Numeracy 32406 – our pilot adventures

23 May 2022 UPDATE: We have tidied up our Starters to use with our Year 10s this year (here). Further info about these is below.

We were fortunate enough to be a pilot school for the new Numeracy standard 32406 in 2021. We are piloting again this year (2022) and I thought sharing what we’re up to might be useful for others.

Useful links

• MOE Numeracy info page
• Curriculum elaborations
• Digital exam preparation for students
• AMA webinar resources

• MOE Supporting co-requisite info page
• 2021 Sample CAA Numeracy
• 2021 Assessment report Numeracy

Our context

Here’s our beautiful new Maths & Stats block that we moved into about a year ago now 🙂.

Cashmere High School – Te iringa o Kahukura We are a large (~2150 students), co-educational, decile 9 state school situated in southern Christchurch. Overall, our students are great and we have awesome staff with a strong relational teaching philosophy. As both a school, and a community, we have had a tough run over the last decade or so but the school is looking superb with our significant earthquake re-build projects now completed.

Our Year 9 learning programme has three teaching periods a week and is based around students mastering curriculum level (CL) 4 and starting CL5. Our Year 10 learning programme is based around students mastering CL5. As a school, we only piloted the Numeracy standards in 2021 (both Numeracy and Literacy are being piloted in 2022). The table shows that our Year 10s have been going pretty well over the last few years.

Our initial thinking

We wanted to assess these co-requisites with our Year 10 students as we think this is what is likely to happen moving forward with the NCEA change programme – having an opportunity for students to have their Numeracy (and Literacy) co-requisite box ticked before starting on their NCEA Level 1 adventures seems a sensible choice.
Our teaching and learning (T&L) programme in Year 10 is aimed at mastering CL5 – the Numeracy standard is assessing at CL4, starting CL5 so our theory was that the Numeracy standard should just fall out of our current programme. Yes, we had to keep reminding our teachers that the Numeracy standard was NOT our T&L programme – its an easy trap to fall into, especially when the published materials use phrases like “Learning Matrix“.
When multiple assessment times are available – we are thinking we will run ONE assessment opportunity for our Year 10 students, in the end of year session (end of term 3?), then use the other sessions throughout the year for senior students who have not passed their Numeracy.
We did enter ALL our Year 10 students, including our Learning Support classes – information from MOE seems to be around only entering students when they are ready but we know our students can surprise us. Our default was to enter all students, and then withdraw those that it would be detrimental to them, for whatever reason, if they weren’t ready to sit.
Note that for the pilot Not Achieve grades were NOT recorded, so entering students who were borderline was low risk; exposing these borderline students is potentially a positive learning experience regardless of outcome because it will build familiarity – not just with the Numeracy Assessment but with NCEA as a whole (because most haven’t experienced it yet).

Important note here…

We have designed (and are sharing) what works for OUR context – what will work in YOUR context might be quite different, especially if your Year 10 students are not YET mastering CL5 by the end of the year. Please keep this in mind – how to get students mastering CL5 by the end of Year 10 is a whole different conversation!

NOTE NOTE – having a really good handle on what each curriculum level looks like is super-important. We spent time as a faculty unpacking this with our curriculum elaborations again last year – don’t just assume because you’ve done it once with your staff a few years ago that they will all remember it! The curriculum elaborations are here.

Preparing our students

Our junior teaching and learning programme has been designed to reflect what we do in senior courses – it is “chunky” with topics often taught and assessed discretely – the Numeracy assessment covers all curriculum strands. Therefore we needed to keep reviewing other strands while adding new content to students’ ketes.

Short starter tasks were our strategy – we used some of our Accord day time to source and create them. The intent was that each set of starter questions would be skills-based and aim to have some questions at CL4 plus some questions that stretched students that needed it (or were more open-ended to allow for this). The questions should take about 5-10 minutes at the start of class. Starters for each day were based on the same strand, and teachers were encouraged to cycle through the sets but not doing the strand that was the main teaching content of the day.

This is an example of the notes of what starters I’d used when – this snip is from when our main topic was STATISTICS so I wasn’t using any Statistics starters in class.

This was our faculty’s first attempt at this sort of thing, and there were some good starters and some that missed the mark – either because they were the wrong curriculum level (too low OR too high), too long, nothing for extending out top students, confusing, tricky to do with a projected set of questions etc etc etc! We sourced our starters from a wide variety of places, and no – we weren’t any good at capturing where they came from sorry. As we develop things that can be shared without copyright things being an issue, we will. Watch this space…

23 May 2022 UPDATE: We have tidied up our Starters to use with our Year 10s this year (here). We have made a checklist for teachers to keep track of what they have used with their classes, how things went, and if handouts are needed etc. Please email me if you find any MAJOR issues! (we haven’t tested all of this year’s updates yet).

We spent all the class time from the start of Term 4 (about 6 or 7 periods) preparing with students preparing for the assessment – a strand per day, with some strands running across multiple days. I set up google docs with the content of the Numeracy standard, like this one. Students were assigned these docs and could work through them at their own pace, ticking things off the list when they had them sorted. We used lots of online resources,
our 2021 set is here if you want a look. (yes, we need to thank ManvsMaths for all his wonderful resources which are widely utilised in these docs! – I think I’ve updated all the links so they work, but just email if not.)

The assessment logistics

Keep in mind that we are a LARGE school, with 493 students entered this digital exam. Like the MCAT – we were given a timeframe where we had to do the assessment (a week), but all our students had to sit it at the same time.

PREPARATION – before the assessment

• Students needed to log onto the NZQA website, and practiced/seen how to get onto the digital platform
• Students needed to check that their device was compatible with the digital platform
• We made sure as many students as possible had their own calculators!
• We needed to train staff up on using the digital platform
• We needed to enter students into rooms digitally so the supervisors could access these students
• Sort our SAC students for reader/writers etc – because this was a computer-based assessment, we didn’t need writer/computer SACs, only readers (who worked from the paper copy)
• Plan the logistics of the actual assessment! (this was BIG – those practical things like rooming and staffing and booking laptops and talking to our IT guys…)
• We contacted home and made sure parents were aware the assessment was comping up, and were able to support their tamariki in bringing a fully charged laptop and/or their laptop charger to school

THE ASSESSMENT – on the day

• We ran the assessment Period 4 & Period 5 Thursday afternoon, giving us a slot from 1.15 to 3.10 – remember the assessment is aimed so most students get through it in an hour but time shouldn’t be an issue for them.
• Students came out of their normal timetabled classes to do this Numeracy assessment instead – staff of those classes were used to supervise the exam (the non-digital supervisor)
• By giving ourselves a wide time buffer it meant we could reassure students who were struggling to get onto the platform, who had computer issues, who got thrown off the platform, and as staff we knew that if we took a few minutes getting these issues sorted it was fine.
• Students were all asked to bring a non-computer something to do after they had finished, most students had.
• We had 19 rooms of students, with two supervisors per room (a requirement of the digital exam, we tried three teachers between two rooms – this wasn’t really enough in some spaces, fine in others – it just depended where the issues popped up!)
• Four floating staff to sort issues/loan laptops
• There were physical papers available – these were used to solve some technology issues and for our SAC students

Reflections in terms of the actual running of the assessment…

• Overall the digital platform seemed to handle the traffic, and our school network coped well.
• We need to give more details to our exam supervisors (actively roving, lurking BEHIND the students so they can see screens etc), and emphasise that this is AN EXTERNAL ASSESSMENT so should be supervised with the same vigilance as our end of year exams.
• Morning would be better for our students rather than the afternoon! We’re working on that for this year.
• We need to encourage students to turn off screen pop-ups during the assessment – if they click anywhere other than the digital platform, including closing these notifications, they get thrown off the platform and staff need to let them back in.
• The cost to the school in terms of staffing hours was significant

For this year

This year, we’re looking at doing things in a fairly similar way. We will review/re-write/tidy up our skills-based starters (yay, done). We would like to craft some starters nearer the end of each set that are more contextual, like students saw in the actual assessment (we’re working on these and will share once completed). We will review our preparation docs (the ones we used for in class revision just before the assessment) to ensure they have some contextual questions in there.

