| The Ultimate Textbook |
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| Wednesday, 04 March 2009 04:18 | ||
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Consider a mathematics textbook designed solely for electronic use. What would the ultimate textbook look like?
Arbitrary removal and addition of sections. Rather than having to pick and choose which pages to read or which problems to do, teachers could streamline the student experience by letting them see only the text and problems they need. “Color” tidbits like historical notes could be added by teacher who wants enrichment and removed by the teacher who wants focus. Every problem has an answer. No need for “evens” and “odds” in an electronic format – the teacher should be able to choose when the students are allowed to check their answers. Furthermore, the teacher could allow the answers to be simple (given only “26” without explanation, forcing students to redo work) or complete (giving all the steps) or a mixed format (so some answers are given complete as a help, whereas others are giving as simple or even omitted). These could also be provided in a time-lapse format, where students can check how problems are done only after an assignment is turned in. Mathematical artifacts should have flexibility. In general, any interesting graph of picture in a textbook will have complete problems with them, preventing the students from forming their own mathematical framework. The teacher should be able to present any element of the textbook with as few or as many external elements as possible. For example, one could start a class with: What are we seeing here? What do the axes mean? Gradually this would lead to the students establishing their own problems to solve. If the teacher would rather present the information as a fixed problem to solve, the same graph could look like this in the textbook: The above graph following represents the distance over the ground in a Ferris wheel. How long does it take to complete one revolution? What would the equation of the graph be? Teachers should be able to easily edit the presentation and even be able to add their own questions. (For much more detail on this, I recommend reading Dan Meyer’s post about how digital media in the classroom should be presented.) Interactivity at every example. Some students eventually tire of steps in solutions being meted out slowly (“next we need to cancel the multiplication of 4 by dividing by 4 on each side of the equation”) while others need that level of detail. Students should be able to expand or condense any part of an algebraic solution with a mouse click, even expanding all the way to reminding the student that subtracting a negative number is equivalent to addition or how to add fractions. Furthermore, with an electronic textbook it should be possible to have randomly generated practice. Such practice exists on the Internet but I have yet to see it fully integrated into a textbook. Interactive graphs. Printed books must pick a particular set of axes to depict a graph and stick with them. There is no reason that any graph presented in an electronic textbook can’t be given controls to allow panning and zooming. In some cases integrating full graphing calculator interaction would be worthwhile. 6. Worldwide connectivity. If an electronic textbook is provided off a central place, there is no reason why all the teachers using it can’t be networked. Imagine teaching a new section and being able to pull up every class in the world currently also teaching that section – new possibilities would open for remote collaboration. … I have seen fragments of all six features from different sources, but never all at the same time. I believe electronic textbooks still cling to things only required in the print medium. What would be in your dream textbook?
POSTED ON HOTCHALK.COM
Comments (2)
Re: The Ultimate Textbook written by G Johnson, March 04, 2009
Yes! Don't forget 7: Less expensive than current books!
On one hand, McDougal-Littel has been giving free access to many of their fine textbooks. Yay ML! On the other hand many publishers are using or imitating Pearson CourseSmart. CourseSmart charges about 1/2 the cost of a textbook for 180 days of access. To add to the partial solutions you noted... hotmath.com is one of those services that offer step-by-step reveals of practice exercise solutions. It lacks ability for a teacher to control access, though there is a way to track what problems each of your students has visited. That's a significant step toward understanding student effort. It's hard enough for me as a geeky math teacher to make math presentations in electronic form. To make the full loop, students must be able to write math electronically. Technology for math notation is still emerging, though there are promising developments. Associated with hotmath is an online tutoring service which can handle math notation and boxes/arrows diagramming we like to do by a paint-with-mouse whiteboard. Asciimathml is a free technology I use a lot. It lets teachers and students enter calculator-style expressions like `sqrt(beta-1)` and have that come out in traditional notation. Associated with it is an vector-graphics technology for drawing pictures. My students use this to contribute to forums, blogs, and chats. Wikibooks [url]http://en.wikibooks.org/wiki/Wikibooks:Mathematics_bookshelf]Wikibooks shows promise in establishing a framework in which many teachers could collaboratively create online textbooks. Grin, it would fly if those wanting to contribute and competent to contribute only had the time to contribute. For more grins, go to YouTube.com and enter a math keyword of your choice, say, "Pythagorean". You'll find dozens of talking head videos from teachers. There's quite a mix of pedagogical quality and production quality. Ditto for teachertube.com and other such places. Many years ago, a local University math chair tried using Mathematica to present introductory Calculus. This provided what he called a "living book". Type your expression, see a graph, even an animated 3D graph. Of course, Mathematica could go ahead and symbolically solve many problems. You could make up your own problem, and see what the computer gets as an answer. Since then graphing calculators have taken some of this role. Graphing calculators also avoid some hurdles in learning to use the tool, and remove many of the practical risks of using a general purpose computer for assessment. So, yeah, we've not got all the technological pieces of the Ultimate Textbook integrated to the point that most *students* can use these tools productively, but there's hope. report abuse
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Jason Dyer
holds degrees in Fine Arts Studies and Math and teaches at Pueblo High School in
Arizona. His school mascot is the Warriors and his other blog of residence is 
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Imagine that it is a textbook page on Nazi Germany or something. Starting with the college version, that goes into great depth using many paragraphs the user could click the (+) or (-) to expand or condense the text to reveal/hide parts of the paragraph. By condensing it they would get the sentences that work more as a general overview (such as you would need for middle/high school) which usually is the topic sentence and sometimes the conclusion.
Users would be able to expand/condense per paragraph (such as expanding only when they want to know a little more about something) or they can set the whole page to a level (MS, HS, or Uni) by clicking a link at the top of the page that would then expand/condense all the text to match that level.