. IMPROVEMENT PRACTICES

Participants will gain knowledge and practice in developing instructional activities and strategies for teaching algebra in the middle school classroom in order to positively affect student achievement. Participants will also improve their own mathematical competencies in the area of algebra.

4. COMPETENCIES

Participants will be able to:

  • Select and use appropriate technological software to explore, analyze, and represent algebra problems
  • Communicate their mathematical thinking by expressing their reasoning, analysis, and extensions of the mathematical concepts associated with an investigation in written, verbal, and visual forms
  • Modify algebraic investigations for appropriate use in the middle school classroom
  • Make connections between InterMath experiences and standards-based reform documents, such as the NCTM standards

5. PERFORMANCE INDICATORS

As a result of this course, participants will demonstrate their ability to:

  • Incorporate technology into the learning and teaching of algebraic concepts
  • Communicate mathematical understanding of a variety of algebraic concepts in the form of an online portfolio of investigation solutions
  • Plan middle school instructional activities based on InterMath experiences

6. COURSE REQUIREMENTS & ASSESSMENT

Participants will be assessed on the content and quality of their online portfolios. Feedback and suggested modifications for a select number of write-ups will be provided throughout the workshop. Assessment will be based on use of representation, analysis, appropriate selection and use of technological tools, creation of extensions, and accuracy of mathematics. In addition to the investigation write-ups, the participants will also create two mathematics lessons that integrate technology and algebra for use in their own classroom. Students will also maintain a reflective journal starting with the initial class meeting.

Electronic Journal: As a part of this course, you are expected to maintain a reflective journal (preferably online). This journal is a log of your experiences within the course. It should include thoughts about new skills and accomplishments that you acquire; critical incidents that occur; and your thoughts and feelings about content (mathematics/algebra investigations) and technology. If you are experiencing difficulty keeping a journal, discuss it with your instructor who can provide you with additional suggestions and assistance.
 

 Electronic Portfolio of Write-ups: Each person will develop a personal Web Page for the course. There will be a set of "Write-up" projects. These are the "homework" for the course. Each Write-up will be prepared as an HTML document (i.e. a Web Page document) and linked to your personal web page.

What is a write-up?

The "write-ups" represent your synthesis and presentation of a mathematics investigation you have done --usually under the direction of one of the assignments. The major point is that it convincingly communicates what you have found to be important from the investigation. A write-up should communicate the essential material you have synthesized from your investigation. The format could be entirely in a word-processing document. After all, an HTML document is basically a word processing document with links. The HTML format, however, can combine narrative, pictures, and program applications in a dynamic document. Write-ups should be posted to your personal Web Page. If you work as a team on a write-up, post the write-up into each team member's Web Page but label collaborative effort. Criteria should include correct mathematics, use of technology, and how well you communicate. "Solution" might be another word for "Write-up."

Electronic Portfolio of Lesson Plans: Participants are required to create two mathematics lessons that integrate technology and algebra for use in their own classroom. The "lessons" are to be your creations of material to incorporate technology into classroom lessons. The material can be individual lessons or a unit of material. Your criteria should be on its usability in your classroom or in other peoples classroom and something you feel good enough about to share with colleagues over the web.

7. COURSE OUTLINE

I. Class 1

A. Introduction to InterMath
B. Introduction to Technology
C. Work through an algebra investigation as a whole class using technology
D. Discuss the components and structure of a write-up (including extensions)

II. Class 2

A. Participants engage in investigations of Variables and Expressions.
B. Participants add write-ups to their online portfolios
C. Participants work on variable and expression investigation, spreadsheet skills, and/or other topic covered in class

III. Classes 3-4

A. Participants engage in the Patterns investigations
B. Participants begin their first web page write-ups to include in their online portfolios
C. Continued technological teaching and support (especially with Excel and the structure of a write-up)

IV. Class 5

A. Introduction of graphing program
B. Class works through an algebra investigation together that uses the graphing program technology and graphing calculators
C. Participants explore investigations using graphing software and graphing calculators
D. Participants add write-ups to their online portfolios

V. Classes 6-7

A. Participants engage investigations of Equalities and Inequalities
B. Participants add write-ups to their online portfolios
C. Revisit and revise a write-up

VI. Class 8

A. Participants engage in investigations of Functions
B. Participants add write-ups to their online portfolios

VII. Class 9

A. Participants begin Linear Function and Linear Inequalities investigations
B. Participants add write-ups to their online portfolios

VIII. Class 10

A. Participants continue Linear Function and Linear Inequalities investigations
B. Introduction of dynamic geometry software
C. Participants add write-ups to their online portfolios

IX. Class 11

A. Participants engage in investigations of Nonlinear functions
B. Discuss and brainstorm ideas about modifying InterMath experience for a middle school mathematics classroom

X. Class 12

A. Participants engage in investigations of Polynomial Functions
B. Participants add write-up to their online portfolios
C. Adapt an InterMath investigation into an instructional activity for middle school students ­ Whole class or small group activity

XI. Class 13

A. Participants engage in investigations focused on Inverses of Functions and Systems of Inequalities in Two Variables
B. Participants add write-ups and middle school lesson plan to their online portfolios

XII. Class 14

A. Each participant creates a technology-enhanced mathematical investigation for their own classroom
B. If the activity was implemented in the classroom, participant will discuss what went well, what was difficult, what can be improved, etc.
C. Each participant will take a mathematics exam

8.  MATHEMATICAL CONTENT EXPLORED THROUGH THE INVESTIGATIONS
 

(Click Here to see a list of selected InterMath investigations clustered for Algebra )

Patterns

  • Model and solve contextualized problems using various representations, such as graphs, tables, and equations
  • Recognize, investigate, analyze, extend, and generalize numeric patterns
  •   Formulate a rule for a pattern
  • Understand the concept of variable
  • Evaluate expressions and solve equations (single and multi-variable)
  • Explore the concept of linear combinations
  • Explore problems associated with converging and diverging sequences and series, including arithmetic, geometric, recursive, infinite, and the Fibonacci sequence
  • Investigate patterns related to Pascal's Triangle
  • Consider patterns and relationships associated with square and triangular numbers

Functions and Equations

  • Represent the concept of function verbally, numerically, symbolically, and graphically
  • Apply algebraic ideas such as the Pythagorean Theorem and trigonometry to geometric problems
  • Understand linear function concepts, such as slope and intercepts
  • Formulate the equation of a line in various forms
  • Study quadratic functions and parabolic graphs
  • Investigate tangent lines and their equations
  • Solve a system of equations
  • Solve problems associated with linear inequalities
  • Generalize the effects of a graph as the coefficients of its equation are modified
  • Find the roots of a function algebraically and graphically
  • Determine the minimum and maximum values of nonlinear functions
  • Explore converging and diverging end behavior of a function
  • Solve equations graphically by considering intersecting functions
  • Solve equations numerically and symbolically
  • Translate verbal expressions into algebraic expressions/sentences and vice versa

Graphing

  • Investigate quadratic functions and properties of parabolas
  • Analyze the slopes of parallel and perpendicular lines
  • Solve for an equation graphically
  • Find the equation of a circle centered at the origin or centered at the coordinate (h,k)
  • Transform a graph by modifying its equation
  • Use and apply the distance formula

(Click Here to see a list of selected InterMath investigations clustered for Algebra )

Rockdale County "Modeling in Algebra" Participants

Cyndee Griswold

Jill Jackson

Laura Thomas

Shirley Crawford

Teresa Johnson