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An exciting opportunity –> Draft NCEA L3 subject list

When I saw the proposed NCEA subject list changes for Mathematics & Statistics that came out at the end of last term (info here) I was both scared and excited when I saw that a third subject had been proposed at Level 3; scared because in its current form I thought this proposed third subject just looked like “old-school maths”- the maths standards that Calculus didn’t want potentially with some token Statistics standards thrown in to keep us Statisticians happy, and would be pitched at the students who couldn’t manage Calculus. I was excited though as it showed that there was space for a third Mathematics & Statistics subject at Level 3.

I spent most of my holidays reading, thinking, and picking my good friend and Stats-heroine Anna’s (@annafergussonnz) brain, about what this potential third subject could look like. Statistics is a gateway to Data Science and the workshops Anna’s run recently give us a glimpse through this gate.  If you’ve been fortunate enough to have attended some of these, then you will also know that she very generously provides tools to adapt her wonderful ideas for use with our students in our current Statistics classrooms (see her Statistics fun times post for some cool inspiration).

I’m running a session with my faculty today to put together our feedback for the proposed NCEA subject list changes and thought I’d share with you my powerpoint. Don’t panic, my faculty know my Statistical biases well, and know I will be trying to convert them to the Data Science side of the story. (Wed update – they’re converted to the possibilities of DS 🙂 )

Here’s my powerpoint for you too (in editable form), with links and notes included where I could to give you a flavour of what I am planning on talking through with my faculty. My takeaways and thinking are near the end of the powerpoint, but here’s a few slides to give you a taster: 

Use it however you can to start/continue the debate about what this third subject at Level 3 could look like in a brave new world. Direct from MoE in their latest material for our next Accord day “I know at times change is frightening. I know it’s looking at something and thinking, I’ve done this like this for 10 years, or however long. I know my way around it, I’m happy and safe with it. But we need to have change. Change, in terms of looking at all the parameters that have been set up, and the developments that need to happen, is something that’s vital. Something we should be embracing and having a bit of fun with.” (Jane Dewar SEG English)

We can do this right by our ākonga if we advocate together for this exciting new opportunity.

Ngā mihi nunui
Michelle

Level 3 Inference → getting ready for the online adventure (if we need it!)

I’ve just finished my planning for the introduction to Bootstrapping confidence intervals. Just google docs and slides sorry, nothing as flash as what Liam put together with our L2 Inference site. Feel free to use as you like.

I haven’t done teacher notes for each of the activities, but I have uploaded our Sequence of Learning experiences –> although it doesn’t match this set of lessons exactly, it does hopefully give enough details for you to follow the gist of things.

I’ve included my awful videos – very cringee, and quickly done – does anyone else manage to watch their own videos without feeling really silly? NOTE: a little of the things in here will be specific to our context at Cashmere – just ignore/adapt as needed. NOTE-NOTE: some of our Year 13s haven’t seen any multivariate data analysis since they were Year 10s, hence the need to go back and develop WHY we need confidence intervals.

Here’s my planning document, and hopefully all the links from there take you to the right place :). The folder with everything is here (for self-service to resolve link-issues… there’s lots of links!)
Let me know if there are any issues….

Topic	Teaching Resources
1 Introduction to the topic → sample to population inferences → plan for online world	→ Powerpoint to work through live → PDF version to share with students → Video talking through ppt if students miss live lesson
2 A brief overview of sampling  → Why sample → Features of a good sample	Short Powerpoint  →PDF version to share with students →Video explanation of sampling methods (less than 5 mins, linked in ppt)
3 Repeated sampling to motivate the need for a confidence interval → Doozers used to answer “What is the mean height of Doozers in Fraggle Rock?” → Sampling error & sampling variation → Leading to the need for an interval for population mean	→ Powerpoint to work through live → Doc to assign to students → Sheet to collect repeated sample means → PDF version to share with students → Video (part 1, part 2) to share with students who miss live lesson
4 Introduction to bootstrapping for confidence interval → new analysis tool  → NOTE: this is a BIG lesson (as you can tell from the 5 part video!)	→ Dizzy Doozer Spinner → Anna’s magic sampler → Powerpoint to work through live → Sheet to assign to students → Sheet to collect re-sample means → PDF version to share with students → Video (part 1, part 2, part 3, part 4, part 5) to share with students who miss live lesson
5 Comparison situations → Confidence interval interpretation → Making the call → Impact on question format → NOTE: this is a BIG lesson (as you can tell from the 5 part video!)	→ Powerpoint (part 1, part 2, part 3, part 4) to work through live → PDF version (part 1, part 2, part 3, part 4) to share with students → My call is … student task (assign to students) → Video (part 1, part 2, part 3, part 4, part 5) to share with students who miss live lesson
6 Putting it all together → Investigative question + hypothesis → Analysis graphs & stats (no comments) → Bootstrap distribution → Confidence interval interpretation → Making the call	Yet to be constructed! I’ll update when I have this together…

Level 2 Inference –> the online adventure!

Liam Smyth and I have put together some resources to help our teachers teach the introduction to Level 2 Inference, specifically using the famous Kiwis! data set to develop the ideas of informal confidence intervals, data-card free. Liam has made this beautiful google site with all our teaching resources up there, including links to slides to work through with your students, teacher notes to support and copies of the documents we are using with our students.

Go check it out if you’re starting Level 2 Inference soon.

Workshop resources :)

Auckland Statistics Teachers’ Day 2022

December 2022, Auckland, Michelle Dalrymple, Pip Arnold, Jess Williams

Sample to population inference for Level 2: Making claims
Powerpoint is here.

NZAMT 2022

October 2022, New Plymouth, Michelle Dalrymple

Keynote: Building classroom relationships… don’t leave them to chance.
Abstract: Being a mathematics and statistics teacher is the best job in the world!    A successful teacher is one whose students are mathematically and statistically literate, where fear or anxiety around mathematics doesn’t prevent them from doing the things they dream of doing.  Whanaungatanga, teaching-through-relationships, is crucial if students are to be successful and enjoy mathematics and statistics.  Michelle will share some of her teaching philosophy, how she delivers this in her classroom and ideas for staying inspired and energised as a teacher. 
Resources: Powerpoint from the keynote is here, my notes are here (pretty much a script as yes, I was nervous and didn’t want to fluff it up!). The recording of the keynote is here.

Workshop 1: An introduction to bootstrapping and Level 3 Inferences
Abstract: This workshop will present key teaching activities in Level 3 Statistics focused on formalising students’ sample-to-population understanding (AS 91582 Use statistical methods to make a formal inference). Bootstrapping – the formal analysis tool students use to “make the call” will be introduced with hands-on activities and moving to visual inference tools. Other major aspects of the teaching progression leading to formal inferences will also be covered, and may include describing sample distributions and introducing students’ to research.
Resources: All workshop resources are available here.

