FP-DanLynch

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Contents

Interactive Textbooks for the Mathematically Curious

By Dan Lynch

Introduction

Currently, there is a surge of interest in making complex subject material accessible to everyone, including very young students. This platform strives for the ideal of an educational medium that is universal, crosses language barriers (e.g. non-verbal content), and is accessible to people of all ages. Many in the world do not have access to resources like universities, which makes it even more critical that those who do have access to such resources use it to help those who do not. Factual content is beginning to be expressed through interactive and immersive media such as real-world gaming. Given the towering amount of information now available, it is important to convey information that is as clear and engaging as possible. Thus, while the platform would be searchable for quick learning, it would also offer more immersive environments for deep educational experiences.

Textbooks.png

Scientific content increasingly relies on the presentation and authoring of complex multimedia diagrams and figures, sometimes interactive, to convey information in a non-textual way. Wikis and user-generated hyperlinked content have both been very successful in the case for text---this is what I aim to do for mathematical diagrams.

Digital textbooks are becoming more and more prevalent with the birth of the tablet and various technologies. Most digital textbooks are not interactive with mathematics, however. This system provides a deeper learning for math by providing interactive diagrams, which can make learning more fun and engaging.

Digitizing the Curriculum

I have developed a system that brings interactive, mathematical learning content to the iPad. This system is novel compared to previous systems because a reader can interact with the figures on the page and explore mathematical concepts.

Sequence.png

Deeper Learning

One of the main questions is whether or not this system encourages deeper learning. Does this system catalyzes the learning process: can students learn concepts more effectively when presented with a digital textbook with interactive, mathematical diagrams compared with traditional paper books? Are students more engaged with a digital textbook?

Open Contribution and Open Standards

A web interface has been created to allow users to publish eBooks using a device with a keyboard. The author can add descriptions which can be searched through when readers are creating collections.

Editmath.png

The format we use for the eBooks are a synthesis of two open standards: HTML and LaTeX. This allows the non-programmer to author eBooks for the iPad, which enables the publishing of content that may have otherwise not been published.

Local Storage

Readers can download content from the Web and store collections onto their device for reading without a network connection.

Transfer.png


Implementation

The entire project consists of numerous open-source, open-standards technologies. The implementation thus far is an iPad application accompanied by a Web interface coded in Ruby on Rails for user-generated content. Content can be queried from the Web, converted into Objective-C objects, and then stored permanently in the iPad’s internal Core Data database, giving the user the feel of a book if there is no network connection available.

The languages supported are HTML and LaTeX. Interactive diagrams themselves are hard-coded on the iPad in Objective-C, however, the links to trigger these applications are accessible with specific syntax used by Web authors. Future versions will include a file format for generating dynamic interactive diagrams.

Full list of technologies used:

  • LaTeX
  • MathJax
  • HTML
  • JavaScript/JSON
  • Objective-C
  • iOS Core Data
  • Ruby on Rails
  • MySQL
  • ASIHTTP
  • TouchJSON

Features

  • user-friendly
  • user-contributed content
  • engaging
  • user collections
  • local storage / core data
  • open-authorship
  • LaTeX and HTML format
  • search and navigation

Domain

Specifically I focus on signal processing. This includes

  • convolutions
  • direc and kronecker delta plots
  • function graphs
  • pole zero plots
  • block diagrams
  • vector plots unit circle

Deliverables

PowerPoint

File:Dan.pdf

Poster

File:DanLynchPoster.zip

Paper

File:DanLynchPaper.pdf

Video

File:DanLynchIPadApp.zip

Jvoytek - Apr 06, 2011 04:22:19 pm

Using MathML for generating interactive diagrams might allow this idea to extend beyond iPad books. A platform for generating html embed-able interactive math diagrams could be very useful.

