Digital teaching tips & tricks, ideas, examples, and general thoughts and reflections. Follow my Inquiry.

Wednesday, 14 November 2018

2018 Inquiry: Impact story

What happened for the learners?
My learners had to get used to a completely new way of learning maths.
They learnt to carefully read, talk about, argue, listen to others, and communicate their ideas about a problem
...before attempting to solve it.
They learnt to attempt new problems in groups of 3-4, and insist that their group work together and share their thinking
...before finally agreeing on a solution (or an attempt at a solution)
They learnt to share their ideas and explain their thinking back to a much larger group (15-20 learners)
...before listening to those of another group (or vice versa)
And they had to learn to be able to do all of this before I (the teacher) would offer them much in the way of support with the problem.
Before considering anything else, I think that this alone is a huge thing to have happened for my learners, and I couldn't be more proud of the way they have taken these lessons on.
There are other changes to their maths learning that I will briefly list:

  • Half class groups
  • Mixed ability grouping
  • Flexible groups (i.e. changed regularly)
  • 40-60 minutes lessons
  • Only 2 formal maths lessons a week

To be fair to the inquiry I think student achievement has to be talked about in two different areas. Maths achievement and Dialogic capabilities.

Maths achievement - The ultimate goal of the inquiry. 
Short answer: achievement gain = yes, accelerated shift = no.
I had a target group in mind for this inquiry. 7 learners working around the same level (Late Lv 2/ Early Lv 3). Their results were mixed. These mixed results matched the rest of my class as well.

Dialogic capabilities - What was originally supposed to be the vehicle for achievement.
At the beginning of the inquiry I never thought of dialogic capabilities or skills as something that needed to be achieved, instead I thought of them as the necessary tool or vehicle that would drive the maths achievement. In most regards this holds true, however what I didn't anticipate was the amount of learning that would need to happen (dialogic learning), in order to use it as the tool for maths achievement. As stated above this learning was massive, and although was not something that I formally recorded or captured, that changes in the class behaviour and practice is very noticeable. Does this mean that every kid became capable of these skills, unfortunately no. In fact it became more and more noticeable which leaners continued to stay quiet and allow others to speak. 
Short answer: Dialogic increase = BIG YES, Whole class: no

What evidence do I have of this happening?
As stated above I had a target group in mind for this inquiry. See their PAT results below
As you can see the results are positive, however mixed. What you might find interesting to know is that the learners from this group who had the most growth, also showed more development in their Dialogic capabilities. This pattern was reflected across the rest of the class, however there were many outliers that did not fit to this correlation. i.e Some of my least talkative learners still had big gains in their maths learning. So although there appears to be some evidence that good mathematical discourse and critical discussion can lead to gains in mathematical understanding and achievement, perhaps the learners who listen and reflect on the discourse internally can gain understanding just as well. 
I also noted that there appeared to be a similar pattern of achievement from these learners in their literacy. How and if this inquiry is connected, or whether the literacy gain helped to lift the maths is yet to be determined...
Dialogic capabilities
Unfortunately this was not recorded or captured throughout the inquiry. Having seen the achievement gains in this area I wish that I had, although I'm not entirely sure what this would have looked like. Perhaps a simple audio or video recording that could have acted as a comparison could have sufficed.

Language acquisition
The acquisition and use of precise mathematical language was an intended part of this inquiry and again unfortunately was not captured well. I battled with the best way to have achieved this but kept getting stuck. For example a pre and post vocab test would have been simple when starting a new unit. But it ran the risk of teaching to a test, rather than allowing the vocab to be learned authentically and needs based as part of their mathematical reasoning. However, anecdotally I believe that the student-talk IS helping the acquisition of language among the students. At least you can hear them questioning and correcting each others language throughout the lessons. This was most noticeable when working with decimals “wait you mean tenths, not hundredths” “its not 5 its 5 tenths” etc. I also believe that the discourse that the students engaged in greatly impacted their understanding in our geometry unit, where the students argued over whether they needed to solve the perimeter, area, or volume etc.

What did I do to make this happen?

