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«Mathematics Teaching-Research Journal On-Line A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos ...»

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Mathematics Teaching-Research Journal On-Line

A peer-reviewed scholarly journal

Editors: Anne Rothstein (Lehman College)

Bronislaw Czarnocha (Hostos Community College)

Vrunda Prabhu (Bronx Community College)

City University of New York

Volume 2 Issue 1 Date September 2007

Editorial

With this issue of the Mathematics Teaching-Research Journal, we begin the theme of

democratization of mathematics and science education. Over the next several issues, our

articles, your thoughts and the discussion will create the climate to arrive at a common shared understanding of what it means to have a democratic access to mathematics education. The word democratic includes equal access and existence of a level playing field. Do these two phrases also then include, creating the conditions necessary to address the learning needs of the students?

Section 1 of the current issue addresses different aspects of the process of democratization. In Section 2 we bring mathematics classroom innovations from around the world and in Section 3 we present two reflective pieces upon our teaching work.

Editorial News Our journal is now funded jointly by the National Science Foundation and CUNY's Office of Undergraduate Education.

A new project undertaken by the teaching-research methodology - VISUALIZE- A TRNYC project is aimed at creating a base, where students combine their tactile and visual sense to guide themselves in visualizing the geometry they create out of making paper models of polyhedra. The project is conducted jointly with the Siedlce group of teachers and mathematicians in Poland. The nets for the polyhedra, largely a creation of Waclaw Zawadowski and Krystoff Mostowski, are entertaining students of all ages in mathematics classes and outside.

Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for non-commercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MTRJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 1 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 Acres of Diamonds in New York’s High Stakes Testing Environment;

Empowering Educators via the Internet Steve Watsoni The Jefferson Math Project as a Prototype The Jefferson Math Project (JMAP) is grounded in the New York commencement level high school mathematics curriculum. It is a non-profit initiative of two New York City Teaching Fellows, who both began their teaching careers at Thomas Jefferson High School in Brooklyn in

2003. As we initially worked to develop our own subject matter and teaching expertise in mathematics, we began developing and refining a database and other resources for exploring and analyzing historical assessment practices in the Regents Math A/B curriculum. We soon found that we were looking at high stakes testing through a pragmatic new lens that facilitated the alignment of instruction with state assessment practices, and we also found that other teachers wanted the resources we were developing. We began giving away these resources through teacher training programs at Thomas Jefferson High School, Brooklyn College and City College.

In March 2005, we presented JMAP at a symposium celebrating the fifth anniversary of the New York City Teaching Fellows, after which 2,500 copies of the JMAP 611 CD-ROM were created Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 2 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 by the New York City Department of Education (NYCDOE) and distributed to mathematics teachers throughout the City in September 2005.

JMAP also established a website (www.jmap.org) for mathematics teachers in March 2005, and provides lesson plans and teaching resources on all aspects of the New York Math A/B curriculum, as well as the new curriculum currently being implemented. These materials include over three gigabytes of JMAP books, workbooks, worksheets, solutions, grids, graphs, exams, etc., which are available in MS Word, Adobe pdf, and other electronic formats. JMAP materials are intended for the use of teachers in the classroom, but students and researchers are welcome to use JMAP’s resources as well. Several thousand visitors, mostly from the City and State of New York, regularly download lesson plans and teaching resources from the JMAP website. During Regents week in June 2007, the website averaged over 5,000 visitors each day.





JMAP is listed as a resource for teachers by the Association of Mathematics Teachers of New York State, Math for America, the Drexel Math Forum, the New York Math Exchange, the Home School Math Network, NYLearns, and many other groups interested in mathematics education in New York State. JMAP is not affiliated with any publisher, school, or other corporate entity, though its co-founders are both high school math teachers employed by the NYCDOE and both have personal affiliations with either universities or publishers. As such, Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 3 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 JMAP provides a prototype for a relatively low-cost lesson plan and resource management system with high potential for influencing teaching praxis.

–  –  –

The following diagram provides a high level overview of the major elements of a lesson plan and resource management system based on the JMAP model.

Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 4 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 This vision for a new system involves user friendly, readily available software, which seamlessly

integrates the following features:

 database management of static and dynamic resources;

–  –  –

Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 5 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007

–  –  –

Commercially available, integrated suites of software, such as Microsoft’s Office Suite and Adobe Acrobat/Reader, provide all required functionality in single integrated packages, and can serve as the central core of such a lesson plan and resource management system. A fundamental assumption behind this design specification is that teachers are more likely to invest the time and intellectual effort necessary for systems mastery when the lesson plan and resource management system is free of additional costs and grounded in pre-existing, user-friendly software with which the teacher is already familiar. If such a public domain lesson plan management system is created, curriculum specialists/website coordinators could then focus on the development and dissemination of databases and teaching resources that are consistent with a sponsoring organization’s topical and/or pedagogical agenda. Wikipedia style, refereed websites for the development and dissemination of model lesson plans in editable formats could be used to identify and disseminate best teaching practices.

The incremental costs of such an initiative would be limited to salaries or stipends for the curriculum specialists/website coordinator(s) plus the relatively low costs of maintaining a website. These curriculum specialists/website coordinators could be inside or outside the official bureaucracy of public education. (JMAP is an example of curriculum specialists/website Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 6 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 coordinators who are outside the official bureaucracy.) These databases and resources, once developed, are easily shared with large numbers of teachers (and students), as evidenced by the JMAP statistics. To the extent that the lesson plans and resources thus developed and delivered via Internet are value adding, they will be sought out and used by teachers, thereby constituting a powerful means of communicating and influencing the implemented, as opposed to the stated, curriculum.

Existing Prototypes of Lesson Plan Management Systems and Their Weaknesses Many textbook publishers produce some form of technology-based lesson plan and resource management systems on CD-ROMs, which typically accompany the teacher’s edition of

the textbook. Examples include:

 Prentice Hall’s Resource Pro and Worksheet Builder;

 Saxon’s Test Generator; and  McGraw Hill/Glencoe’s Teacher Works.

The above referenced programs are examples of proprietary programs belonging to “for-profit” publishers. Their contents are typically copyrighted, non-editable, and relatively unfriendly to users who wish to modify or adapt them to fit specific individual and/or classroom needs.

Almost all resources in these programs are presented in difficult or impossible to manipulate Readers are free to copy, display, and distribute this article, as long as the work is attributed to the author(s) and Mathematics Teaching-Research Journal On-Line, it is distributed for noncommercial purposes only, and no alteration or transformation is made in the work. All other uses must be approved by the author(s) or MT-RJoL. MT-RJoL is published jointly by the Bronx Colleges of the City University of New York.

Mathematics Teaching-Research Journal On-Line 7 A peer-reviewed scholarly journal Editors: Anne Rothstein (Lehman College) Bronislaw Czarnocha (Hostos Community College) Vrunda Prabhu (Bronx Community College) City University of New York Volume 2 Issue 1 Date September 2007 formats, presumably and understandably to protect the proprietary interests of the publishers.

Any teacher seeking to adapt or change such fixed-format resources for the benefit of a specific individual or classroom faces intentional technological impediments imposed by the publishers as well as potential copyright infringement issues.

Teachers frequently draw resources for a single lesson from several sources. Proprietary lesson plan management systems are typically not designed to facilitate the development of lesson plans from more than a single source, and are limited to that which is provided by the textbook publisher. This severely restricts teacher creativity in meeting the needs of students.

Although these resource and lesson plan management systems are promoted by textbook publishers as being user friendly, this writer can attest to numerous obstacles encountered while adding over 1500 Regents Math A and Math B questions to the databases, and in formatting and printing hundreds of resources from the enhanced databases. Such obstacles are simply overwhelming to the majority of teachers, thus preventing the realization of the potential of these database management systems. These obstacles are overcome through the JMAP prototype, in which responsibility for systems mastery, database management, and desktop publishing of ready-to-use, high quality teaching resources is concentrated in individuals who are motivated and competent in the associated technologies and academic content areas.



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