In my capstone class for future secondary math teachers, I ask my students to come up with ideas for engaging their students with different topics in the secondary mathematics curriculum. In other words, the point of the assignment was not to devise a full-blown lesson plan on this topic. Instead, I asked my students to think about three different ways of getting their students interested in the topic in the first place.
I plan to share some of the best of these ideas on this blog (after asking my students’ permission, of course).
This student submission again comes from my former student Michelle Nguyen. Her topic, from Pre-Algebra: probability and odds.
A2. How could you as a teacher create an activity or project that involves your topic?
As a teacher, I would place 100 red marbles and 25 blue marbles in a bag and have each group of students draw a marble each time from a bag for five times. After drawing a marble, the student would put the marble back and then redraw. After five times, the class would come together and the students would compare how many red marbles to how many blue marbles they have. The students will compare the ratios and guess if there are more red marbles or blue marbles in the bag given. By doing this, the students will see whether there is a big chance of drawing a red or blue marble. After doing the activities, I would ask questions that will scaffold the students into saying that there is a higher probability in picking a red marble than a blue marble because the red marbles are picked more often when compared to the blue marbles that got picked.
D1. What interesting things can you say about the people who contributed to the discovery and/or the development of this topic?
With the popularity of gambling rising in the French society, mathematical methods were needed for computing chances. A popular gambler named De Mere talked to Pascal about questions about chances. Therefore, Pascal talked to his friend Fermat and they began the study of probability. The created the method called classical approach which is the probability fractions we use today. In order to verify the results of the classical approach, Fermat and Pascal used the frequency method. During this method, one would repeat a game a large number of times with the same conditions. Bernoulli wrote a book named Ars Conjectandi in 1973 to prove the classical approach and the frequency method are consistent with another one. Later on Abraham De Moive wrote a book to provide different examples of how the classical methods can be used. As time passed by, probability moved from games of chance to scientific problems. Laplace wrote a book about the theory of probability but he only considered the classical method. After the publication of this book, many mathematicians found that the classical method was unrealistic for general use and they attempted to redefine probability in terms of the frequency method. Later on, Kolmogorov developed the first rigorous approach to probability in 1933. There are still researches going on about probability in the mathematical field of measure theory.
C1. How has this topic appeared in pop culture (movies, TV, current music, video games, etc.)?
In the movie “21” there is math problem that is similar to the popular Monty Hall problem. In the movie, a kid is given the chance to pick one out of three doors with a car in it in order to win. Once a door is chosen, the announcer will open a door without a car. Therefore, the start off is 33% of a car existing and 66% with an empty door. Since a door was open, the chance of switching your choices gives you a higher winning percentage because the one you chose at the beginning will still be 33% while switching will change your chances to 66%. This youtube video is a clip from the movie:
http://www.youtube.com/watch?v=Zr_xWfThjJ0
References:
http://www.math.wichita.edu/history/activities/prob-act.html#prob1
http://staff.ustc.edu.cn/~zwp/teach/Prob-Stat/A%20short%20history%20of%20probability.pdf
http://www.examiner.com/article/21-and-the-monty-hall-problem
Mean Green Math 