Workshop 2:An introduction to randomisations and Level 3 Experiments
Abstract: This workshop will present key teaching activities in Level 3 Statistics focused on formalising students’ causal inferences understanding (AS 91583 Conduct an experiment to investigate a situation using experimental design principles). Randomisation – the formal analysis tool students use to make a causal inference will be introduced with hands-on activities and moving to visual inference tools. Other major aspects of the teaching progression will also be covered, and will include experimental design aspects and introducing students’ to research.
Resources: All workshop resources are available here.

AMA HOD day 2022

Friday 1 July, Michelle Dalrymple

Numeracy session – The overview doc is here and all slides are in this folder

Workshop: We have the best job in the world!
Abstract: Michelle is proud of her awesome faculty and is excited to be able to share some strategies and approaches she has used to get to where they are today. A wide variety of topics will be covered including building faculty culture of high expectations and reflective practice, developing faculty systems and working with strengths of staff. This workshop will give you an opportunity to think about your next steps and how you might tackle them in your leadership role.
Resources: Workshop powerpoint is available here.

CMA bite size workshop 2022

Tuesday 12 April, Michelle Dalrymple & Amy Hooper

Numeracy Pilot session – slides here

Auckland Statistics Teachers’ Day 2020

Monday 30 November 2020, Michelle Dalrymple

Keynote: 10 teaching activities: whanaungatanga – teaching through relationships
Abstract:

Email from Anna back in August:
We would very much like to invite you to be this year’s (currently face-to-face) Statistics Teachers’ Day on November 30th, as our inaugural classroom-active statistics keynote speaker!!! 
At the end of the day, instead of workshop four, we are going to bring everyone back to hear from an expert classroom teacher (you!) who will share practical ideas and solid inspiration for teaching statistics.
We are hoping you will say yes! Tell me you’ll say yes and then we can talk more about details 🙂

Michelle – immediately freaks out, feels honoured to be asked, humbled, scared and her imposter-syndrome bells start ringing big-time… then reads the email more carefully…
… clicks that she’s been given that awesome (cough cough) last session of the day so freaks out some more, reads the last line of the email and realises that Anna’s done a beautiful job of making sure it would be really hard to say no!
So here we are at the end of November and almost the end of one of the weirdest years of my teaching career, with a keynote that is aiming to be more like an interactive workshop within the confines of a giant lecture theatre!

I have 10 statistics-themed activities I use with my classes to share with you – both big and small, both new and classics. We will reflect on how these activities support whanaungatanga, strengthen relationships within the classroom, support curriculum learning and high expectations, and are often fun and make me laugh. I hope to spark your thinking about your favourite classroom activities, why you like them and what essential elements they support in your classrooms.  Please make sure you have old-fashioned paper and a pen (as in real paper and a writing instrument of your choice, not a laptop).
Resources: Powerpoint used in the keynote is available here. I have tried to add in details where needed – just email if I’ve missed something.

Workshop: 1D Trialling digital assessments for Level 3 probability distributions
Abstract: NZQA has been working with teachers to develop and trial digital materials to assess students for this externally assessed standard. We’ve been exploring what assessment of probability distribution modelling ideas could look like, facilitated by technology and new digital tools. This workshop will provide you to have a look and try the activities, followed by a summary of the trial.
Resources: Powerpoint used in the workshop is available here.
NOTE: If you want to look at the activities, and/or use them for teaching and learning in 2021, then please
email Neil Marshall: neil.marshall@nzqa.govt.nz

CMA Teachers’ Day 2020

Thursday 12 November 2020, Michelle Dalrymple

Workshop 1: An introduction to bootstrapping and Level 3 Inferences
Abstract: This workshop will present key teaching activities in Level 3 Statistics focused on formalising students’ sample-to-population understanding (AS 91582 Use statistical methods to make a formal inference). Bootstrapping – the formal analysis tool students use to “make the call” will be introduced with hands-on activities and moving to visual inference tools. Other major aspects of the teaching progression leading to formal inferences will also be covered, and may include describing sample distributions and introducing students’ to research.
Resources: All workshop resources are available here.

Workshop 2:An introduction to randomisations and Level 3 Experiments
Abstract: This workshop will present key teaching activities in Level 3 Statistics focused on formalising students’ causal inferences understanding (AS 91583 Conduct an experiment to investigate a situation using experimental design principles). Randomisation – the formal analysis tool students use to make a causal inference will be introduced with hands-on activities and moving to visual inference tools. Other major aspects of the teaching progression will also be covered, and will include experimental design aspects and introducing students’ to research.
Resources: All workshop resources are available here.

AMA Saturday morning Term 3 2020

Saturday 12 September 2020, Michelle Dalrymple

Keynote: Setting up and maintaining a successful classroom
Abstract: There is nothing better than a classroom full of enthusiastic Maths & Stats students; enjoying learning, contributing positively and making our job as teachers’ awesome. This session will cover some of the aspects and practices that Michelle values and uses in establishing and maintaining a positive learning culture with her classes. Her goal with all her classes is for students to be both successful academically and enjoy coming to Maths & Stats. The session will encourage all teachers to reflect on their established practices and search for improvements
Resources: My workshop powerpoint is here, and here’s some extra notes with links and answers to a few questions. The google sheet I used to capture your marshmallow times is here (in case you want to adapt this for your use) and we did get a few horses! Thank you :). The link to the recording of the session is here (thanks AMA)

Auckland Statistics Teachers’ Day 2019

Friday 29 November 2019, Michelle Dalrymple

Workshop: Developing statistical thinking in our Statistics scholarship students
Abstract: Statistical and critical thinking are crucial for developing a deeper understanding of the concepts that encompass our Statistics curriculum. Michelle and Robin will share some activities that support and challenge students. Their aim is for students to be successful in scholarship, as well as taking these concepts with them in their future. (Please note that this workshop is a repeat of the workshop I ran at Otago Mathematics Teachers’ day.)
Resources: My workshop powerpoint is here, with lots of weblinks included. Please share your awesome Statistics scholarship resources with me (Michelle drd@cashmere.school.nz)!

Workshop: Apply probability distributions in solving problems
Abstract: Michelle will share some of her key teaching activities for Level 3 Probability Distributions, including tasks to introduce binomial and Poisson distributions, sampling variation linked to distributions, Fergusson’s framework for statistical modelling, and some quick starter activities to reinforce students’ learning. You will also have an opportunity to meet the almost-famous Distribution Plushies!
Resources: My workshop powerpoint is here. The Russian multi-choice quiz is here, the tee shirts I made for the Parkinson’s disease simulation are here and the normal distribution foldable is here.

Workshop: Sample-to-population inference: an informal giant leap
NOTE: I covered this workshop on behalf of Mark Hooper, Otago Boys’ High School
Abstract: A big challenge and opportunity we face as Statistics teachers is the seemingly quantum leap from describing a single sample of data to using the ideas of sampling variation and making an inference for a population. This presentation will use the foundations of Level 5 and 6 on the curriculum as we head on a journey to constructing informal confidence intervals. Real data sets will be used to explore the ideas. The presentation will be practical, using both unplugged and web based tools.
Resources: Here is a folder with my slides and sequence of learning experience that I have developed for the Cashmere High School team.  These resources were originally developed from material from Pip Arnold and Lindsay Smith. Please be respectful and give credit when sharing, and note that all the work is being shared under creative commons (you may not use the material for commercial purposes).  NOTE that some of the work is now a few years old so links may not be current. I’ve tried to include the files that I mentioned in the workshop but let me know if I’ve missed anything vital!

