Using Videogame Poker to Learn Probability
Research Proposal
Submitted by
Adam R. Carberry
May 2, 2005
Table of Contents
Abstract2
Introduction3
Research Question4
Research Goals4
Technology Description5
Research Methods8
Sample8
Design8
Data Collection9
Data Analysis9
Deliverables9
References10
Appendices11
Abstract
Students today are more interested in their video gaming systems than they are about schoolwork. One way to combat this plague is to teach students in a way that seems like a game. In this study the mathematical concept of probability is introduced through this ideology via the popular game of poker. Using such a game addresses the need to make learning more interesting and fun while also making learning more inquiry-based and discovery oriented. Students can learn about permutations, n-factorials and probability all while playing a game and learning strategies based on these concepts (Packel, 1981).
Introduction
If you have 40 students in a class and none of them understand the mathematical concept of probability, what is the probability of randomly selecting a student who cannot do probability problems? The answer in this question when calculated is one, but it shouldn’t be the final answer. Why? The question should be responded to with another question asking why is it that students are having difficulty with probability. Is the concept too difficult? Are teachers teaching it ineffectively? What is the reasoning behind all the difficulty? The answer is three-fold lying in the teaching approach, the inability to consider all possibilities and the lack of interest (Peard, 1996). As it is with many subjects, students are asked to memorize a number of equations. These equations are then in turn used to solve problems, which have no real life bearing for the students. Learning in this sense is also designed in a way that focuses on knowing the equation as opposed to understanding the equation. As a result the operation becomes mechanical and just accepted without thought or reasoning (Garfield & Ahlgren, 1988).
In order for students to learn, understand and retain probability more efficiently, there are three main changes that need to occur:
1)a learner-centered approach to teaching should be employed
2)understanding should be integrated along with content
3)content should be related to real life to spark interest
Through the use of games and technology, these three changes can be achieved resulting in a better understanding of probability(Beasley, 1989; Miller, Charles, Vern, Heeren & Hornsby, 1997). This proposal looks to investigate the specific integration of videogame poker as a new approach to learning probability (Emert & Umbach 1996).
Research Question
- Can the game of poker assist students in learning the concept of probability?
Research Goals
Implementation of videogame poker to improve learning of probability looks to incur three changes: 1) create a learner centered environment for learning probability, 2) teach understanding along with content and 3) spark interest.
To use a learner-centered approach requires that students have the ability to experiment and figure out many concepts on their own. Discovery of “new” ideas gives meaning and a sense of possession to the students. A higher number of students thrive in this environment as compared to rote memorization typically enforced in a teacher-centered atmosphere. Through the use of a game such as poker, students will be intrigued to play the game and learn what they can do in order to perform better.
Along with allowing students the ability to work on an inquiry-based level, students will be taught reasoning behind the theories. This can be accomplished by students formulating their own hypotheses/equations and determining why they work or don’t work. This method will combat the lack of understanding correlated with a student who memorizes an operation or conjecture. It is evident that understandingis not only essential in order to perform a particular task, but understanding leads to a much higher retention rate of concepts (Ramsey, 2002).
For the previous two changes to be sincerely effective, students need to be interested in the subject. Students don’t care about the probability of choosing a red marble over a blue marble. They are however interested in games. Poker is just one game that is fun and interesting to all age levels. The benefit to poker over other games is that it requires a high level of thought, understanding and knowledge of probabilities.
Technology Description
The poker videogame that will be used in classrooms will be a hybrid of what can be bought commercially or used online. The first alteration will be three designed levels of play. The first stage will be an introductory level. In this level, studentswill inquire about possible permutations using playing cards. Users will be presented with tasks that ask how many possible combinations are possible. The program will propose a number of questions to the students making them focus on what is required for one permutation:
1)When filling the first empty slot, how many possibilities do you have? (4)
2)When filling the second empty slot, how many possibilities do you have? (3)
3)When filling the third empty slot, how many possibilities do you have? (2)
4)When filling the final empty slot, how many possibilities do you have? (1)
Students will be taught that they can determine all the possibilities by making a chart but that their technique is tedious and impractical if there are a high number of combinations. The teacher can then ask the students to make some broad generalizations.
Following the first introductory stage of discovering permutations and determining a number of broad generalizations, a second intermediate stage will be presented to give the students problems to solve and to introduce the concept of the n-factorial. These slightly more difficult problems will lead students to discover that in order to determine the desired number of permutations they need to determine the total number of permutations and remove the permutations that are repeats through a mathematical calculation. Students’ previous generalizations for one permutation will be modified into a more systematic way identifying with the concept of n-factorials:
- n ways of picking the first slot
- (n − 1) ways of picking the second slot
- (n − 2) ways of picking the third slot
- 1 way of picking the last slot
Once the concept of permutations and n-factorials has been discovered by the students they are ready for the third and final stage. In the third stage, students are introduced to probability and the actual game of poker. With less instruction than the previous two stages, students are shown that poker is a game of 52-cards where players bet based on a five-card hand. Students are shown the types of hands possible and then asked to determine the likelihood (probability) of obtaining one of those hands in a 52-card deck. Students are asked to produce Table I.
Table I: Poker Probabilities
Hand / # of Ways / Probability / Percentage (%)royal flush / 4 / 0.000002 / 0.0002
straight flush / 36 / 0.000014 / 0.0014
4 of a kind / 624 / 0.000240 / 0.0240
full house / 3,744 / 0.001441 / 0.1441
flush (not a straight) / 5,108 / 0.001965 / 0.1965
straight (not a straight flush or royal flush) / 10,200 / 0.003925 / 0.3925
3 of a kind / 54,912 / 0.021128 / 2.1128
2 pairs / 123,552 / 0.047539 / 4.7539
1 pair / 1,098,240 / 0.422569 / 42.2569
nothing / 1,302,544 / 0.501179 / 50.1179
total / 2,598,960 / 1 / 100
The stage then allows for students to play the game of poker within their class in a manner which allows the teacher to monitor the activity. Each student is presented with a hand of cards that the teacher can see. Before students can bet, they are asked to determine and input the probabilities relating to their particular hand.
