"If some one say: "You divide ten into two parts: multiply the one by itself; it will be equal to the other taken eighty-one times." Computation: You say, ten less thing, multiplied by itself, is a hundred plus a square less twenty things, and this is equal to eighty-one things. Separate the twenty things from a hundred and a square, and add them to eighty-one. It will then be a hundred plus a square, which is equal to a hundred and one roots. Halve the roots; the moiety is fifty and a half. Multiply this by itself, it is two thousand five hundred and fifty and a quarter. Subtract from this one hundred; the remainder is two thousand four hundred and fifty and a quarter. Extract the root from this; it is forty-nine and a half. Subtract this from the moiety of the roots, which is fifty and a half. There remains one, and this is one of the two parts."

~ Muḥammad ibn Mūsā al-Khwārizmī (Source: **Wikipedia**)

The tools for doing algebra have evolved over the years. When Muḥammad ibn Mūsā al-Khwārizmī was working on algebra, he did all of his work in words (see above). The symbols we have invented are a different tool we use for solving algebra problems. The fundamental structure of algebra is therefore something different than either of these tools.

Can we do algebra with a computer (which is today's new tool for doing algebra) and preserve the underlying qualities that are algebra? How does access to a computer, and knowledge of programming, change what we can do with algebra?

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David is a Formative Assessment Specialist for Mathematics at **New Visions for Public Schools** in NYC. He has been teaching since 2002, and has worked in Brooklyn, London, Bangkok, and Vancouver before moving back to the United States. He has his **Masters degree in Educational Technology from UBC**, and is the **co-author of a mathematics textbook**. He has been published in **ISTE's Leading and Learning**, **Educational Technology Solutions**, **The Software Developers Journal**, **The Bangkok Post** and **Edutopia**. He blogs with the **Cooperative Catalyst**, and is the **Assessment group facilitator for Edutopia**. He has also helped organize the first **Edcamp in Canada**, and **TEDxKIDS@BC**.

- Creating a WiiMote interactive white board at my school for under $50.
- 20 reasons not to use a one to one laptop program in your school (and some solutions)
- For whom are Interactive White boards Interactive?
- What is Edcamp?
- Mathematics education blogs
- Forget the future: Here's the textbook I want now
- Eight Videos to Help Teachers Get Started Using Twitter
- Why educators should blog: A helpful flowchart
- There are no aha moments
- Paper use in schools
- 15 things kids can do instead of homework
- Online Geogebra training
- The difference between instrumental and relational understanding
- Why teach math?
- What is The Effect of Technology Training for Teachers on Student Achievement?
- Using Google forms for a "Choose your own adventure" style story
- Ways to use technology in math class
- The Death of the Amateur Mathematician
- We are homeschooling our son
- A Fundamental Flaw in Math Education
- 25 Myths About Homework
- A Restitution Guide to Classroom Management
- Migrating away from Google Reader
- Free tools for math education
- The Role of Immediacy of Feedback in Student Learning

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