Workshop: Sample-to-population inference: bootstrapping, way more than just a cool name
NOTE: I covered this workshop on behalf of Mark Hooper, Otago Boys’ High School. Mark’s article in Statistics and Data Science Educator is here, which is what he was going to loosely base his workshop on. I do apologise to workshop attendees for not quite hitting his mark (yes, pun intended), and just being a bit shattered and rambling by the end of the day!
Abstract: We all know that New Zealand has an envied, innovative and future focused Statistics curriculum. As we embrace the curriculum at its highest level, ideas allow us to make population inferences from samples that are more formal. There are many great activities and resources that build on the ideas of sampling variation from Level 6 and 7. This presentation will showcase some visual based and tactile activities from the bootstrapping resampling process to confidence intervals. The presentation will be practical, using both unplugged and web based tools.
Resources: Here is my powerpoint, and here is a folder of resources from an earlier workshop. This earlier workshop also covered re-randomisation so there are doozers, pugs and some extra things in there too!

OMA Conference 2019

Friday 15 November 2019, Michelle Dalrymple

Workshop: Developing statistical thinking in our Statistics scholarship students
(with Robin Turner)
Abstract: Statistical and critical thinking are crucial for developing a deeper understanding of the concepts that encompass our Statistics curriculum. Michelle and Robin will share some activities that support and challenge students. Their aim is for students to be successful in scholarship, as well as taking these concepts with them in their future.
Resources: Our workshop powerpoint is here, with lots of weblinks included. Please share your awesome Statistics scholarship resources with me (Michelle drd@cashmere.school.nz)!

Workshop: Apply probability distributions in solving problems
Abstract: Michelle will share some of her key teaching activities for Level 3 Probability Distributions, including tasks to introduce binomial and Poisson distributions, sampling variation linked to distributions, Fergusson’s framework for statistical modelling, and some quick starter activities to reinforce students’ learning. You will also have an opportunity to meet the almost-famous Distribution Plushies!
Resources: My workshop powerpoint is here. The Russian multi-choice quiz is here, the tee shirts I made for the Parkinson’s disease simulation are here and the normal distribution foldable is here.

Wellington HOD day 2018

Friday 16 November 2018, Michelle Dalrymple & Grant Ritchie

PLENARY: WE HAVE THE BEST JOB IN THE WORLD!
Abstract: Michelle and Grant are really proud of their awesome faculty and are excited to be able to share some strategies and approaches they have used. A wide variety of topics will be covered including building faculty culture of high expectations and reflective practice, developing faculty systems and working with strengths of staff.
Resources: Here are our plenary slides.

Workshop: HOW DO WE HANDLE THOSE DIFFICULT SITUATIONS?
Abstract: Michelle and Grant will share a little more in depth about various scenarios they have dealt with in their leadership roles.  This workshop will give you an opportunity to discuss a variety of “typical” scenarios that we find ourselves dealing with including teacher issues, complaints, success rates and personal staff issues. Grant and Michelle will share their experiences and together we will develop some positive approaches and potential solutions.
Resources Here are the scenarios we discussed at our workshop, including attendees suggestions of how to deal with the situations.

Wellington PCT Day 2018

15 November 2018, Michelle Dalrymple & Grant Ritchie

SETTING YOURSELF UP FOR SUCCESS
Abstract: Michelle and Grant’s aim with all their classes is for students to be both successful academically and enjoy coming to Maths. They will share ideas to help support you to set your classes up for success. Some scenarios of common student-issues including the “avoider”, the “guidance-groupie”, the “can’t be bothered”, and the “dominator” will also be discussed.
Resources: A pdf of the workshop slides is here.  Hopefully the notes pages capture a little of the flavour of what we spoke about.  I’ve added an extra slide with some links to a few growth mindset resources, and an extra slide with Bill Rogers info on it.  Remember, use each other for support and do feel free to email Grant or myself (Michelle) if needed.

Auckland Statistics Teachers’ Day 2017

28 November 2017, Michelle Dalrymple & Grant Ritchie

Workshop 1: FUN + RELATIONSHIPS + CURRICULUM = AWESOME
Abstract: Does building strong relationships in the classroom happen by chance?  What can we do to foster the development of student-teacher and student-student relationships within our curriculum activities?  Grant and Michelle will share a few of the statistical activities that they have used successfully in their classes.  Come prepared to play, laugh and enjoy being a “student” in their class.
Resources: Our workshop powerpoint is here

Workshop 2: Junior Probability
Abstract:Is year 9 and 10 really just about flipping coins, rolling dice and playing fun games?  In this workshop, Michelle and Grant will look at Junior Probability and how important it is to build Probability foundations for future success.  You will have a chance to try some activities that start conversations about randomness, chance, unpredictability and risk.
Resources: Our workshop powerpoint is here (Bangers font makes it look better!)
Some of the activities presented came from Gage & Spiegelhalter’s book, Teaching Probability (here); Wonky Dice (skew dice) are available from The Dice Lab.

NZAMT Conference 2017

3 – 6 October 2017, Michelle Dalrymple & Grant Ritchie, Christchurch

Activities for building strong relationships
Abstract: Does building strong relationships in the classroom happen by chance?  What can we do to foster the development of student-teacher and student-student relationships within our curriculum activities?  Grant and Michelle will share a few of the activities that they have used successfully in their classes.  Come prepared to play, laugh and enjoy being a “student” in their class.
Resources: Our workshop powerpoint is here

Auckland Statistics Teachers’ Day 2016

25 November 2016, Michelle Dalrymple

Sampling variation just keeps turning up everywhere!
Abstract: Sampling variation seems to be a tricky concept for students to grasp.  And it just keeps turning up in places they don’t expect it, such as simulations or probability distributions.  Michelle will share some of her activities and ideas she uses to help students understand sampling variation, including a focus on the sample-to-population inference progressions and sampling variation with data derived from a probability situation.
Resources: Workshop powerpoint is here.

Auckland Statistics Teachers’ Day 2015

27 November 2015, Michelle Dalrymple & Grant Ritchie

Workshop 1: “Stats is my FAVOURITE subject!”
Abstract: “Mum made me take maths”, “I didn’t have any other subjects to choose”, “I can’t do maths”, “I hate stats, but not you Miss”.  Sound familiar?  We will share some of the strategies we are using to make maths and stats awesome; 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 just gross and quirky.  (Please note that this workshop will be very similar to that presented at NZAMT13 in July this year.)
Resources: Our workshop powerpoint is here.

Workshop 2: Junior Probability – planning for learning
Abstract: Is junior probability just about rolling dice and playing games at your school?  Is it often left to the end of the year as a filler?  In this workshop, Grant and Michelle will give you an opportunity to try some hands-on activities that have been chosen to deliberately develop key probability thinking in preparation for senior school.  They will discuss how they are working with their teachers to think about why they use particular probability task, what are the learning intentions, where does it fit into the bigger learning programme for that year and beyond.
Resources: Our workshop powerpoint is here. Note – Anna’s modelling tool can now be found here. (Please note that this is the same workshop presented at CMA Statistics Teachers’ Day 2015)

Canterbury Statistics Teachers’ Day 2015

23 November 2015, Michelle Dalrymple

WORKSHOP 1: Clarifying inferences at Level 3: Sample-to-population inferences & Experiment-to-causation inferences
Abstract: Most Level 3 Statistics courses cover some work on both sample-to-population inferences and experimental-to-causal inferences.  Students often find it difficult and confusing when they need to distinguish between the two.  The aim of this workshop is to clarify the differences between the two inference types.  Teachers will work through the key teaching activities for development of students’ understanding of both the bootstrapping and randomisation analysis tools.  If time permits, we will share other teaching activities we have used with our students for both sampling and experiments.
Resources: All my inference workshop resources are in a folder here, including my powerpoint. The folder contains both Doozer (first developed for Cognition workshop series) and Pugs files needed for developing students understanding of bootstrapping. Also included are the High-jumping-dogs files for developing students understanding of re-randomisation techniques. This workshop is essentially a “speed” version of the initial roll-out workshops presented nationally back in 2011/2012 using different data sets.
(please note that this workshop is a repeat of the workshop given at CMA Statistics Teachers’ day in 2014)

WORKSHOP 2: Junior Probability – planning for learning
(with Grant Ritchie)
Abstract: Is junior probability just about rolling dice and playing games at your school?  Is it often left to the end of the year as a filler?  In this workshop, Grant and Michelle will give you an opportunity to try some hands-on activities that have been chosen to deliberately develop key probability thinking in preparation for senior school.  They will discuss how they are working with their teachers to think about why they use particular probability task, what are the learning intentions, where does it fit into the bigger learning programme for that year and beyond.
Resources: Our workshop powerpoint is here. Note – Anna’s modelling tool can now be found here.

