Better questions for statistical thinking

MTBoS blogging initiative, week 3!  This week’s topic is better questions.


Kiri Dillon (@DillonK_Chch) and I have spent some time looking at ways to develop our students statistical insight – that is, how to encourage them to be deeper statistical thinkers.

Briefly what I mean…  Here’s a sample of weekly income by gender.

surf incomesurf income summary

Most of our students have got reasonably good at describing what they SEE in the samples, the median weekly income of these males is about $300 higher than the median weekly income of these females etc.  But what questions or prompts can we give students to encourage them to think beyond just what they are seeing?  Why might we be seeing this big difference in gender? Were we expecting this? What other variables might help explain this?  What else might be going on? …  Which might lead them to exploring things like:

surf income 2

which shows that the hours worked per week is also important.

And the best questions we have found to get the students thinking further are the simple ones…

  • Why?

  • So what?

And then just repeating them to students (you know, like your annoying five year old that just wants to know more and more and more and more…)  It works surprisingly well.


My Favourite* starter


*Favourite = New Zealand spelling!!  Sorry to anyone else reading it, it’ll just have to look wrong to you…

I’ve decided to write about STRIKE-MERE for my post for Week 2 #MTBoS 2016 blogging initiative – my favourite starter that I incorporated into my class routines last year – every Tuesday.

Firstly, a big thanks to Jane Gray who shared this with me 🙂

How to play: Students pick and write down four numbers from 1 – 6, repeats allowed.  I then roll my dice (big and soft with a really annoying bell in it) four times.  Students win if they have the same number as rolled, in the same position as I rolled it.
The prizes are as follows:

  • STRIKE ONE (one number matched) = high five from me (or fist bump upon request)
  • STRIKE TWO (two numbers matched) = one sticker
  • STRIKE THREE (three numbers matched) = one thing from my treat box (stocked with a variety of stationery, lollipops, silly toys from the party section at the cheap shop – sticky-men were very popular last year, no idea why…)
  • STRIKE FOUR (all numbers matched, in the right order) = one day playing games, at a time agreed by myself and the winner (to avoid the run up to high stakes assessment, or when the winner will be away)

For example: if a student picks 4 5 1 4 as their numbers, and I roll 3 5 6 4, then they win Strike 2 (for the 5 in the second position and the 4 in the last position) – make sense?

Why I like this game so much: This is a fast, quick game (takes about five minutes at the start of class).  Students all seem to enjoy it a lot.  You can work out the probabilities and expected number of periods playing games (about once every two years, on average but don’t tell…) if students seem inclined to head down this direction but (and this is the part I love the most) … I noticed last year, in the process of wandering round the class to see who had won, I checked in with every single student – it might have been a quick commiseration with them that they didn’t win, a smile and a high five when they did, a “don’t let sticky-man distract you” comment when they picked him from the treat box, or a very loud full class cheer when a STRIKE FOUR was rolled – I connected with every single student in the first few minutes in class.  And it was easy, natural and in good humour (NZ-spelling again)

Things I do to run STRIKE-MERE smoothly in class:

  • Students need to write their numbers down on paper quickly when they arrive at class (or get their more organised neighbour to write them down for them).  There is a bit of trust going on here – and I let my students know this.
  • Late students to class get to roll the dice (their lateness is acknowledged, but not in a bad way – those things can be dealt with later individually if needed)

That’s it…. and my favourite thing 🙂

First lessons – Year 12 Statistics


The start of the year is super-important in all my classes – it’s the time when I try to set up the culture, climate and expectations that I want to foster all year.

Here’s what I’ve got planned for my Year 12 Statistics class for the first couple of weeks.

Firstly though – a bit of background…

I’ve joined the #MTBoS 2016 blogging initiative.  Let’s see how long I last!  Timing wise – its a bit trickier over here in New Zealand – exploreMTBoS
my first day of classes for the new year isn’t until Tuesday 2 February, so I’ll miss the 31 Jan date for blogging about one of my classes… I’m running a start of year morning with my staff which will be done in time for me to write about.

My faculty has 15 Maths & Stats teachers, including 3 new teachers to the department starting this year: one first year teacher, one second year teacher, one experienced science teacher who hasn’t taught maths or stats since her teacher training.  We also have in the mix another second year teacher, and one returning from maternity leave, alongside a wealth of experience.  I willingly share my resources, ideas and lessons with all my staff – writing this blog is my way of making it easier to record what happens in my classes for me and for them to refer to.

