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 🙂

Too much laughter?

I decided last week I wanted to share a small activity that I’ve used successfully in the past that incorporated humour, student imagination, and key ideas for learning around developing students statistical literacy.  The week culminated with a custard class with my Year 12 students (US grade 11?) last period Friday which prompted me to think more widely about my actions in class.

A bit of background… This year we are working on a variety of strategies to improve the culture and achievement in our mid-band classes – classes where the majority of students are only taking maths because their mother told them to or they didn’t have any other option choices, the students that are happy to put in the bare minimum of effort and just “cruise” through the year, the students that ask “is this worth credits Miss?”, our soggy middle kids.  You know the ones?  Anyway, we’re trying to change things around, in these classes using a variety of strategies including purposely developing positive relationships with students, teaching students about growth mindsets and how their brain works when learning and using tasks that have a high emotional connection – whether it is humour, a powerful connection to the real world, or are just gross and quirky.

The task that started things… I’ve heard this one called Pictionary-Dictionary.  Basically, students get given a strip of paper (I used A3 paper cut in half long-ways) and have to fold it into five about even sections.  They are then asked to draw a scene in the first section of paper – it can be of whatever they like as long as its appropriate for a classroom and has a little bit of detail.  The paper is then passed to a second person who writes a description of the scene and folds the original picture over.  The paper is then passed to a third person who has to draw a (second) picture from the description only (remember the original picture is folded back) and then folds over the description.  A fourth person then has to write a (second) description from the (second) picture, and then folds over the picture.  The last person has to draw a (third) picture from the (second) description.  Finally – unfold and watch the laughter start.

I used this task as a way of explaining to my students how important it is to write detailed descriptions of what they see.  I’ll probably resurrect it later in the unit but with given dot plots/box plots in place of the first picture.  I also used it as a good way to start our new unit of work after finishing with an assessment the day before.  Students had an opportunity to use their imagination and creativity in a fun, laughter-filled environment – there was gentle ribbing about people’s drawing, but the positive class culture was great – everyone was sharing, asking who had drawn what, and having fun. Students WILL remember that lesson – yay! successful lesson!

A few of their creations…


and the final picture…Drawings_Page_02

This one looks promising with the detailed description to start with… but it all turns to custard with the second description


and the final picture…


A simple situation should work okay??


All going well until someone brings their imagination into it!


But by Friday… Remember, this is last period Friday.  We started off class well with our Friday Funnies (thanks NCTM and your book of really bad maths jokes!), did some revision work and then moved to the key learning for the lesson – a big idea around the need for a confidence interval.  Students, as often is the case on Friday last period, were chatty, struggling to stay focused, and generally having fun.  I’d moved two students, sent another one outside to recover from her laughing fit, placed one at the front facing the board (I didn’t have any more spare desks) and was still battling to get them quiet to listen to these BIG ideas I was trying to get across.  By the end of the class there were three students I held back to have that conversation about “crossing the line between fun and taking things too far”.  I walked away feeling flat, like I hadn’t taught the students anything and like I’d lost the Friday battle this week.

My actions contributed…  I love this class because we do have fun – we often tease each other, and spend plenty of time laughing together.  I spent a lot of time over the weekend contemplating that Friday class and came to the realization that what happened in class was really my own fault – I had just spent three days winding them up – what did I expect!  It started with the Pictionary-Dictionary activity on Wednesday and continued from there.  Students named all the dogs on their new homework book, we made fun of fat kiwis (the birds, not people) and teased Ben when he thought they were people and not birds.  I threw out lots of those one-liner quips which students enjoy, but which don’t help with calming down the atmosphere and of course there was the student standing with his forehead on the board, whilst still laughing I must add in my defense!).  In this all this hilarity, making my big learning point by loudly announcing “you’re all wrong” really didn’t have the intended effect. [They had all just made a point estimate of the population median from their sample data – we were developing ideas of sampling variation and that all samples will be different, so we can’t just give a point estimate of the population median, we want an interval that we’re pretty sure that it lies between – because they’d all made a point estimate, they were all wrong].  They just had fun telling me “you can’t say that miss”, “we can’t all be wrong”, “that’s not nice miss” etc etc.

The conversation with the class on Tuesday…

Very fine line

I had a really good conversation with the students on Tuesday, the first time I saw them after Friday’s custard lesson.  I showed them the picture above and explained that I thought we both went over that very fine line between having fun AND learning on Friday.  They seemed pretty receptive, and then coped well with a lesson that was a lot of teacher-talk developing big ideas with them.  Just to make it interesting, I did introduce our “Big Ideas Sticks” – more about them in another post!

So… can you have too much laughter in class? How do you know when you’re winding your students up too much and taking them across that very fine line? How do you bring them back? (I’m really lucky with my class as they seemed to have the maturity to be as aware of their actions as I was – but I didn’t try and have that conversation on Friday while they were wound up).