WORKSHOP 3: Working collaboratively & leading statistical discussions
(with Kiri Dillon, Lincoln High School)
Resources: Our workshop powerpoint is here. (Please note that this is the same workshop presented at CMA Leaders Day 2015)

CMA Leaders’ Day 2015

17 November 2015, Michelle Dalrymple

WORKSHOP 1: Supporting our new teachers
(with Mitchell Howard, St Andrew’s College)
Resources: Our workshop powerpoint is here.

WORKSHOP 2: How to write and moderate assessments
(with Mitchell Howard, St Andrew’s College)
Resources: Our workshop powerpoint is here.

WORKSHOP 3: Working collaboratively & leading statistical discussions
(with Kiri Dillon, Lincoln High School)
Resources: Our workshop powerpoint is here.

WORKSHOP 4 IGNITE SESSION: Relationships matter in the classroom… and are what makes being a teacher so awesome

NZAMT Conference 2015

7 – 10 July 2015, Michelle Dalrymple, Auckland

WORKSHOP 1: Developing students’ statistical insight in Years 9 to 13
(with Kiri Dillon, Lincoln High School, guest appearance from Christine Franklin, US)
Abstract: Typical discussions among statistics teachers include questions like: What does statistical insight mean for our students? How do we help students develop their statistical insight?  What do we look for in activities? In this workshop, we will share our thoughts and experiences in encouraging our students’ higher level thinking. We will also share some thinking frameworks we are adapting and some activities that have worked successfully in our classes.
Resources: Our workshop powerpoint is here.

WORKSHOP 2: Making experiments awesome.
(with Grant Ritchie)
Abstract: This year we have aimed to make our Level 2 and Level 3 Statistics courses as AWESOME as possible.  We tackled this challenge with lots of fun, learning through doing, and encouraging a positive collaborative classroom culture.  In this workshop we will share some of our experiences teaching Level 2 & Level 3 Experiments.  We will endeavour to discuss: good experiments to do in class, incorporating the research component and key teaching moments.  We also plan to brag about our inaugural annual “Experiments Camp”.
Resources: Our workshop powerpoint is here. Please note that marshmallows were used in this workshop – always give a health and safety briefing with marshmallows (and other edibles).

WORKSHOP 3: “Maths is my FAVOURITE subject!”
(with Grant Ritchie)
Abstract:  “Mum made me take maths”, “I didn’t have any other subjects to choose”, “I can’t do maths”, “I hate maths, but not you Miss”.  Sound familiar?  We will share some of the strategies we are using to make maths and stats awesome; 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 just gross and quirky. 
Resources: Our workshop powerpoint is here.

CMA E-learning Day 2015

May 2015, Michelle Dalrymple

Basic introduction to iNZight
Abstract: Michelle will share how Cashmere High School incorporates iNZight into their teaching and learning programme.  She will cover basic iNZight use, features of iNZight that help “unpack the stories in the data”, show you how you can use Excel and iNZight to generate samples, and touch on using iNZight use in Level 3 Statistics courses.  This workshop is aimed at beginner-to-intermediate iNZight users.  Advanced iNZight users are welcome to attend, but are likely to be asked to share their expertise!  It will be an advantage if you come to the workshop with iNZight already installed on your computer.
Resources: My workshop powerpoint is here.

Otago Mathematics & Statistics 
Teachers’ Day 2014

December 2014, Michelle Dalrymple

PLENARY: A year of thinking
Abstract: Time to explore the current thinking in mathematics and statistics education; time to read books that have been waiting for you for years; time to read blogs that come through your email and actually follow those interesting links to the next interesting link…; time to complete all those online courses you started; time to have conversations with leaders in mathematics education, icons in New Zealand statistics education, and other really interesting people; time to think and reflect on personal practice as a leader and classroom teacher.  Time is a luxury that teachers rarely have enough of. 
Michelle was fortunate to be awarded a Teacher Endeavour Fellowship this year and did have time during terms 1 and 2 when she embarked on her “thinking journey”.    This thinking has continued with her return to school. 
Michelle will share a diverse mix of some interesting, thought-provoking, celebrating and humorous snippets about what she has experienced this year.   This may include big data, the never-ending quest for data-sets, leadership and leading change in pedagogical practice, research on mindset and mathematics achievement.  She aims to leave you thinking too, and hopefully with a few ideas you can take back to your classroom.
Resources: My plenary powerpoint is here.

WORKSHOP 1: Junior Probability
(with Grant Ritchie)
Abstract: Developing students’ probability thinking and probability literacy (Levels 3 – 5)
Resources: Our workshop powerpoint is here. ( Please note that this is the same workshop presented at CMA Junior Statisitcs Day 2014)

WORKSHOP 2: Introduction to mulitvariate data
(with Grant Ritchie)
Abstract: “Making the call” up to Level 5
Resources: Our workshop powerpoint is here. ( Please note that this is the same workshop presented at CMA Junior Statisitcs Day 2014)

WORKSHOP 3: Junior Statistics
(with Grant Ritchie)
Abstract: Developing students’ statistical thinking and statistical literacy (Levels 3 – 5)
Resources: Our workshop powerpoint is here. ( Please note that this is the same workshop presented at CMA Junior Statisitcs Day 2014)

Auckland Statistics Teachers’ Day 2014

November 2015, Michelle Dalrymple

Probability…the pathway to Year 13 from Year 9
Abstract: This workshop will focus on unpacking the key probability learning concepts at each curriculum level.  The aim is to assist teachers in developing a pathway in probabilistic thinking that is appropriate at each level.  There will be an opportunity for teachers to evaluate where their school is currently at, and to identify what sequential building blocks are needed for students. If time permits, teacher will be encouraged to share probability activities they have found worked well in their classes. It would be useful if workshop attendees bring a copy of their school’s current probability progressions.
Resources: Our workshop powerpoint is here. (Please note that this is a repeat of the workshop given at CMA Statistics Teachers’ Day 2014.)

Wellington Mathematics & Statistics 
Teachers’ Day 2014

November 2014, Michelle Dalrymple

Developing students’ statistical insight in Years 9 to 13
Abstract: Typical discussions among statistics teachers include questions like – What does statistical insight mean for our students? How do we help students develop their statistical insight?  What do we look for in activities?  In this workshop, we will share our thoughts and experiences in developing our students’ higher level thinking.  We will also share some activities that have worked successfully in our classes.
Resources: Our workshop powerpoint is here. (Please note that this is a repeat of the workshop given at CMA Statistics Teachers’ Day 2014.)

