An Online Math Tutor
David Bowen
Teaching in the New Millennium conference
March 9, 2000 at Wayne State University

Link back to FLS web site

[You will be able to follow along with the demonstration, using either a Mac or a PC. If you want to do this, start the computer booting now.]

Circa 1985 - I had some ideas about teaching math, including algebra and units for the physicial sciences, that had worked for students. I also had experience with computers and networking, and started thinking about an automated math tutor that would be universally available.

1993 - Started working on this. Clear that universal computer communication would be a foundation. Stalled, but decided on name - Flexible Learning Systems project (FLS). Start with projects that did not involve academic credit, but at this point also teaching online courses.

1995 - realized that the World Wide Web was the universal computer communication medium, ready to go. Put free web server software on my desktop and started working.

Note: on the web, whenever you fill in a form or click a box, and send in information, there is a customized computer program to handle that data and tell the web server how to reply. Using the web for a tutor therefore involves writing a set of customized programs.

Goals

• Math tutor universally available
• Would adapt itself to each user, learning his/her level and style, adjusting itself
• Clearly would have to store and analyze tracking information about the session
  • We also wanted to use the tracking information for research in cognitive science. Comparing times to answer seemingly comparable questions has been a rich source of information about how we store and process information.
    • "Isa trees"
    • Mentally turning blocks

  Collecting information about users requires an informed consent protocol.

• Tutor should be configured by a script file, not built into the computer programs, so that it could be used by others and adapted to other areas. (Computer programs are a necessary component, but the way they work should be controlled by script files.)
• Should be useful at each stage of its development (seems to require bottom up development)

Structure

• Learning materials - text, graphics, sound
• Problem presentation - configurable
• Model of user
• Executive or control unit

• David Bowen

Graduated:

• Xun Li
• Min Wang
• Mark Puttnam
• Huaguo Xi
• Christine Koss
• Hui Wu

Current:

• Kathy Xu

An open project…

What is the Tutor today?

• This is the tour, feel free to play along. We have some learning materials and some problem presentation.
• http://www.cll.wayne.edu , then link to OnLine Math Tutor (go directly by adding on /olmt)
• Login, confirmation and informed consent
• Learning materials for binary arithmetic and arithmetic with signed whole numbers (integers.)
• Problem presentation for WSU Mathematics Proficiency Exam
• Problems
• Hints
• Explanations
• Response to your answer
• Correct answer
• Explanation
• Your score, overall and broken down into categories

Problem presentation for arithmetic

• Many varieties
• Randomly generated - an inexhaustible supply
• Biggest problem - generating wrong answers - answers that are wrong but plausible

At this point, the math tutor has not been widely publicized. This is because the structure needs improvement before it is ready for prime time. Still, we average one new user per day, 80+ for example during the year 2000.

• About 13% of people don’t want to use the Tutor if this requires tracking them (it does)
• About 81% say it is OK to track their personal progress, but not to use their information in any other way.
• About 64% say we can also use their tracking information for improving the operation of the tutor.
• About 58% also give permission to use their tracking information for research in cognitive science.

Lots of anecdotal information that this is useful, at least for many people. There have been some complaints that the hints and explanations are already too difficult for a few. Adding more basic levels for user choice would not be difficult. Also, some users complain about the lack of features, features that are already covered in other sections. So navigation may be difficult.

Next steps

• Updating information about MPE
• Additional problems for MPE section
• Algebra for random problems
• Solving login problems (AOL, timeouts)
• Reorganization
• Publicity

A real Tutor

• "Following the user into the problem"
• Teaching the algorithm, practicing the algorithm, e.g. for adding two whole numbers
  • Lining up the numbers
  • Starting with units column on right
  • Adding up column by column
  • Carrying tens to next column
• Identifying specific user problems with algorithms, remedying them
• There is some evidence that these small steps are the way the processes are stored in our minds. Students almost universally avoid remedial or developmental courses. An online tutor can avoid triggering feelings of embarrassment. But more to the point, for people who didn’t learn math the first time around, or who have forgotten it, this kind of focused process debugging and repair might be highly efficient.
• Identifying users who probably need to move up or down a level
• Referring for other methods

These tutors are in a development section of the CLL web server. If you put in these URLs, the first time you will be asked for a User Name and Password. (this is not to protect proprietary information, but to make it clear that this is an experimental area.) For this conference, the User Name and the Password are both "March9" (without the quotes). If you want to get back in after today, send an email to me at d.r.bowen@wayne.edu.

• Literacy tutor - project with Adult and Lifelong Learning Research (ALLR) project
  http://www.cll.wayne.edu/clltest/allr
• Either choose "Testing for Old user login" and user1, user2, … user30
  (password the same)
  OR (depending on which we have working!)
• "Testing for New user login" making up your own User Name and Password
  
• Types of questions - "Sentence interpretation" and "Picture - word association"
  We will be adding audio directions and audio in questions
• Cannot randomly generate words, so we randomly pick words from a database. We also pick similar parts of speech from the database, for wrong answers.

Writing and grammar tutor at http://www.cll.wayne.edu/clltest/olgt . Examples for questions on

• punctuation
• parts of speech
• vocabulary
• organization

These examples are only for thought-starters

Next steps - which way to go?

• Analysis of data already collected, publication
• Improving present math tutor by adding more questions, integrating resources (e.g. questions, learning materials), publicizing
• Finishing tutors that are not online yet
• Going to the next level on the math tutor by encoding algorithms, tracing users’ algorithm or error in algorithm, providing specific remediation in that
• To follow up, contact d.r.bowen@wayne.edu