GRED 667: Topics and Research in Mathematics Education

Summer 2013

Class Place: 301 Satterlee Hall

Instructor: Dr. Sergei Abramovich

Office: 210 Satterlee Hall

Office Hours: by appointment.

Phone: (315) 267-2541 (office);

e-mail: abramovs@potsdam.edu;

http://people.potsdam.edu/abramovs

This course provides an opportunity for pre-service and in-service teachers to examine advanced topics in secondary school mathematics, to learn about methods of making advanced ideas accessible to pre-college students, to review research on current issues related to secondary mathematics, and to develop a paper that addresses current recommendations by the Conference Board of the Mathematical Sciences for the preparation of secondary school mathematics teachers. These include the importance of the development of capstone courses within which fundamentals of secondary school mathematics are explored from an advanced perspective in technology-rich environments allowing for connections between collegiate and pre-college mathematics to be established. Towards this end, topics to be discussed in this course are:

- History of the secondary school mathematics curriculum development in the U.S.;
- Technology-enabled explorations of functions and equations with parameters;
- Trigonometry;
- Transformation of graphs;
- Summation formulas;
- Method of mathematical induction;
- Fibonacci numbers;
- Deductive proof techniques;
- Partition of integers and their reciprocals as hidden mathematics curriculum;
- The method of generating functions;
- Inequalities and their use in spreadsheet modeling;
- Geometric probability.
- Calculus applications to secondary mathematics concepts.

Students will gain experience in designing a set of lessons, exploring mathematical concepts from an applied perspective, using different types of computer software, connecting various concepts, posing exploratory questions about mathematical situations, and developing means for answering such questions.

The course work consists of seven assignments:

Assignment 1: Context, connections, and rigor in high school mathematics curriculum.

Assignment 2: Counting techniques, summation formulas, mathematical induction, and Calculus applications.

Assignment 3: Geometric probability, Pick’s formula, and Definite Integral.

Assignment 4: Fibonacci numbers revisited.

Assignment 5. Inequalities, spreadsheet modeling, and unit fractions.

Assignment 6. Exploring quadratic equations with parameters through the locus approach.

Assignment 7. Hidden Mathematics Curriculum.

Students are expected to:

- work on these assignments either individually or collaboratively (including the instructor),
- communicate with the instructor during class time regarding their progress in completing the assignments,
- present work done to the whole class and discuss it,
- make corrections, alterations, and additions based on the discussions,
- keep notes of all completed assignments, and finally
- develop a follow-up project based on the ideas presented in the assignments.

Electronic course materials (including all seven assignments) have been put on a local server (**abramovsclass** volume of the **Helios Server**, folder GRED 667). Assignments 1-7 are MS Word documents labeled A1.doc, A2.doc, A3.doc, A4.doc, A5.doc, A6.doc, A7.doc, respectively. Some materials for the course have been put on reserve at Crumb Library. These materials are listed in the assignments.

Computer graphics software titled *The**Graphing Calculator 4.0* (required for many of the assignments) is available on laptop computers in Satterlee 301.

The Library at SUNY Potsdam exists to support your learning. The expert assistance of the reference librarians, as well as the collections and subscriptions to electronic resources, are there for your use. You SHOULD take advantage of these resources. How? Start your search for information at the library home page (www.potsdam.edu/library.html). There you can link to online resources, the library catalog (Bearcat) AND “Ask a Librarian – and get help,” a page that describes all the ways you can get assistance from an information specialist in using the many electronic and print resources available to you through the College Libraries.

The final grade for the course is a combination of participation, discussion, and presentation of assignments (20%), technology use (10%), collecting assignments in a portfolio or notebook (30%), and the completion and presentation of the course project (40%). This project should be **prepared as MS Word document with computer-generated pictures and diagrams imbedded into this document**.

Grades will be assigned according to the following scale:

range 100%-94% - 4.0; range 87%-93% - 3.7; range 80%-86% - 3.3;

range 73%-79% - 3.0; range 66%-72% -2.7; range 59%-65% - 2.3;

range 52%-58% - 2.0; below 52% - 0.0.

*It is expected that all work will be the students own otherwise documented. Failure to credit others for direct quotations and ideas will be considered plagiarism and will result in the student receiving a grade of 0.0 for that assignment.*

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Sergei Abramovich's publications.

Alfors, L., et al. (1962). On the mathematics curriculum of the high school. *American Mathematical Monthly*, 69(3), p. 189-193.

Conference Board of the Mathematical Sciences. (2001). *The Mathematical Education of Teachers*. Washington, D.C.: Mathematical Association of America.

A web site for for teachers of mathematics at all grade levels http://mathforum.org/mathtools/sitemap.html