Canterbury Statistics Teachers’ Day 2014

13 November 2014, Michelle Dalrymple

WORKSHOP 1: Clarifying inferences at Level 3: Sample-to-population inferences & Experiment-to-causation inferences
Abstract: Most Level 3 Statistics courses cover some work on both sample-to-population inferences and experimental-to-causal inferences.  Students often find it difficult and confusing when they need to distinguish between the two.  The aim of this workshop is to clarify the differences between the two inference types.  Teachers will work through the key teaching activities for development of students’ understanding of both the bootstrapping and randomisation analysis tools.  If time permits, we will share other teaching activities we have used with our students for both sampling and experiments.
Resources: All my inference workshop resources are in a folder here, including my powerpoint. The folder contains both Doozer (first developed for Cognition workshop series) and Pugs files needed for developing students understanding of bootstrapping. Also included are the High-jumping-dogs files for developing students understanding of re-randomisation techniques. This workshop is essentially a “speed” version of the initial roll-out workshops presented nationally back in 2011/2012 using different data sets.

WORKSHOP 2: Probability…the pathway to Year 13 from Year 9
(with Grant Ritchie)
Abstract: This workshop will focus on unpacking the key probability learning concepts at each curriculum level.  The aim is to assist teachers in developing a pathway in probabilistic thinking that is appropriate at each level.  There will be an opportunity for teachers to evaluate where their school is currently at, and to identify what sequential building blocks are needed for students. If time permits, teacher will be encouraged to share probability activities they have found worked well in their classes. It would be useful if workshop attendees bring a copy of their school’s current probability progressions.
Resources: Our workshop powerpoint is here.

WORKSHOP 3: Developing students’ statistical insight in Years 9 to 13
(with Kiri Dillon, Lincoln High School)
Abstract: Typical discussions among statistics teachers include questions like – What does statistical insight mean for our students? How do we help students develop their statistical insight?  What do we look for in activities?  In this workshop, we will share our thoughts and experiences in developing our students’ higher level thinking.  We will also share some activities that have worked successfully in our classes.
Resources: Our workshop powerpoint is here.

Canterbury Principals meeting 2014

September 2014, Michelle Dalrymple & Mark Wilson

The Prime Minister’s Education Excellence Awards – finalist
Resources: Powerpoint is here. Our finalist video can be viewed here.

CMA Nibbles session 2014

September 2014, Michelle Dalrymple

Interactive notebooks – a brief introduction
Resources: My powerpoint is here. Other interactive notebook files (foldables) I have developed are available here.

Junior Statistics Day 2014

5 June 2014, Michelle Dalrymple & Grant Ritchie

WORKSHOP 1: Junior Probability
Abstract: Developing students’ probability thinking and probability literacy (Levels 3 – 5)
Resources: Our workshop powerpoint is here.

WORKSHOP 2: Introduction to mulitvariate data
Abstract: “Making the call” up to Level 5
Resources: Our workshop powerpoint is here.

WORKSHOP 3: Junior Statistics
Abstract: Developing students’ statistical thinking and statistical literacy (Levels 3 – 5)
Resources: Our workshop powerpoint is here.

AMA HOD Day 2014

May 2014, Michelle Dalrymple, Auckland

Big Data, Leadership & Pedagogy
Abstract: Michelle has been fortunate enough to be on an Endeavour Teacher Fellowship for Terms 1 & 2 this year.  She will share an eclectic mix of what she has been working on and thinking about with you.  Topics may include: Big Data – interesting stories, lessons and careers; Leadership – challenges and thinking; Pedagogy and the growth mind set; other classroom lessons with a statistical focus.  The aim of the workshop is to leave you thinking, challenged, and with some resources you can use back in your classroom.
Resources: My workshop powerpoint is here.

CMA mini-conference 2014

March 2014, Michelle Dalrymple

Understanding big data
Resources: My workshop powerpoint is here. Some weblinks I shared are here.

MAV annual conference
(Mathematics association of Victoria) 2013

5 – 6 December 2013 Michelle Dalrymple, Melbourne
Developing students sample-to-population inferential reasoning
Abstract: Developing student understanding of formal statistical inference methods has always been a challenge in the classroom.  The world-leading New Zealand Statistics curriculum takes students on a journey that includes hands-on activities, “movies” and other visual representations to move students from informal to formal inferential thinking over a four year time frame.  Emphasis is placed on using appropriate language to tell stories with data.  This session will give a brief overview of this learning trajectory from Year 10 to Year 13, specifically in relation to comparison situations, and some practical experience with some of the key teaching activities.
Resources: Prezi presentation link is here

NZAMT conference 2013

1 – 4 October 2013, Michelle Dalrymple, Wellington

Developing students’ sample-to-population inferential thinking
Abstract: 2013 has been the culmination of our Year 13 students’ sample-to-population inference journey which started with our students as Year 10 students in 2010.  This workshop will provide an overview of our sample-to-population inference progression at Cashmere High School.  Some activities that worked well with our students will be covered and presented.  We are still improving our teaching and student understanding in areas such as sampling variability, shape and literacy.  Our experiences in these areas will be shared alongside some activities we have been developing to enhance student understanding.
Resources: My workshop powerpoint is here. Also the kangaroo jump files are here (informed-fictional data) including the original data, graphs and summary statistics and a matching analysis statements activity. Note: please also see my series of blogs on the Inference progressions and developing students sample-to-population understandings (Part 1 is here) .

Auckland Statistics Day 2012

November 2012, Michelle Dalrymple, Auckland

Use Statistical methods to make a formal inference, the end of the high school journey
Resources: My powerpoint is here.

Junior Statistics Day 2011

June 2011, Michelle Dalrymple & Grant Ritchie

Resources: Our powerpoint is here.

Sampling and building relationships

Have you ever seen bullmastiffs taking a random sample? What about a pug?  Well… you’re in for a treat!

The backstory

I introduce sampling to my Year 12 students with a lesson progression adapted from Lindsay Smith (here).  The day before this lesson, a brilliant homework task was assigned – students had to find a silly dog picture to add to our wall – the story behind the wall is a completely different post that I’ll try to get written one day!

The next day we introduce sampling… the short version goes something like this:

• Hand out class rolls to pairs of students
• Ask them to come up with five different ways of selecting five students
• Then share back the different ways they come up with – generally the basic methods are covered such as simple random sampling, stratified sampling (one from each group of desks or x boys and y girls (are girls are more likely to do homework?… hmmm…. you can see where this would lead to nice class discussion), convenience sampling, self-selected sampling 
• I then go formally through the different sampling methods, and we take a sample using each method from the class, with replacement obviously.
• If a student is selected and they have done their homework they get a lolly…. if they get selected and they haven’t done their homework then there is a “punishment” as deemed fit by the class.

The “punishment” is an opportunity to have some fun with the class, with good humour – we have a range of options for them to choose from that the class decides before we start.  This year we included star jumps, press ups, and drawing a horse (more on that in the promised later post).  Much laughter ensured this year as Louis, who of course hadn’t done his homework, was picked four out of the five times! He choose to draw each time, along with quite a few others, and my whiteboard ended up covered in a variety of creatures.  Here’s two that I managed to keep for a while amongst the rest of my busy back whiteboard

The new exciting part…

The one sampling method that was fresh for me this year, that my students had never come up with before, was to get my dogs to select a sample – I think maybe I’ve shared too much about them with my classes!  Always up for a challenge, and an excuse to do silly things with my dogs, I roped in the help of my husband that evening and here’s the results:

Cornelius sampling

Daisy sampling

 

Tess sampling part 1

 

Tess sampling part 2

As you can see… the student names were spread out in a circle in my garage, and what you might not quite be able to see, is that there is a small dog treat on every piece.  The dogs were spun to get a little dizzy (not harmed in anyway!) to aim for a “random” start point.

