Alex Jacoby
ajacoby@gmail.com
A. Philip Randolph Campus High School
443 West 135th Street
New York, NY 10031
Grade Level: 9  12 Math B (Geometry, Algebra II/Trig)
About the Grant: 
The goal of the project is to help students prepare for the New York state Math B regents exam. Working together, students create a comprehensive review wiki covering
two year's of topics. Each student chooses (or is assigned) one topic and creates a wiki page for it. The content of the page varies depending on the topic, but almost all pages
include at least a general description, sample problems, practice problems, common mistakes to watch out for, and links to other sites where more help can be found. Students are also
encouraged to link to other relevant pages in the wiki when possible. Thus students review one topic deeply while creating a resource that will be used by classmates and others.
How it Works  Give examples of what students do and learn.
Students work individually or in small groups on a wiki page for their assigned topic.
They start by researching resources online and using their class notes and textbook. This helps them relearn a topic they may not have seen for almost two years, gives practice
with online and offline research, and reinforces the importance of good notetaking.
After completing their initial research, students sketch out a rough draft on paper of the content they wish to include in their wiki: in what order do they wish to present their content,
and which examples, formulas, images do they need? The teacher gives feedback to help students understand differences between online content design and the traditional paper reports
that they are accustomed to.
The bulk of the time in the project is spent creating the wiki page. Students type their content using the online wiki editor, along with special tools to create mathematical expressions,
graphs, and other diagrams. Students learn about what a wiki is, as well as the strengths and weaknesses of this style of publishing. Students learn how to properly typeset
complex mathematical expressions using LaTeX, MathType, or OpenOffice.org Math. Depending on the wiki platform (website) chosen, students may also have to learn some basic HTML editing. Elements
of online style are taught, stressing the importance of conciseness and effectively mixing text with images and other media.
Finally, students peer review each others' work and revise their pages based on the feedback given. Each student is assigned two other pages to review, so every student gets feedback
from a variety of perspectives. Students then make final revisions to their pages prior to the final review by the teacher.

How This Grant was Adapted: 
This project enables students to teach each other, and gives the teacher a clear assessment of what topics students are still struggling with. It gives students an opportunity
to explore new modes of publishing and collaboration. It teaches them professional methods of typesetting mathematical formula. Its openended nature allows students to work far
beyond expectations and in unexpected directions. By encouraging students to link to relevant internet resources (rather than copying them), students learn to collaborate on a global
scale, and can more clearly differentiate between their own unique contributions and plagiarism.
Clear expectations are key. You may want to provide a checkoff list for students to
keep track of which page elements they have completed. Make it clear that they should not
be limited by the list, but that it provides a baseline for what they should include.
Make a couple of example wiki pages so that you have experience with the issues that your students will run into. It can also serve as a guide for them as to what their final product
might look like.
Do a test run in the same environment where you will be teaching the class. On my first attempt I did a fair amount of work from home, preparing a wiki with examples for the class,
only to find in class that that particular wiki site did not work correctly from behind the school proxy. Luckily I had experimented with three different sites, so I was able to find
one that worked, but it would have saved me a lot of time if I had done my initial work in the actual school lab environment.
Find students who can help others. This helps more students more quickly, gives the helper students more experience, and saves you time.
Stress that the criteria for inclusion on the wiki is simple: will it help a student pass the Regents exam? If a factoid is unlikely to be relevant, it may be best to leave it out. On
the other hand, keeping space for humor and entertainment is rarely a bad idea.
Required
Computers with internet access
Web browser (at least Firefox 3, IE 7, Safari 3, or Chrome)
Optional
For formulas: MathType, Equation Editor, or OpenOffice.org Math (alternative: use online LaTeX tools)
For diagrams: GeoGebra or Geometer's Sketchpad (alternative: online diagram tools) 
Project URL 
http://aprmathb.pbworks.com 
Objectives 
Objective 1: Mastery of assigned topic (different for each student)
Objective 2: How to create and edit a wiki page
Objective 3: How to type mathematical formula
Objective 4: How to create mathematical diagrams on a computer
Objective 5: How to write for an online audience of peers
Objective 6: What topics need to be reviewed

Websites Used 
Link 1:
http://pbworks.com
Description: Wiki platform used by my class. Not perfect by a long shot, but workable.
Link 2:
http://wikidot.com
Description: Another wiki platform to consider. This was my first choice until I discovered that it did not work correctly from behind the school network. My instructions there can
be found at http://aprmathb.wikidot.com
Link 3:
http://wikispaces.com
Description: Another popular wiki platform to consider.
Link 4:
http://sitmo.com/latex
Description: Online LaTeX equation editor. Eases students into LaTeX.
Link 5:
http://codecogs.com/components/equationeditor/equationeditor.php
Description: Another online LaTeX equation editor. More powerful than the one above, but also more complicated. I recommend students start with Sitmo and move on to CodeCogs
if they find something that cannot be accomplished with Sitmo.
Link 6:
http://dessci.com/en/products/mathtype/trial.asp
Description: Some teachers may prefer having their students use MathType to upload their formula to the wiki.
Link 7:
http://graphsketch.com
Description: Easytouse website for graphing functions.
Link 8:
http://geogebra.org
Description: Geogebra is similar to Geometer's Sketchpad, but free. It allows students to create accurate diagrams, which they can save and upload to their wiki.
Link 9:
http://precalcfinal09.blogspot.com
This blog is open to invited readers only
Description: Kate Nowak's similar project, creating a class blog to help review for a precalculus final exam. At the bottom of the blog (the earliest entries) she also posted some
great instructional videos for how to use equation editors and insert diagrams into the blog.

Standards Addressed: 
Standard 1: Use multiple representations to represent and explain problem situations (e.g., spatial, geometric, verbal, numeric, algebraic, and graphical representations)
Standard 2: Construct various types of reasoning, arguments, justifications and methods of proof for problems
Standard 3: Work in collaboration with others to propose, critique, evaluate, and value alternative approaches to problem solving
Standard 4: Evaluate the relative efficiency of different representations and solution methods of a problem
Standard 5: Recognize and verify, where appropriate, geometric relationships of perpendicularity, parallelism, congruence, and similarity, using algebraic strategies
Standard 6: Provide correct mathematical arguments in response to other students' conjectures, reasoning, and arguments
Standard 7: Evaluate written arguments for validity
Standard 8: Communicate verbally and in writing a correct, complete, coherent, and clear design (outline) and explanation for the steps used in solving a problem
Standard 9: Use mathematical representations to communicate with appropriate accuracy, including numerical tables, formulas, functions, equations, charts, graphs, and diagrams
Standard 10: Students will communicate their mathematical thinking coherently and clearly to peers, teachers, and others.
Standard 11: Students will analyze and evaluate the mathematical thinking and strategies of others.
Standard 12: Students will use the language of mathematics to express mathematical ideas precisely.
Standard 13: Students will recognize and use connections among mathematical ideas.
Standard 14: Students will create and use representations to organize, record, and communicate mathematical ideas.

Lesson Plans: 
All lessons available at: http://aprmathb.pbworks.com


Alex teaches 11th and 12th grade math at A. Philip Randolph Campus High School in Harlem. He started teaching in 2004 as a New York City Teaching Fellow. Before that
he worked around the world as a computer programmer, often doing math tutoring on the side for fun. Alex has taught almost everything from Algebra through AP Calculus and AP
Computer Science. He uses technology extensively in the classroom, from interactive whiteboards, to clickers, to online discussion boards and class wikis and blogs. He
also teaches figure skating when he can find time.