Developing Mathematical Inquiry Communities (DMIC), is a complete overhaul of our mathematical teaching practice. It involves spending more time allowing learners to attempt problems collaboratively without teacher support, to share their thinking, and listen to each other's ideas. It involves the teacher listening to the students and identifying misconceptions that can be addressed at the end of the lesson. 
This meant that in my practice I needed to adopt the use of the talk moves in maths discussions, and allow the students time to wrestle with the problems on their own. Identifying and predicting misunderstandings and misconceptions during the planning process. Then later responding to students needs during the “connect phase” of the lesson.
Instead of being grouped by level or ability, the learning groups are of mixed ability allowing students to learn from each other, and not have their learning capped by their groups achievement “level”. Lessons last 40mins to an hour, rather than 20 to 30 mins.
Instead of taking 2-3 maths groups per day, I only take 1 a day instead because of the time constraints. 

 Wonderings for what next?
At this point in time I’m not sure that I can claim that the inquiry has led to accelerated student achievement in maths. However there has been a growth in student dialogic capabilities in maths. 
It does appear to be leading towards a growth in mathematical understanding, however I believe that because the dialogic learning needed to come first, that we won’t see the intended the results within this academic year. 
A truer test will be to follow these same students next year (assuming their Year 7 teacher will continue using the DMIC approach in the classroom next year), now that their foundation dialogic skills are already there. Because there are lots of indicators to show that this inquiry is on the right track, at least in line with my initial hypothesis. I’m hearing a lot less “is it a plus” and more questions like “what is it asking us to do” “how do we do that”. 
Another example has been the problem solving ability through dialogic conversations of the students in other curriculum areas. - I have been experimenting with students and different Digital coding applications. I have offered limited support and set challenges for the students to complete (in a similar fashion to their DMIC lessons). Throughout these lessons I have heard the same types of critical discourse and dialogic discussions, that the students use in their maths learning. They are solving complex problems and learning to do things far beyond the guidance I have given them. The students have been allowed to form their own groups and interestingly have followed the DMIC model and naturally formed mixed ability groups. The ‘expert’ students in the class tending to group themselves with less capable peers, rather than teaming up.
The student-talk I believe IS helping the acquisition of language among the students, at least you can hear them questioning and correcting each others language throughout the lessons. This was most noticeable when working with decimals “wait you mean tenths, not hundredths” “its not 5 its 5 tenths” etc. I also believe that the discourse that the students engaged in greatly impacted their understanding in our geometry unit, where the students argued over whether they needed to solve the perimeter, area, or volume.
This is the first time in my short career (5 years) that I have had to really “unlearn” something to change my practice. The DMIC pedagogy is so different to how I had previously been teaching maths that it took me a lot longer than I expected to become proficient at it (and I am still learning and not at the level I hoped to be). Because of this, my own learning journey affected that of the students, it felt like it wasn’t until term 3 that we really started to learn maths again, instead of learning DMIC.
This meant that I didn’t get to see the growth in language that I hoped to see in this inquiry. Yes I saw a growth in dialogic discussion and discourse skills from the students, however these skills were necessary in the first place for me to test my hypothesis. It feels like my work in this inquiry was about setting up the foundations for what I wanted to investigate, rather than actually investigating my theory.
Do I feel like my practice or professional learning has grown in this inquiry cycle - Absolutely yes. I have done lots of work around dialogic conversation before (mostly in literacy), however I have never attempted a complete overhaul of my practice in the way that I have for DMIC. My use of the talk moves, and my ability to set up and maintain group norms has grown. 
There is still a tonne of work that I need to improve in my practice in DMIC, for example; accurately pitching the problems at the right level, tracking all students (including the quiet ones), assessing the students, maintaining group norms, and time management.
There are also parts DMIC pedagogy that I am still yet to fully understand, most notably the mixed ability grouping. This is an area where myself and my team have become very frustrated and stuck in how to meet the needs of all the learners in the group.

Wednesday, 12 September 2018

Scratch w/ DMIC style groups

Student coding applications (such as Scratch) involve large amounts of problem solving by nature. This means that many of the skills and communication strategies that we have been learning as part of the DMIC approach can cross over.