Were the dogs random?  I don’t know about the big dogs – yes, the start point was random, but they just went into hoover-mode from there so it depended on whether the names were also randomly spread in the circle (I have to admit, I don’t think they were). But… I’ve found a skill that a blind, deaf, losing-her-sense-of-smell, old-lady pug has!  I think Tess was quite random!  It took her ages to find each piece and make her selection – the clips above are just a small portion of the 2 minutes it took her to choose five students.

Why this was so cool? – other than having dogs sample of course – it gave me an opportunity to continue to reinforce the positive relationship I have with my class: they enjoyed seeing my dogs, I enjoyed being able to share a little of my dogs with them and involving them in class – we often, as teachers, seem to work really hard to remember to check in with students after their big sports event, competition, work experience, camp, music, new job, new sibling, new dog…. and its nice having this interest and care reciprocated.

The reward for being selected by Cornelius, Daisy or Tess…. a picture of them to keep!  Here’s Mya’s book – who was lucky enough to be selected by both Daisy and Tess:

The power of sorry

It feels like a long time since I’ve written anything here – I meant to write up this post at the start of the year, but now, with term 2 starting tomorrow, I’m finally getting there.  Oh well, better late than never (sigh).

Reflections on the start of year…

In our faculty session at the start of the year I showed Rita Pierson’s Ted Talk “Every kid needs a champion” (again – I showed it to the faculty last year and I’ll probably show it next year too 🙂   )  If you haven’t seen it I’d highly recommend you go and watch it now.  Its here.  One of her suggestions in building relationships with students is to say sorry.

One of the other things we discussed as a faculty that morning was bringing consistency into some of our behaviour expectations of classes, including introducing The RED Box in each class.

The idea for The RED box came originally from Sam (thanks Sam!) last year, a few of us trialed it successfully and hence the roll out to full faculty this year.  It is for cell phones (and other distractions) in class.

My method for using it is as follows: when I’m ready to start the lesson, I say to the whole class something like “okay, lets get started – now is the times for phones to go away”.  They know this means in bags or pockets.  Then, if there is a phone out during class, I just quietly walk over to the student and hold out the box for them to put their phone in, I don’t stop what I’m doing, its just a really low-key non-confrontational way of dealing with the ongoing distraction of cell phones in class.   Also note that in the bottom of each box, there are red cards – if a student argues about the phone at all, they get the choice of putting it in the box or getting a red card – simple!  I’ve not had to give out a red card yet, but have threatened a few times when they start the “I was just checking the time…” arguments.

This method works really well – students know what to expect, know how the system works and I don’t make a big deal over it with them.  As an aside – I’ve moved back to using my basket that I used last year – I found the lid on the box annoying.  A second aside – yes, I sometimes forget to give the “phones away now” signal, so when I see a phone out I just say something like “thanks Nigel for reminding me that its time to put phones away , phones away now please”.

Right – that’s the brief background.  Day 1 in my MAS201 class (Year 12 Statistics, last period after a full day, first day back at school for the year) – my goal was to establish positive relationships while making sure routines and expectations were clear.  Yes, as part of this, I introduced The RED Box to my class and made a really big deal over the “phones away now” signal.

A few minutes later, I spot a phone out… yes, at the back of the room… yes, from a J-name boy! (what is that??!).  I went over, and held out the box, just like we’d discussed.  He started arguing about how he was checking the time, of course, I mentioned the red cards and J-name reluctantly placed his phone in The RED Box.

A wee while later – The RED Box vibrated from the front of the room.  J-name calls out “can I get that, it’ll be my Mum?”.  Unfortunately, I made a classic teacher-mistake of discussing this with J-name across the class, and after a bit of too-ing and fro-ing I ended the debate with “please see me after class”.  (thiank goodness, now at the start of term 2, I can’t remember all the details!)

When J-name came to collect his phone from me at the end of class, our debate continued re using his phone in class, the appropriateness of answering it, even if he knows it was his mother, how come his mother was calling in class time etc etc.  It wasn’t pleasant, nor a moment that I felt I handled well at all.  J-name is a big personality in class, I knew I needed to get him onside, I was pretty sure I’d blown it – I worried and mulled over it all night before realising that I needed to channel Rita.

So the next day… the first thing I did as J-name had come into class and sat down (yes, at the back again) was to go over to him and apologise for the way I’d handled things yesterday – I told him that I’d worried about it all night, and I really wanted to just start fresh today.  I was really impressed with the reaction from J-name.  He also apologised and said that he had been a dick (yes, his word) and yes, that we should start fresh from then on.  Whow! How to turn things around Dr D…

But hang on – J-name’s phone was out again near the end of that period, I made a judgement in the moment to ignore it that time aiming to build that positive relationship.  Next day, I mentioned to J-name at the start of class that I’d seen him with his phone out again yesterday and that I was disappointed.  I’d have to get The RED Box out if it happened again – it did, but no argument at all this time (and I remembered to ask him to turn it off before it went in); when he collected it I suggested that he was welcome to put his phone in The RED Box at the start of the period when he came in as a preventative if he wanted to.

J-name hasn’t done this, I’ve had his phone (and plenty others) in The RED Box over the term but no grumbling about it at all from him and I think we have a pretty good relationship now, and lots of good work is being done.

Moral of the story – apologise, be humble, keep working on building the relationships but keep your expectations high and keep working towards them in a way that supports all the other things you are trying to do.  Never give up on your students.

From Rita: “Teaching and learning should bring joy. How powerful would our world be if we had kids who were not afraid to take risks, who were not afraid to think, and who had a champion? Every child deserves a champion, an adult who will never give up on them, who understands the power of connection, and insists that they become the best that they can possibly be.  Is this job tough? You betcha. Oh God, you betcha. But it is not impossible. We can do this. We’re educators. We’re born to make a difference.“

 

PART 3 – COMPARING TWO GROUPS Developing big ideas with sample-to-population inferences …

This is the third part of a series of posts on sample-to-population inferences, and progressively developing students understandings.

Comparing two groups:

Is what we are seeing when we compare the features of our samples of our two groups (in particular the median/mean) MORE than just sampling variation?

Our way of judging this difference gets more sophisticated as we move up our curriculum.  We essentially have a four-stage progression with details found HERE for NZ Curriculum Levels 5 to 7.  The fourth stage introduces formal bootstrapping methods for constructing confidence intervals.

STAGE 1: Curriculum Level 5 guide (Year 10 – 11ish):  if the median of one group is outside the middle 50% of the other group then  you can make the call that “group 1 tends to be bigger than group 2 back in the population” (for samples of size 20 – 40).

I usually convince students that this works in two ways.  Firstly, by using the lesson progression developed by Pfankuuch et al (here are the key resources, but make sure you check out the workshop 1 material too.  This wiki also has all the resources and a summary together nicely (thanks Pip!).  The lesson progression uses a class investigation where students to take multiple samples from Karekare college, firstly comparing boys vs girls heights and secondly comparing times to school for students busing or walking.

Students CAN make the call that students who bus tend to take longer to travel to school than students who walk back in Karekare College – this is seen visually by the consistent shift between the multiple samples.  

This idea is reinforced with arm-waving again.  It is important this time to make sure you have bling on each arm (in this case watches) to represent the medians.  You can see below that we have the situation where the two groups are so far apart that although the middle 50%s move (each arm) with repeated sampling, the medians (watches) are consistently outside the middle 50% (arms) of the other group (for at least one group).  Please note that this one is a bit tricky to pull off – our arms aren’t quite designed right for this sort of functionality…

Students CANNOT make the call that boys tend to be taller than girls back in Karekare College – visually the multiple samples don’t show the same consistency.  That is, there isn’t enough of a shift between the samples of the two groups to say whether boys tend to be taller than girls or if girls tend to be taller than boys back in the population.

