Interactive Probability Theory Activity

Introduction/Background: Claudia De Grandi

Goal/s: Have a good understanding of what the standard deviation is and what it means to diffuse in space.

Class: PHYS170: Physics for the Life Sciences

Procedure: 

  1. Prior to the activity, students have just seen in class the basics of probability theory, as the definition of standard deviation and the binomial distribution. They were given a handout with instructions given before the day of the activity, and some questions to answer online the day before the activity.
  2. With a class of about 140 students we implemented an ensemble of 1D random walkers by staging them outdoors in a big square. Students generated and recorded ahead of time their own series of random steps (+ 1 and -1) by flipping a quarter several times.
  3. On the day of the activity they arranged themselves on a straight line in the middle of the square, side by side. By marking the time with the sound of a gong, everyone moved simultaneously according to his or her recorded random steps.
  4. At different times during the walk, students were asked to stop and observe their surroundings, reflecting on how they were spread in space (a video of the activity can be watched http://www.youtube.com/watch?v=zsIz9Yh1pQU&feature=youtu.be).
  5. After the outdoor portion concluded, the activity continued inside in the classroom, where students were asked to analyze and answer some questions about the data collected from their random walks. For instance, by looking at the histograms of their position they could extract an estimate of the standard deviation for the various steps and analyze the dependence in time.

Follow-up: They worked together as a group answering some questions on the data extracted from the activity. While answering the post-activity questions in class, students were guided to understand and grasp the correct answer, by the end of the activity most of them gained a better understanding of the standard deviation.

Comments: It is fun and original, the students' feedback was very positive. It connects some theoretical knowledge, as statistics quantities and probabilities, with something concrete, an experiment that students can implement easily all together. The strength of the activity is the visualization part, both by performing the random walk all together and as well by observing the data in class, students are offered a more intuitive way of understanding the concept of diffusion. Being the concept of the standard deviation so important in any scientific discipline, this activity would be useful to reinforce students' understanding of it. 

Please be very organized in order to save time and plan every details carefully, tell the students exactly what they are going to do ahead of time with clear instructions.

For future advise, I would also ask the students to "bin" themselves at the end of the random walk, that means from their final position walk to a starting reference point to sort of build a histogram of their position, a human histogram.

Materials/Resources: handouts and a small sequence of random steps written on a piece of paper that they had to generate previously by flipping a coin.

1d_walkers.pdf245 KB
lc_randomwalka.pdf197 KB
lc_randomwalkb.pdf38 KB