A problem instead, is that I myself don't have the content knowledge required to help them out. Many of my learners have extended themselves to the same level of proficiency as my myself, or in some cases further than I can go. At first, I thought it this was a barrier that meant I wouldn't be able to do a lot of Scratch until I was up-skilled.

Instead, I have been trying to use aspects of the DMIC approach, and learning alongside my class as one big collaborative Inquiry community.

Our lessons are very exploratory, and can look like peers, groups, or even 'expert-students' running workshops for others students.

The beautiful thing about Scratch in particular, is that it has been designed by Educators to be used for this very purpose, and in this exact way. There is already functions within the programme that let kids make tutorials and search for student made "help sheets" and "tips and tricks" within itself.

Once a new skill has been found or cracked by one our 'experts', it isn't long before the skill is picked up by the other 'experts', and eventually it will filter down throughout the class. Sometimes it's not even an expert who is the first to crack something new.

Although our lessons are not strictly 'DMIC' nor do they contain all the aspects of a 'DMIC lesson', the kids are using the same skills to collaboratively tackle a problem. I hear the talk moves being used across the class, and statements like "can show me how to do make gravity again, I keep getting confused with the y and x axis" are all too common.

Friday, 31 August 2018

Roald Dahl Box Set

Our class Library Shelf is continuing to be a success this term.

Out of all the books on the shelf, the most popular books by far had been the Roald Dahl novels. I think part of this enthusiasm can be attributed to me reading Matilda to the class, but to be honest I didn't care why Roald Dahl was the favourite, as long as they were queuing up to read his books!

From the Op shop I had found a few different books, but they seem to be the type of book that people hold onto rather than donate. I decided to try my luck, and ask the school if they thought buying some more Roald Dahl books (that I could then borrow for my class until the end of the year) would be possible...?


In fact the school bought us the whole box set! The kids were pumped. Almost every book was being read as soon as they were available.
What was really cool too, was the fact that now we had doubles of some of the stories. This meant kids could read the stories the same time as their friends.

Wednesday, 15 August 2018

Op Shop Books and our own class library!

My silent reading push has been working well.

There were some problems however, that I should have thought through. It's the Duffy Book choice problem, the Scholastic Books problem, the Library Books problem!
Kids choose dumb books with cool covers!

Too many of my students were picking dumb books, that were based on movies or comic book heroes, or simply covers with cool pictures. Their enthusiasm for the books would diminish within the first few pages, and often they wouldn't get past the first few chapters.
I tried helping the students choose their books and found some success with Paul Jennings novels, Morris Gleitzman, and a few random titles that I knew they would enjoy. It was a losing battle though, and too many were losing interest in silent reading time fast.

That's when I had the brilliant idea to use some of my class budget to start buying books for our own class library shelf! I started with just a few from the Op Shop. Some Roald Dahl,  Morris Gleitzman, Maurice Gee, some more Paul Jennings, as well as few novels that I thought would catch the eye of the Girls. I was explaining the situation to some of the staff here at school, when I was offered a box of new library books that hadn't been integrated into the library system yet.
I jumped at the chance, and soon we had our own little library shelf!

There was a sense of pride from the kids with all our books on display, and the more limited (yet handpicked) choice of books meant that kids began competing to read certain books (or authors). I still took the class to the library, but now less than half were keen to change their books each time. Many choosing to instead, read the ones from our own shelf.

Together we came up with a system for our library shelf that would stop our books from getting mixed up:

  • The Top shelf would be books that had been taking out of the school library.
  • The Middle shelf would be books from the Op Shop (or Mr Goodwin's collection)
  • The Bottom shelf would be the "Special Library books" (the books that hadn't been integrated into the school library yet)

Everyone would keep their bookmark in the book that they were reading.

Thursday, 2 August 2018

Library - Bookmarks

This term I've tried to give chapter books a really big push.
I felt like the 'love of reading' was missing in my class, and I wanted to change that.