My faculty are the best…

I see it was teacher appreciation week last week over in the United States.  It would have to be one of the occasions that I’ll advocate we take up over here in New Zealand in some form.  In honour of that, I’d like to brag about the awesome people I work with.  My faculty are the best – not only do we spend most of the day laughing together, sharing ideas, consoling over that awful class and helping pick up the pieces for next time, we are always striving to do the very best for our students by improving our pedagogical practice.  They patiently let me discuss my new ideas for the faculty, bring me back to reality when needed, and run with those that are do-able (that’s the next blog post).

Last year, my faculty’s awesomeness was acknowledged by being named finalists in our inaugural Prime Minister’s Education Excellence Awards, the only faculty group finalists across the country.  Our story can be found here.  Disclaimer: we are definitely not the only Maths & Stats department in New Zealand doing great things – I was just lucky enough to be off school on a fellowship, which gave me the time to pour over the research and put the application together.  We do have some very good research published in NZ on teaching and Mathematics, and pedagogy generally – check out our Best Evidence Synthesis series here.  These are a systematic review of international education research that showed improvement in student outcomes.  I especially recommend the Effective Pedagogy in Mathematics summary document – every maths teacher should have a copy!

Finally, writing a blog!

Kia Ora Koutou

I’m finally getting round to starting my blog, something I’ve wanted to do for a few years now.  I’ve had big ideas swimming round in my head of explaining how the New Zealand education system is different from the US, explaining the projects I’m working on with my faculty, reflecting on where I have got to over the last 10 years of teaching etc etc etc.  Instead of procrastinating by writing BIG blog posts in my head, I decided to just share a few of my lessons with you this week to get myself started.

I was lucky enough to attend NCTM in Boston last month – meeting some of the crew from #MTBoS, including @gfletchy@maxmathforum and @TracyZager was awesome and kind of surreal at the same time.  Graham did some gentle nudging for me to “get myself out there more”, but the real inspiration for finally getting round to blogging has to go to Laila Nur and her call to action at ShadowCon.  Here’s where I purposely used humour and an unusual story in two of my lessons this week, and my reflections on them.

I started on our Relationships in Bivariate Data standard with my Year 13 (US Grade 12 I think) Statistics A class this week.  Keep in mind I arrived home from the US Sunday morning, Monday was a public holiday and then Tuesday was back to school.  I was very pleased that I remembered everyone’s name, and all my classes tried distracting me with “how was your holiday Miss?” The Bivariate Data topic started with this quiz:

BVQuizQ1BVQuizQ2 BVQuizQ3

The main point of these questions was to “hook” the students into the topic and generate discussion around both the context and the data.  It worked really well.  The first question generated discussion around seeing a relationship (we hadn’t introduced correlations yet) and causality.  The second question caused the students big issues as firstly they weren’t sure what a “rostrum” is on dolphins, and then they realised that they had no information about the dolphin in the picture! “So you mean Miss, that you just want us to guess?” (with surprise in her voice – they’d obviously forgotten about my quirky sense of humour while I was away).  The third question also generated a good conversation about how different students knew different amounts about dogs, puppies, different weights of dogs etc.  I pretty confident no one knew anything about the relationship between dogs’ heart and body weight.  They all just guessed the body weight from the photo (its a bullmastiff puppy, so quite heavy).

On reflection, I think the quiz was successful in reaching my goals for it and the students were engaged, on topic and animatedly discussing things between themselves.  Not bad for my first lesson back with them still completely jet-lagged.

I used an idea from Michael Shadbolt (Otumoetai College) from his talk I went to last year: Nine weird tips for adding awesomesauce to statistics. Here’s my slides I used with my class:



NOTE: the heart is an animated gif that pulses when projected 🙂  Here’s my story for this slide:

“You need to know Brian’s body weight so you can work out his medication.  Looking at the data, you think that you should be able to make a pretty good prediction of Brian’s body weight if you know how much his heart weighs, so…You prep Brian for surgery…[miming actions as you go] You very carefully take out his beating heart [which is pulsing in your hands as you tell the story] and weigh it…It weighs 48 grams…You put the heart down and pick up your graph…And predict that Brian will in fact weigh about 3.4 kg…You rush to tell the vet how much medication Brian needs but…Unfortunately you had carelessly discarded Brian’s heart in your mad rush and Brian hasn’t pulled through.  He no longer needs any medication.  NOTE – this heart is NOT Brian’s actual heart – it is only here for dramatic effect…”

BVBrian5 BVBrian7BVBrian6

Again, this had the reaction that I wanted – “ewww, gross Miss”, “that’s really morbid Dr D”, “how could you Miss” etc.  Michael’s premise is that students remember things that they have a strong emotional connection to.  This wasn’t a humourous situation, but students WILL remember it.  They won’t mix up their axes!  (Although there could be a good argument here that my story-telling abilities were “humourous” – I am a maths teacher after all – not a drama teacher)

Nga mihi nui