With similar arm-waving ideas as previously – this time with repeated sampling we show that if the two group in the original sample are close together,  the middle 50% (arms) and medians (watches) may stay in the same positions or may switch round with repeated sampling due to sampling variation – so we can’t actually tell from this sample what’s happening with the difference between the two groups back in the population.

STAGE 2: Curriculum level 6 guide (Year 11ish):  if the distance between the medians is greater than a proportion of the “overall visible spread” (OVS) then we can make the claim that B tends to be bigger than A back in the population.  The proportional relationship between the medians and OVS is linked to both sample size and spread.

The idea that sampling variation is influenced both by sample size, and spread of the population is an important idea to start developing with students.  We work as a class to create multiple samples of different sizes (as discussed in Part 1) and to explore the link between the difference in medians and the size of the overall visable spread.  Resources are available on Census@School here.

STAGE 3: Curriculum level 7 guide (Year 12):  if the informal confidence intervals for the medians do not overlap then we can be pretty sure that the median of B is bigger than the median of A back in the population.  

Students take to this guide quite naturally and just run with it if the work has been put into developing their understanding of informal confidence intervals, why we need them and how we incorporate sampling variation measures.  We need to make sure we emphasise the slight difference in the conclusion we are drawing – this time it is directly about comparing population medians.

Again, I reinforce ideas of sampling variation and confidence interval construction with hand-waving.  When our groups are close together, with a sample size of n then the confidence intervals are THIS wide and with repeated sampling they will “jiggle” round quite a bit due to sampling variation.  [insert suitable sound effect at *].  If we increase the sample size then the confidence intervals will get narrower*, AND there will be less “jiggle” so we can be pretty sure that back in the population we will see the differences in the medians of the two groups.

STAGE 4: Curriculum level 8 (Year 13):  Students complete their sample-to-population inference journey with us in their last year of high school by meeting a formal re-sampling method, namely bootstrapping, to create confidence intervals.

Further details on teaching bootstrapping for understanding can be found here  or here  (original roll-out teacher professional development). 

Part 1 – Sampling variation

Part 2 – Confidence intervals

PART 2 – CONFIDENCE INTERVALS Developing big ideas with sample-to-population inferences …

This is the second part of a series of posts on sample-to-population inferences, and progressively developing students understandings.

The need for a confidence interval (NZ Curriculum Level 7/Year 12-ish onwards)…

The next step in developing students’ appreciation of sampling variation is for them to understand that making a sample-to-population inference where they give a point estimate of the population parameter is setting them up for failure – they will always be wrong.  Instead they need to use an interval of plausible/believable values within which the population parameter is most likely to fall between, based on our best estimate of the size of the sampling variation.

My lesson progression, outlined briefly below in relation to developing the Level 7 informal confidence interval, is adapted from others’ work including Pip Arnold (Pip’s work) and Lindsay Smith (Lindsay’s work).

1. Introduction to/ recap of sampling methods including how and why we sample.
   I set a silly homework assignment the period before this lesson, then get the students to brainstorms all different ways we could select five students to check their homework.  Generally students come up with our standard sampling methods needed (eg simple random, systematic, stratified, convenience…), occasionally with a little prompting from me. We then “check homework” which always involves students receiving a lolly if they get selected.  This does lead into interesting conversations on RANDOM (see my previous blog on this!) and our perception of RANDOM.  It does pay to save a few lollies for the end for any students that haven’t been selected!
2. The need for confidence intervals – meet the Kiwis… 
   Students work in pairs each take four samples (n=15) from the kiwi population and use their samples (after creating dot plots, box plots and summary statistics) to finish the following sentence “From my sample data I estimate that the median weight for all New Zealand kiwis is….“.   Usually students who have worked together will give the same/similar answers but we get a variety of answers across the class.  Sometimes we even get a student or two who give an interval for their answer – send them to stand in the back corner of the room immediately!  The big reveal, of course, comes with the teacher-prompt of “but your answers are all different – who is right?“.  Generally your more confident personalities will claim that they’re right, while the quiet students sit quietly looking concerned.  Pad this out as long as you need to to make your point that “they are all wrong“.  How can they know EXACTLY what the population median will be?
   NOTE: Exactly how you deal with this will depend on the relationship you have with your class – it may be better to soften this statement to “you might be right, you might be wrong – in the real world you would never know…”.  I enjoy stirring my class a little and the reactions I get are always lots of fun!
   We now bring back into the room the students sent to the back of the class and praise them for being three steps ahead of the rest and putting an interval around where they thought the population median would be.
   We could use our medians from our repeated sampling (collect the class results on a big graph) and read off where most of the medians lie to give us a good idea of the interval for the population median.  This works fine in the classroom where we have easy access to the population to actually complete repeated samples, but in reality we want methods that we’re happy working with when we only have one sample.
3. Increased sample sizes = decreased sampling variation. Therefore our interval should get narrower as our sample size increases.  See PART 1 for how I reinforce this with students.  Hand gestures are very useful again here: If your confidence interval is THIS wide for this sample size – what happens when you INCREASE your sample size? – make sure you include a sound effect as your confidence interval gets narrower with the increased sample size!
4. Increased spread in the population = increased sampling variation.  Therefore our interval should get wider as our spread increases.  I use the simple situation (from Pip) of comparing student heights for new furniture in an intermediate school (Year 7 & 8) or a middle school (Year 7, 8, 9 & 10).  We ask which teacher is likely to get a closer estimate of the students heights?  
   Bring back your hand visuals again:  If your confidence interval is THIS wide for this spread – what happens when you INCREASE your spread? – make sure you include a sound effect as your confidence interval gets wider with the increased spread!   Of course, both here and for increased sample size we can start showing the ICI visually with a (red) line on our box plot, centered about our median.
5. Formula for informal confidence interval (ICI).  I introduce the suggested formula for students to use, and we check that it meets our requirements.  Yes, the bit we add on or subtract does get smaller when we increase the sample size (as we’re dividing by a bigger number); yes, the bit we add on or subtract does get bigger when the spread (interquartile range IQR) increases (as we’re multiplying by a bigger number)
   
6. Checking our informal confidence interval formula works most of the time.  We have class set of 100 different samples from the kiwi population (here if you want it) where students calculate 5 different ICIs themselves, then we collect these to check whether they captured the population median or not (collection sheet is here).  I am very clear to reinforce with students that we are working in TEACHING WORLD so we can do exactly what we’re doing – testing our ideas to convince ourselves they work.
7. Reinforcing the ICI has been developed and tested by people who know what they’re doing, ready for us to use this year in class.  It is a step along our sample-to-population inference journey which culminates next year with the introduction of formal methods for constructing confidence intervals.
8. EVERY TIME!!!!! you construct a confidence interval you should be interpreting it (even if it’s just in your head!).  This is almost a mantra in my class.  Students need to continually remind themselves what the point of creating the confidence interval is, and by interpreting it carefully we are doing this.  Remember, every confidence interval interpretation should include the statistics, the population, “pretty sure” (or equivalent indication of uncertainty), the variable, numbers and units.  For example “we’re pretty sure that the population median height of all Year 12 boys in New Zealand is somewhere between 173cm and 182cm“.
   Other formative assessment questions such as “Would it be believable that the median height of Year 12 boys in New Zealand is 185cm? Why? Why not?” are also super-important to check students’ understanding.  And of course slipping in annoying questions such as “Why do we use confidence intervals?”

Part 1 – Sampling variation

Part 3 – Comparing two groups