I was about a third of the way into reading Matilda by Roald Dahl to my class when I began to notice and overhear how many times my class was referencing the book in their personal jokes and conversations.
"She went full Ms Trunchbull"
- Student when talking about how grumpy their Nan had got in the Weekend.
"Is she like Miss Honey Mr?"
- Student in response to when I was explaining how lovely the Kiwi Sport coach is.
They simply loved the book, and were loving the story. I reflected on my guided reading lessons, and how little the learners were engaging with the characters and the stories that we read.
I decided I wanted to therefore make a big push for chapter books and try and recreate that same excitement based on there own reading.

I started simply with a book mark. The idea being that if they had a bookmark, then they would want to have a book to use it in... Seems a bit lame but I remembered how excited I had got when I was a kid, when my Mum bought home a fancy metallic Harry Potter Bookmark from Australia. The first thing I did was grab the nearest book and start reading so that I could use it.
I created a template and let the kids design their bookmarks however they liked. No surprises when half the class made Fortnite themed bookmarks!
It didn't matter though, because as soon as I gave them their laminated bookmarks, the students began begging me to take them to the library. My plan was working!

Friday, 27 July 2018

The Crank it out term

Our principal in staff meeting this week reminded us that this is the 'crank-it-out' term.

No Testing. No Reports. All Learning.
He challenged us to make the most of our timetables.

To make sure we are seeing all our groups
2-3 times per week 
Image result for Clock fast

I thought to myself well of course I am,
but then reflected actually am I?
Truth is I'm probably not.
Actually, I know I'm not - at least not ALL my groups.
The question is why?

I crunched the numbers and realised that I am probably not always making the most of my time in the classroom. Time is tight, and it is way too easy to run out of it.

Lets look at Reading as a subject.

1 group @ 20~minutes per guided reading session 
2-3 times p/w = 40-60 minutes p/w
Therefore 4 groups @ 20~minutes 
= 160-240 minutes p/w
5 groups
= 200-300 minutes p/w

That's a lot of minutes! For my team here at school, that usually all has to come out of our morning block. Even if you take out a fairly low amount of time for writing each week, assembly on Fridays, and our daily news. You find that the time remaining is already quite tight...

Total Minutes

45 Mins

Total Remaining
...and this is before any other interruption, transition, chat on the mat, pack-up, or roam.

In fact, this remaining '315 minutes' is on the assumption that Friday after assembly time can be used for guided reading sessions instead of "Finishing time" as well.

I've realised I need to be way smarter with my time, and smarter with my planning. Even just to see the right amount of groups for the right amount of time. This will also require me to become more precise with some my interactions with the learners, particularly around management and instructions.

Feeling cautiously optimistic
Challenge accepted.

Thursday, 26 July 2018

Oral Language boost from DMIC?

Keeping up the basics

Throughout learning the DMIC process there has been a temptation to forget all that I have learnt in the past... I need to keep myself in check with this as some of things that I learnt last year in my inquiry are really important. They did work. They did make a difference.

One of those things has been basic facts. I understand that within the DMIC style lessons there isn't too much room for old school basic facts learning. However, learning everything that I did last year I don't want to throw away these lessons completely. 

I'm going to experiment with trying to fit them into other times of the day such as:
  • warm-ups
  • pack-ups
  • in-between times
  • end of day
The lessons I am referring to can be read here in my blog post almost exactly 1 year ago.

Sunday, 8 July 2018

ISTE Reflection


Last year I applied for the Manaiakalani Professional Learning Fellowship to attend the ISTE conference in Chicago, USA, and amazingly I was lucky enough to win it.

Last week we boarded the plane and off we went. It was an absolutely amazing experience, and I'm still buzzing from it. I have never been to the States before, and although I have attended Education conferences in New Zealand, I have never experienced anything that resembled the sheer size and the crowds that ISTE provided.

The ISTE (International Society for Technology in Education) conference is an Education conference based out of the United States. It happens every year, and attracts educators from all over the world. The Chicago conference had more than 1000 sessions of all different types that you could attend, and had over 16,000 attendees.

