Teaching the Runs Test for Randomness

The other day in my statistics class, I was teaching the runs test for randomness.  One of my students keeps on asking for an in-class activity, and it happened that I had an extra half-an-hour of class time to spare.  So, I adapted this famous teaching experiment for use in my own class.

The set-up:  I split the class into 8 groups, with 3-4 students in each group.  Four of the groups were labeled ‘Group A’ and the other four groups were ‘Group B’.  Group A went into the hallway while I explained the assignment to Group B.

Group B was the coin tossing group.  They were asked to flip a coin 200 times and record the sequence of heads and tails that they observed.  Once I made sure that Group B understood the instructions, they went into the hallway while I explained the assignment to Group A.

Group A was the random listing group.  They were asked to write a sequence of 200 heads and tails that they thought was random without actually flipping a coin.  Once I made sure that Group A understand the instructions, both groups rejoined in the classroom and started their experiment.

Now, since neither group knew the instructions that the other group was given, or what we were going to do with the data that was collected, it made for a very interesting experiment in itself.  The students came up with very unique ways of recording the data.  Some groups assigned one recorder and then the other two people in the group alternated flips of the coin.  Other groups had everyone in their group flip the coin 50 times in a row simultaneously and then combined their results at the end.  I was OK with this since it would have been no different if the students would have just followed one another in their coin flips.

Finally, each Group A exchanged papers with a Group B and analyzed the sequence using the runs test for randomness.  What I discovered is that because the students did not know why the data was being collected, they did not organize it very well, so the group that they passed it to had a very hard time figuring out what was going on.  This made for a good side discussion on the importance of organizing data properly while it is being collected.

Soon enough the students came up with a process for analyzing the data, most groups used a yellow highlighter to highlight the heads to make the runs a little easier to count.  Once their runs were counted, they were able to analyze their sequence using the runs test for randomness.  The students worked very well together verifying their calculations for the mean and standard deviation of the number of runs.

As suspected, it did turn out that Group A (the random listing group) ended up NOT generating random sequences and that Group B (the coin tossing group) did end up generating random sequences.  This made for an interesting discussion as well, since of course, Group A insisted that their sequence had to be random given the way that they collected their data.

Finding the Standard Deviation from a Frequency Table

Even after telling my students how to find the Standard Deviation from a Frequency Table using the TI-84 several times in class, there was still some confusion.  So, I have broken down and made this 1-page handout.  Surprisingly, it was my first time making a handout like this.

The Beef Taco Dilemma

This is a problem that I wrote for my statistics class.  The objectives for this problem are as follows:

1.  Compute percentages.
2.  Compute the arithmetic mean.
3.  Critically think about whether or not Joe had enough tacos to meet the ‘average’ demand.

What I found was some students had a hard time computing the percentages and some also had a hard time keeping straight how many beef and how many chicken tacos Joe ordered on each day.

First Day Policies and Activities

Below is a list of rules that I plan to give to my students on the first day of class to try to prevent some of the behaviors that bothered me last semester from occurring again during the upcoming semester.  If the tactics in the handout seem a little extreme, good, I mean them to be.  I want students to realize that certain behaviors have consequences, both for the low achieving students and the high achieving students, both at school and at home.  I know that I will not get through to every student, but if you like my handout, feel free to tell some of the stories in your own classroom.

The_Rules.pdf

As for how I am going to present the rules on the first day of class, I am going to use the grid below.  The students will be given a blank version to fill out while I am giving an overview of the course policies.  I plan to give this to the students before I even pass out the syllabus.  So, the first piece of paper the students will receive from me is a sheet of paper that they have to take notes on.  I hope that this will instill in them the importance I place on taking notes in class, as last semester I had way too many students who did not take notes and then when they did not understand how to do a problem, wanted me to redo the entire examples for them.  By the way, I got the idea for the grid from Dan Meyer’s First Day Wiki.  He has example of one that he uses in a high school geometry class there.

Syllabus_Grid_Version_web.pdf

Another thing that I am going to do on the first day of class is the coin problems that are listed below.  I got this idea from last year’s MichMATYC Fall Conference.  The idea is to give students logic problems to work on in small groups on the first day of class so that they can get a feel for working in groups in a less intimidating setting.  I hope that this activity will help instill in my students the importance that I place on group work and participation in class.  I really believe that students learn the most when they are given the time and opportunity to explain the material to each other during class.  And for your convenience, the answers to the problems are on the second page if you want to use them in your own class.  I actually got my selection of five coin problems from a website of multiple coin puzzles.

Coin_Problem.pdf

For those of you teaching statistics, you may be interested in Sugar Coated Statistics or this blog post from the Sage Statistical Blog on Starting it Out Right.

I hope you enjoy your semester!

Histogram Match-Up Activity

When I got this Histogram Match-Up Activity, I liked the concept, but the instructions weren’t very clear for the students.  I’ve cleaned it up some (again, my modifications), and am posting it here.  This activity is different from Histogram Sort as it covers constructing a histogram verses simply sorting the histograms by ‘shapes’.

Histogram Sorting Using Cooperative Learning

CAUSEWeb really does put out some great activities for teaching Introductory Statistics, such as Histogram Sorting Using Cooperative Learning.  In fact, they have an entire Statistics Activity Webinar Series that they do regularly.  I was told that this particular activity would easily be modified for the college classroom (where we sometimes don’t have as much time).  My modification is below.  The file includes a student instruction sheet, three pages of student ‘cards’ and three pages of solutions for the instructor.  Enjoy, and make sure to check out the  CAUSEWeb Statistics Activity Webinar Series!

NOIR: New Statistics Game

NOIR stands for Nominal, Ordinal, Interval, Ratio, and is a game to help students distinguish between the four different levels of measurement.  I had been working on this game all week, and I finally had time for my students to play it in class on Thursday.  After the game, they filled out a review form for the game.  I have already tweaked the game slightly based on their feedback as the cards were not originally numbered, so it was very hard for the answers to be checked.  The students wanted the definitions on the game board somewhere, but I think that having the definitions there would defeat the purpose of helping them learn the definitions.  I did let students use notes during the game, but after they started to get used to the definitions, I saw less and less flipping through the book and notes.

Each group of four students (two teams of two students each) was given two game boards and were asked to play two rounds of the game before filling out the feedback form.  The entire process took about 30 minutes, although I had to cut some groups off in the middle of the second game because we were running out of time.  Surprisingly (to me at least), the students were actually somewhat angry about that!

If you use this game in your class, I would love to hear your feedback!

This list of links was complied somewhere around 2005.  Ugh.  That seems like a long time ago.  I’m a lot better than this now.