Right – Year 12 Statistics … I have six lessons in the first two weeks where I hope to (1) get to know my students and develop the class culture and (2) to cover some activities on RANDOM (that’ll have to be another blog post – see here for a talk last year with Grant Ritchie)


Intros & Admin – we are focusing on being deliberate with our actions to help foster positive relationships among our class members – and this is a really tough question – you know that you get on well with your students, they like you and get good results in your class, but what is it you ACTUALLY DO to foster this culture?  What do you do that other teachers could try? Not all students know each other in our senior classes, so it’s important that we spend some time introducing ourselves to each other.  I share a little about myself (usually introduce them to my dogs) and ask them to share something about themselves that no one else in the class knows about them.  As students are doing this, I record who is sitting where and get started on learning names as quickly as I can.  I’ll then go through basic course administration etc.

Weekly Warm-ups thanks to Sarah Hagan (@mathequalslove) I am using these for a second year.  My plan for 2016 is Good things Monday, Strikemere Tuesday, Taboo Thursday & Figure it out Friday (or possibly Friday Funnies – yet to be decided…).  I don’t see this class on a Wednesday. I’ll explain these more in another blog (that’s at least two more I’ve committed to already!)

Relationship building fun task – whether I complete the pipe cleaner building challenge in groups (from Boston NCTM and ###’s workshop – use the pipe cleaners to build the tallest tower in 10 minutes, after 5 minutes silent work with a quirky story for why, after another few minutes, one are only with a bizarre reason…) or just make shape pictures (an idea that came from Angela Brett, give groups a pile of shapes – they have sixty seconds to make the best space ship or car or crazy animal or whatever you come up with – the prize… high fives of course!) will depend on how much time I have left.

Day 2

Senior Student Survey – Students will complete our senior student survey (copy here if you want to look/borrow/adapt etc).  This will collect a variety of information that we may or may not use for further stats classes.  I’ll share a link when its completed.  I have managed to include a couple of experiments, alongside standard demographics and perceptions of themselves as maths/stats learners,  and more quirky things such as student ratings on things like their intelligence, how scary they find pictures, how awful some noises are, how old they think people are, what age they perceive as “old” and “really old”.

Perseverance (thanks Annie @mfAnnie for introducing me to Game about Squares) – Students will play this game, and then I will use Annie’s post as my guide to leading a discussion on how the way they tackled the game challenges can be transferred into developing their statistical thinking processes and being successful in our course.
A big shout out here to Nathaniel (@nhighstein) for his blog post on building culture in his classes, with specific reference to Annie’s Game about squares – I’ll share the results of the survey if I do one in the same way Nathaniel has.  This may flow into Day 3 a little depending on how the survey goes.

Day 3

Random – Marshmallows… The lesson plan is here.  It covers three big ideas around “random” – what does random look like?; making connections between statistical distributions and probability distributions; and connecting theoretical probability models with experimental situations.



Day 4 & Day 5

Mean – MAD – SAD activity from Christine Franklin and the GAISE Report work.  Resources from Chris are here and here, and my powerpoint I’ve adapted is here.

The sequence of learning will take students through Levels A, B and C of the GAISE framework from viewing the mean as a “fair share” value and looking at variation from “fair”, through to the formal quantity of mean and variation from the mean using SAD (sum of the absolute deviations).  We plan to introduce the Levels A & B progressions to our younger students, but this year’s Year 12 students will not have met these concepts.  I’m hoping that by going through the background development, they will have a better understanding of standard deviation as that is introduced.

Day 6

Still to be confirmed, but likely to either be a lead into our next topic – Experiments or finishing off work things from Day 1 – 5 that we didn’t quite get to!


One Good Thing


The MTBoS Blogging initiative has begun! with two options to blog about.  Unfortunately, (or fortunately, depending on your perspective!) the timing of the blogging initiative is not quite right here in New Zealand – we’re still in summer holiday mode, just starting to wind up ready for the new school year.  I thought I’d better not pick the “a day in the life” option… so here’s my One Good Thing

Week 1: One Good Thing

Wednesday was “results” day for our senior students, where they received notification of how they did in their 2015 NCEA end of year examinations.  As part of NCEA, students can gain a subject endorsement award by performing extra well across the year in both internal and external assessments.  We had almost 60 students getting Excellence subject endorsement in Maths or Stats last year, and I’ve just spent the last few hours writing them each an individual congratulations postcard.

Excellence subject endorsement postcards

Yes, my hand is sore… yes, I’m sick of writing (the same phrase each time, sorry!), but I do love completing these tasks knowing that there will be 60 teenagers with a smile on their face when they realise that there’s some snail mail just for them.  That’s my good thing!

The other side of a postcard….

Right… off to post the postcards 🙂