David Wong - Apr 06, 2011 05:01:05 pm

I think that this is a very cool idea, especially applied to signal processing. I remember the first time I learned convolution, an animation of the process helped solidify the idea of the process. As people have mentioned, it would be good to look extensively into the related work of interactive textbooks and tutorials, especially for domains that have naturally interactive components like a computer science tutorial where you can try typing code directly. Also, there seems to be a wikipedia-like crowd component that can be factored in where the crowd can create the interactive diagrams within the textbook.

Matthew Can - Apr 06, 2011 06:24:37 pm

Nice idea. Like you said during your presentation, it's probably a good idea to focus on a couple kinds of interactive graphs. I'm interested in what kinds of interaction techniques you plan to support. One idea is to use the pinch gesture to change the frequency of a signal. Since the goal of the diagrams is educational, it would be great if you could get a sense of how the interactive diagrams compare to the static ones. I don't think it's reasonable to do a full evaluation with the time you have, but some informal study would be good.

Julian Limon - Apr 06, 2011 07:43:57 pm

I liked how you framed the problem and explained the need for better tools for Math. It is clear that people haven't figured this out yet. I wonder whether you could use some of the techniques of collaborative exploration to provide students with better understanding of the concepts. Some students may have questions or doubts about certain characteristics of the graph and by sharing them with other students they may answer their questions.

Krishna - Apr 06, 2011 08:43:48 pm

Great project ! It was not entirely clear how users can modify and play with equations in your interface, one way would be to design a custom keyboard - not sure you would want to do this. You might want to take a look at this blog: http://www.walkingrandomly.com/?p=2692

Sally Ahn - Apr 06, 2011 09:31:35 pm

I really like the idea of interactive textbooks, and I think your specific problem, math diagrams, would be a great demonstration of how electronic textbooks can enrich the learning experience. One thought I had was whether the interactive diagram had to be presented in a separate view. I think readers may want to refer back to the text while interacting with the diagram. There is some empty space in the interactive diagram view example in your slides; you might want to consider adding a scrollable box there so that the relevant text is shown below the interactive diagram.

Michael Cohen - Apr 07, 2011 12:10:44 am

Sally beat me to it, but I had the same thought: why do I need to leave the page to play with the diagram? There may be a technical limitation here, but in The Future, I hope I can manipulate my e-book diagrams in place! I think LaTeX for input and iPad for output are reasonable choices for a first pass at this (challenging) task, but as much as possible I'd urge you to architect the system such that both formats are as "pluggable" as possible. LaTeX is fairly popular in publishing, but plenty of diagrams are made with the likes of Illustrator and such as well. And, of course, the iPad is king for now, but it has plenty of competition in the e-reader space and publishers will prefer not to limit their interactive content to one platform.

Saung Li - Apr 07, 2011 01:21:10 am

This is a great idea; I know I would have benefited from interactive diagrams when learning math! Since practice problems are so important in learning math, I think it may be worth having interactive problems as well. Interactively showing how to do a problem step-by-step may help people grasp the concepts better and do other similar problems on their own.

Michael Porath - Apr 07, 2011 04:35:53 pm

Something that comes to mind for me is linked visualizations for the same subject. I'm thinking of a Sinus curve and the corresponding circle where you can trace points on the sinus curve and the linked graph would show the corresponding point on the circle, along with the triangle to explore the trigonometric laws.

Michael Hsueh - Apr 08, 2011 01:14:58 am

I think this is a great project. One challenge I sense is using latex for real-time rendering (perhaps I misunderstood and you aren't trying this). Also creating authorship tools that allow flexible, yet easy specification of diagrams. I had the same thought about linked diagrams and of course linked text to diagrams.

Brandon Liu - Apr 09, 2011 10:23:05 am

Do you plan on creating all the interactive graphs yourself? If you use existing ones, how might the design of the iPad affect which ones work well or not?

Siamak Faridani - Apr 11, 2011 04:31:15 am

Here is the ASEE conference that I mentioned in class there are a lot of work around producing multimedia labs for textbooks some of the may give you some inspiration ASEE. This is an annual conference and they have published many interesting articles in ASEE.



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