Because this approach is discovery based, throughout the game students will be introduced to common terms involved with probabilities. Termsdefined will include the terms permutation, n-factorial (n! = n (n − 1) (n − 2) (n − 3) . . . 1) and probability. After it has been shown that the students have at least a basic understanding of how to calculate probabilities, common notation used with determining the number of combinations will also be relatedin order to allow the students to understand common conventions. Here are three notations used to represent the number of permutations:
1)n C r
2)C (n , r)
3)
where n is the number of different distinct objects that can be chosen and r is how many objects are chosen (C is simply to identify the function as “choosing”). Notation should not be introduced earlier to avoid confusion on the part of the students. Notation will simply be described as a short hand notation of what they have been doing the entire time.
Example questions and screens for the program can be seen in Appendix I.
Research Methods
The following methodology is designed to determine the advantage of using video poker games to teach probability over standard teacher-centered techniques.
Sample
The following study will be conducted in two 3rd or 4th grade mathematics classrooms. Both classes,containing approximately 30 students per class, will be taught by the same teacher. One class will be taught the concept of probability using standardized teaching techniques (control group) while the other class will be taught using videogame poker (test group).
Research Design
The two classes will each be taught probability. Students in the control group will be taught probability through the use of a mathematics textbook. As with standard teacher-centered methods, the students will memorize the equations and definitions incorporated with probability; do examples (in class and at home) and take quizzes and exams on the material.
The students learning probability in the test group will be presented with a number of tasks using the poker videogame as opposed to performing a number of repetitive pencil and paper calculations. Using the poker videogame, students will discover permutations, n-factorials and probability on their own, at their own pace. As their understanding of the concepts grows, they will advance in stages to a point where they are strictly playing the game of poker allowing them to practice their probability calculations. After completion of the videogame stages, students will be tested to determine their knowledge of probability.
Data Collection
The groups willeach be given the same examin order to determine the ability to perform probability related calculations. These grades will be used as quantitative data. Both groups will also be sporadically video-taped to analyze the ways in which the students interact with their teacher as well as with the material. A select number of volunteer students will be interviewed from both groups to gain more insight into their scores and how they felt about learning probability.
Data Analysis
Analysis will be conducted on the three sources of data: test grades, video-taping and interviews. Grades between the control and test groups will be compared to determine which approach was more effective at teaching probability. Video-taping and interviews will be coded to identify good and bad language related to learning probability. The coded videotapes and interviews will be correlated to the exam grades to gain more insight into understanding the test results.
Deliverables
From this study I plan to publish results showing that the use of videogame poker can teach students the mathematical concept of probability better than standard methodologies.
References
Beasley, John D. (1989). The Mathematics of Games.Oxford, England: OxfordUniversity Press.
Emert, J. and Umbach, D. (1996). Inconsistencies of "wild-card" poker. Chance 9(No. 3):17-22.
Garfield, J. and Ahlgren, A. (1988). Difficulties in learning basic concepts in probability and statistics,Journal for Research in Mathematics Education, 19, 44-63.
Miller, Charles D., Vern E. Heeren, and E. John Hornsby, Jr. (1997). Mathematical Ideas.8th ed. Reading, Massachusetts: Addison-Wesley Educational Publishers, Inc.
Packel, Edward W. (1981). The Mathematics of Games and Gambling.Washington, D.C.: Mathematical Association of America.
Peard, R. (1996). Difficulties teaching probability, Teaching Mathematics, 21(1), 20-24.
Ramsey, James B. (2002). The Elements of Statistics with Applications to Economics and the Social Sciences. p. 215-219. New York, NY, USA: Duxbury Press.
Appendix I: Example Problems
Stage 1: Introductory
Example:Students are given 4 cards that all read the same number but are obviously different suits (: hearts, : diamonds, : spades, and : clubs). The students are asked to determine the number of possibilities of arranging the 4 cards in the below boxes (work can be done on paper and imputed into the game).
Table I: Possible permutations for four choices.
1 / / / / / 13 / / / / 2 / / / / / 14 / / / /
3 / / / / / 15 / / / /
4 / / / / / 16 / / / /
5 / / / / / 17 / / / /
6 / / / / / 18 / / / /
7 / / / / / 19 / / / /
8 / / / / / 20 / / / /
9 / / / / / 21 / / / /
10 / / / / / 22 / / / /
11 / / / / / 23 / / / /
12 / / / / / 24 / / / /
Stage 2: Intermediate
Example: Students are given the same four cards as before with the same value but 4 different suites. Students are asked how many different ways they can make a 4 of a kind (Table IIa), a 3 of a kind (Table IIb) and a pair (Table IIc) with the 4 cards given? Once they determine the answers are 1, 4 and 6 respectively, a group discussion asks how they came to their conclusions?
Table II a: 4 of a kind possibilities, = 1
1 / / / / Table II b: 3 of a kind possibilities; = 4
1 / / / 2 / / /
3 / / /
4 / / /
Table II c: pair possibilities, = 6
1 / / 2 / /
3 / /
4 / /
5 / /
6 / /
Stage 3: Advanced (Actual Poker Play)
Figure 1:Complete odds sheet which can be calculated by each student based on a 52-card deck.
Figure 2: Calculated odds based on the individual game being played.
Figure 3: Teacher’s screen allowing for the teacher to analyze how the students are playing.
Figure 4: Final poker table where students can just play.
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