This java applet provides students with opportunities to visualize the Monty Hall paradox (i.e., the famous “three-door” problem often discussed in introductory statistics courses). By going through the simulation and reading the accompanying materials, students can better understand concepts related to probability, and they can also see the need to gather data in order to test theories about what might happen under particular conditions (especially since the outcome of the Monty Hall problem tends to contradict students’ initial intuitions).
Type of Material:
Interactive Java script, tally of previous results, explanation and history of the Monty Hall problem.
Recommended Uses:
This can be used as a demonstration in the classroom (as part of a lecture) or as classroom activity for students who have access to computers. It can be used in group situations or individually, and could also be used outside of class as part of a lab assignment or as part of a homework assignment.
Technical Requirements:
Web browser and JAVA
Identify Major Learning Goals:
-Understand through simulation the traditional Monty Hall problem
-Understand the difference between the traditional problem and a variant where the host doesn't know which door hides the car
-Distinguish relative frequency from theoretical probability (secondary)
Target Student Population:
Anyone in a high school or college introductory statistics course that includes a segment on probability
Prerequisite Knowledge or Skills:
This applet can be used in a variety of ways, in different places in an introductory statistics curriculum. Thus, prerequisite knowledge may differ depending on how the instructor wants to use this. If used in a unit on probability, students might need a basic understanding of concepts and terms related to probability. For the "explanation" page, familiarity with the concepts of expected value and confidence intervals is recommended. If used as an introductory course activity designed to highlight the need to gather data to test theories, students can easily work through this without much knowledge at all about statistics. Students do need some familiarity with how web browsers work, however.
Content Quality
Rating:
Strengths:
The Java script is quite good. The graphics include actual pictures of goats and a car. More importantly, the script "reacts" to your first choice, explaining what you've done and what your options are. Since most students aren't familiar with the MH problem, this is a big plus.
The second Java script showing the MH variant is not found on most websites, so it's really nice to have it here.
Running tallies of previous users' results reinforce students' notion of relative frequency and help students see empirically the 2/3-1/3 answer.
The "explanation" page discusses the history of the MH problem in a humorous and non-technical (but still correct) way and provides a visual explanation of the famous 2/3-1/3 answer.
In addition to providing students with opportunities to engage in the “Monty Hall problem,” a lot of rich background information is provided to put the problem in proper context and also explain how the problem works. It was a nice touch to include two simulations—one where Monty does know where the prize is and another where he does not know.
Concerns:
There are many other sites out there that contain information on this particular paradox. It might be nice to include links to other sites with even more information for the interested student. Within the “explanation of the problem” page, there is a link to some articles that appear online about the problem, but it does not appear that this link is still active.
The CI discussion on the explanation page is not very strong. The author provides a large chart of 95% CIs for the *total* number of wins in n tries, which might confuse students in traditional courses (where the emphasis is on a proportion rather than a total).
Also, the author provides CIs for the totals for the "current" values of the game (i.e. based on the sample size to date). This is inappropriate, since the sample total is known, and may cause confusion among students.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This item certainly promotes student discovery through simulation. The "lesson" of the MH problem isn't terribly important, but a teacher could use this in part to emphasize relative frequency v. theoretical probability in a fun way.
With a more sophisticated audience, a teacher could assign students to come up with a rigorous probability argument for both versions of the MH problem (i.e. using conditional probability rather than simulation).
This tool can be easily integrated into a course, and it’s easy to use and engaging. Students have opportunities to explore the simulation on their own and then read about it later on.
Concerns:
It’s not quite clear what students should know going into this applet OR what the intended outcome of using the applet should be. The website itself does not offer any assignment, follow-up questions, etc. Teachers will have to create their own assignments and assessments. Some sample ideas provided to instructors might be very helpful.
Although the Monty Hall problem is interesting, it doesn't offer a particularly important statistics lesson.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Highly interactive. Instructions are clear *and* reactive (a big plus). The Java script is more visually appealing than some other MH websites. The running tally of previous results gives the student a sense of participation in some larger process. The applet is very colorful and it’s easy to follow along with the explanations given as to why it’s better to switch doors (when the host knows where the prize is).
Concerns:
If students don’t carefully take the time to read the directions that appear UNDER the three doors before they click different doors, they might not realize how to work through the simulation. The instructor might therefore need to provide separate directions for students or carefully point out what students should be looking at. Perhaps a list of directions that appear above the doors would help (one that explains what students should initially do AND what they should do after a door is revealed by the host). This applet is part of a larger collection of materials, and the links at the bottom of the page (those marked “back,” “home,” “programs,” “documentation,” etc.) almost all lead to pages that have nothing to do with the Monty Hall problem. This might initially confuse individuals who happen upon this website simply by searching for information about the Monty Hall problem.
The overall web design is rather 20th-century (e.g. cheesy background). The typography is a little unclean and contains some small errors (none statistical).
Creative Commons:
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