Computer Tutor for Probabilistic Thinking

Software	Language with good GUI tools, or Java and XHTML for a web-based system
Covers	Programming, object oriented systems design, psychology of learning
Skills Required	Programming, object-oriented design, some interest in how people learn, not afraid of maths
Challenge	Conceptual ??? Technical ??? Programming ????

Brief Description

Idea borrowed from Brian Kiely, formerly of De Montfort University.

Many people can't make sense of statistical or probabilistic arguments that go beyond bookmakers' odds. This is a serious problem in a democratic society where people expect to have their opinions considered on many important issues where they can't have sensible opinions if they can't assess statistical arguments - where certainty isn't available but strong conclusions can often be drawn from statistical evidence. What can you do about this?

The aim of this project is to develop a tutor for teaching simple probability theory and statistics using questions and answers combined with Monte Carlo simulations to help people develop intuitions for what happens in situations that are uncertain but governed by known or guessable probabilies. You will need to devise a way to describe probabilistic situations in a uniform way such that Monte Carlo simulations can be run by the system and their results displayed to the user - these can then be matched to the problem descriptions that the system displays to the user.

An important part of building an effective computer teaching system is having a teaching strategy that fits how people learn. You'll need to think about what activities and ways of providing correction and reinforcement will fit how people learn, and how to put activities into effective sequences.

Variants

You could design a tutor to teach people one or more aspects of probability theory or statistics (how about a Markov Process tutor, for instance), or design a tutor to provide support for a human-taught course, or design a tutor to develop intuitive statistical understanding in people who aren't trying to master the maths.

Activities the tutor could include is mapping scenario descriptions to the equations that describe them, guessing odds from probabilities described in other ways, and simply seeing what probabilities look like.

One way to interest and motivate people playing with a probability tutor would be to get them to bet notional money on their answers or predictions. The tutor can then both give them feedback on whether their bet is rational and compute whether they win or lose according to the true odds.

An applet or website accessible through the web would be an especially valuable resource for learners and teachers.

Extension

A probability or statistics tutor could function effectively just requiring the users to click on radio buttons. But you could teach more if you developed an interface that allowed the users to describe probabilistic situations themselves and see what happens. How?

Cross-Reference

For some kinds of computer tutors, having a way of measuring how well the students are doing is important, but building a complex testing tool might be an elaborate task, especially if you want to take the results seriously for evaluating student performance. I've proposed an Internet Quiz Administration System as a separate project.

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