With that in mind I had a lot of trouble picking my Conference class list. There was literally hundreds of different lectures or classes that I could attend each day, and usually at least 3-4 on that I wanted to attend at the same time. On the first day of the conference I attended what was called the CS Firehose. Essentially it was pre-conference whole-day session where we had an intro or play-session with different aspects of Computer Science that were going to be represented at the conference. After this, I quickly re-adjusted my entire timetable to fit in way more of these sessions.

Image result for Scratch 3.0I realised that without focussing more of my ISTE classes around a particular subject or theme I wasn't going to make the most of it as a learning opportunity. WIDE and DEEP just like our learners I suppose haha.

Sticking with CS theme, while throwing other interesting things into the mix I had an absolute blast of a conference. Some interesting things that stood out to me most can be read in other blog posts here:
- CS Firehose
- Scratch 3.0
- Micro:Bit and Make code

The biggest take home for me has been the CS/ Digital Curriculum integration (or STEAM integration). I have become extremely excited to give some of what I saw ago, and put into action all the ideas that my head was spinning while at the conference. While a tonne of it was inspiration that needs a lot of further thought and reflection for how I could implement it here at Pt England. Some stuff I can run with it straight away, or adjust how I am using it in the classroom to be more reflective.

Incredibly grateful and humbled for the opportunity, hoping to be able to update with some exciting learning experiences soon.

Tuesday, 26 June 2018

Makecode and Microbit - ISTE 2018

As part of the CS Firehose I went to hear about MakeCode and Micro:bit.

Micro:bit is a pocket size computer, in a similar style vein to a Raspberry Pi, (though not as powerful I believe, more like a code-able Makey-Makey), and Makecode is visual based coding software that can be used to programme it.

I thought that MakeCode was a very similar to Scratch and wouldn't be an issue for students or teachers to switch between them. The logic was very similar, as was the interface, AND IT WORKS STRAIGHT OUT OF THE BROWSER! (and therefore is ready to go on the chromebooks!)

Image result for makecode

I also really liked the Micro-bit, and what it can do. There were some really cool and easy-to-get started ideas that are fun and engaging. 

Within 30 seconds of opening the software and plugging in the Micro:bit I was able to get my name to scroll across the LED lights on the device... Really cool, really simple.
Within 10 minutes I had a simple question across the screen, with 2 answer inputs and relevant responses for them.
Is this fun?
[Yes] ---> Awesome!
[No]  ---> Boooo!

This straight away told me that this product has a very accessible floor, where pretty much anyone can plug it in and run with. Yet in the presentation I also got to see examples of some really cool robotic projects, where the ceiling was far far higher. 


Another really cool think about the MicroBit, is that is compatible with Scratch. Therefore there is this fantastic opportunity to extend the Scratch projects that the learners are creating using physical and tangible objects. At least thats the pitch I was sold, I din't get a chance to do this myself, but it's definitely an exciting concept that I'm interested to try out.

Overview (Copy pasted from site) 

  • 25 individually-programmable LEDs
  • 2 programmable buttons
  • Physical connection pins
  • Light and temperature sensors
  • Motion sensors (accelerometer and compass)
  • Wireless Communication, via Radio and Bluetooth
  • USB interface
  • Let's take a look at what these components do and discover how to code them!

Monday, 25 June 2018

Introducing Scratch 3.0 - ISTE 2018

After hearing Dr. Mitch Resnick introduce Scratch 3.0 in the Keynote for the CS Firehose I was really excited to hear him talk more about it in a later session.

Scratch 3.0 is currently still in development, and the Beta version won't be available till about August-ish. However there is a preview version of the software available to try. Which I did. See here.

There are some obvious Visual and interface differences that makes it seem more modern and user friendly. There is also upgrades coming for Sprites and backdrops, Paint Editor, Sound Editor, and Compatibility. Read more about the upgrades here

Current Version

Scratch 3.0

CS Firehose Keynote - ISTE 2018

ISTE Computer Science Network- CS Firehose 2018

Opening Session and Keynote

Dr. Mitch Resnick - Kids, Coding, and Creativity
Professor of Learning Research at the MIT Media Lab.

