5 spread sheets
& Math History
||The What, When, Where, How, Why, and Who of Math Tokens
- They are pictures that can move on a spread sheet as one might move tokens on a board. Besides
being moved, the tokens or pictures may be copied, pasted, deleted, and may be used to enhance a document as well as complete a
computation. The instructions on their use might give you a better idea of what they are.
- Math Tokens are a blend of math's history and its future.
- Tokens predate cunieform writing and were created by
a very math savvy Sumerian / Babylonian culture about 8,000 to 12,000 years ago. Spread sheets are a 20th-century invention, part of our
present world, and a tool very likely to be in our math future in some form or another. Math Token spread sheets are both.
- These reasons are not in any kind of order.
- The power of the manipulative is PROFOUND!
- The power of the spead sheet is PROFOUND -- both as a computation tool and as a word processing and
- Math Tokens blend the power of the spead sheet with the power of the token.
- They are a way to model (teacher uses or demonstrates) when the actual manipulative (student uses or handles concrete
things) would take too much costly time or too much effort logistically to use.
- They are a way for a teacher to model an action when the actual manipulatives are in the students' hands.
- They are an outgrowth of work in using multiple modalities,
languages, in the math classroom.
- When students are working in the concrete, the digital tokens are a way to summaries, debrief, visualize, move to the
- When students are working in the symbolic, the digital tokens are a way to explain a difficult concept without having
to return to a more basic manipulative.
- They are a cost-effective way to pass to the next teaching generation the tools of past generations often left to gather
dust in a museum or in a closet. THEY KEEP MATH HISTORY ALIVE.
- They are the ideal way to conduct an internet course or inservice or webseminar involving manipulatives.
- They are easily stored and retrieved using a web browser.
- They are digital.
- They are easily edited producing and improved version or a new use.
- In a digital classroom, work on a Math Token spread sheet may be
- stored as notes on a spread sheet,
- captured as a image and stored as an image or on a spread sheet,
- left as is with little time needed for cleanup and storage.
- In a digital world, work on a Math Token spread sheet may be
- begun in class then completed for homework,
- shared between documents or applications,
- shared by people for public and private use.
- Often they are the ideal, rather than an alternate, way to introduce, teach, or review a topic.
- They're fun, and clean, and neat.
- They inspire creativity.
- When, Where, How
- On the web, in the classroom, in the privacy of your own home.
- Save and edit a math token spread sheet for yourself (for not-for-profit purposes), but keep the
original copy right, author and source page on the table of contents where you also might add notes. Use the resources
on the left to assit you in your work.
- Who can use them? You. Your students. Your children.