Random random random…

MyLesson

Start of year madness has developed and I’m just a wee bit late with my Week Four post of the 2016 #MTBoS blogging initiative – I’m working on the theory of better late than never…

I found this blog post last year from Bob Lochel (@bobloch) – we’ve now run it successfully with quite a few of our Year 13 classes, but I ran into a slightly different scenario with my awesome MAS302 students last week (MAS302 at Cashmere High is our second tier Statistics course).

In a nutshell, the activity requires students to generate a string of 50 coin flips while the teacher is out of the room (either randomly using the RandInt function on their calculator or making them up) .  They place their results sheet on the whiteboard.  The teacher then comes back in after an allotted five minutes (it’s enough time to make a cup of coffee and catch up on a few things, trust me) and sorts the students’ results sheets into “guts” (as in the students made the results up) or “random” using hints such as how many strings of heads or tails in a row, or whether they alternate a lot at the start etc.  See Bob’s post for a much better and more detailed description!

I really like using this activity right at the start of the year as, not only does it allow a discussion around what “random” looks like,  and how tough it is for us to be random, but it lets your students know that you trust them right from go.  My class did this activity in our third lesson of the year.  I purposefully let the students know that I trusted them to do what they needed to do, and walked out of the door with confidence.

I did set things up a little differently from normal this year after speaking to another teacher.  Students don’t know if they will be generating numbers at random or making them up until I’ve left the room (I just have a big pile of instruction sheets mixed up for them to come and collect one) so I showed everyone how to generate the required random numbers on their calculators IN CASE THEY GOT THAT SHEET.  I left the room with a “make sure you read your instructions carefully”.  When I returned, I did really well finding the “random” sheets, but got all but one of the “guts” sheets wrong – when we’d sorted the sheets into the right groups I gave my class a funny look – all except one group had randomly generated their numbers!  I knew I’d made sure there was about half-half of each sheet (another cunning trick to sway things in my favour) so knew something was up.  We discovered that lots of students in my class aren’t the best at reading written instructions, and figured that because I’d showed them how to use their calculators then they should be doing that…. hmm…. best to know this now I suppose… and yes, I’ve teased them about it every day this week!

We did manage to wrap up with a conversation about how its really hard to be random, and looked at the graphs from our senior student survey of our “randomly” picked numbers between 1 and 10, and between 1 and 100.  Here they are:

random1to10

Some students knew that most people pick 7 when choosing a number between 1 and 10, and interestingly, when you look at the year level, you can see that many more Year 12 students have chosen 7 than Year 13s –  in discussion in class we thought it was likely to be because a lot of Year 12s didn’t know about picking 7, whereas lots of Year 13s did (after conversations like this one in class!).  Everyone in my classes who knew about 7 being picked most often made sure they picked another number. (try here for a short explanation of the 7 thing).

random1to100

Yes, the second clear mode here is at 69… my comment with this one in discussion with classes was: “what would it have looked like in Year 10?”  I’ve colour-coded it here for fun, and it’s just like my classes suspected it would be (boys are in red) – I refused to do this in class.

Random came up again in my MAS302 class this week – we were running an independent group experiment, very well designed (cough, cough) where our treatment was forks or chopsticks and our response variable was the time taken to get 20 M&Ms into your mouth, one at a time, using your utensil.  We were all slightly scared about how long it would take us with chopsticks and decided we wouldn’t put a time limit on things unless we really had to (like if the bell was about to ring…).  In my superb teacher-planning pre class I hadn’t remembered to organise how I would randomly allocate to the two groups.  Luckily I found a box of dice in the draw – I gave everyone a dice and we decided that an even number put them in the fork treatment group and an odd number the chopsticks group.  We then rolled our dice all at once.  We got more forks than chopsticks and there was some great discussion around whether the difference was so big that I should suspect people cheating…  (I got a fork that time, thank goodness, with a time of 23 seconds, quite respectable).  I made this excel demo quickly for the next day to continue the discussion (see below).  If you’re like me, and not the best at chopsticks then my big hint is to make sure there is no requirement in the experimental design that says “utensils must be used in the proper way”.  I’ve got away with that twice now, using the chopsticks to scoop up M&Ms.  It makes for a great discussion in the debrief of the experiment about things we maybe should have considered.

giphy