His Lifelong Kindergarten research group develops the Scratch programming software
and online community (, used by millions of young people around the
world. The group also collaborates with the LEGO Company on the development of new
educational ideas and products, including LEGO Mindstorms and WeDo robotics kits.
Resnick co-founded the Computer Clubhouse project, an international network of 100
after-school learning centers where youth from low-income communities learn to
express themselves creatively with new technologies.

Projects, Passion, Peers & Play

Stories about Kids on Scratch

Abhi - makes scratch animations very cartoon like to express himself - computationally
  • Scratch community provides him with feedback and encouragement.

Bubble103 - School projects. Water Cycle, and research projects
I love the idea of working with kids from round the world
Love Colour Divide RPG - Trailer (made by Bubble103)
Comfortable taking risks and making mistakes. -An opportunity to learn something new.

Charlottes Web - book review, some very good Maths problems here that would fit with DMiC
Storytelling through scratch
Perspective - Making the pig get smaller to show its further away. In the code she had multiplied the size by a fraction

Sunday, 24 June 2018

Balancing Strand and Number with the DMIC process

Before I started DMIC this year I always felt that the balance between teaching Strand and Number was difficult to get right. If you spent too long on Strand you felt like you didn't progress your students enough in Number Strategies.

With the DMIC process I spend the majoritysds of my teaching time in Strand, however there is a strong focus on Number through the Strand teaching. In fact often the Strand element of the problem is only to introduce the number.

For example when teaching a Measurement problem, the context may be converting Kilometers to Meters or vice versa (and that will be a crucial piece of strand knowledge to have/ obtain). However, the actual problem will require the use of number knowledge to solve.
When introducing the strand concept of conversion I would keep the number problem relatively simple, as the conversion is the focus. i.e. 5km plus 3000m or something.
However, as we become comfortable with the idea of converting measurement units then this simply becomes the context for tricky number problems. i.e.  3.05km - 1200m, 0.32m x 4 etc.
Students then decide for themselves whether or not the conversion aspect is necessary.

For this reason the Strand and Number balance has become really easy.
The basic principal is:
- If the Strand knowledge is the focus keep the number aspect simple.
- If the Strand knowledge isn't the focus then complicate the number aspect.

Wednesday, 30 May 2018

Learning new Vocab in a Geometry Unit

As mentioned in a previous blog post I have been attempting to build new maths vocabulary in a meaningful and authentic way. To do this I have been focussing on a particular strand in maths as a kind of "topic" to build on each lesson, for 4-5 weeks in the term.

This term I have focussed on Geometry on and Measurement. I realised from looking at their MathsWhizz results, as well as observations during our daily lessons that a large majority of my class had huge misconceptions around Geometry and Measurement. Particularly anything to do with 'shapes'. In fact when I quizzed few of my kids across all of the ability groups it was very clear that this was an area of confusion and uncertainty for our class.

Not really knowing where to start, I went straight to the curriculum expectations for Level 3.
This really threw me off if I'm being honest. It was too much, and I didn't know how to do it. 
I started with names of shapes thinking this was a logical place to start... it wasn't. In fact all I did when I reflected on my lessons was teach kids how to cram. "Lets learn a whole bunch of names and try to remember them".

I decided that this wasn't going to achieve my goal for "authentic learning". There was no real reason to learn these names other than 'the teacher told me to'. Instead I picked ONE bullet point.
  • Find areas of rectangles and volumes of cuboids by applying multiplication.
In fact I only intentionally planned to teach 3 "words":
  1. Perimeter
  2. Area
  3. Volume
Naturally*, as we battled with these three concepts using the DMIC process, there was a TONNE of vocab that we had to use and understand to be able to be successful in these problems.
*I say 'Naturally' but it wouldn't seem natural at all unless you are familiar with the DMIC process.

I didn't explicitly teach nor plan for these words, but just as you would expect new vocab to be learned in a topic surrounding 'flight' for example, we came across and had to use/ learn a whole bunch of words related to Geometry and Measurement during our problem solving questions.

~5 weeks later~

According to MathsWhizz since the beginning of Term 2, my class average has improved 11.5 weeks in "Shape and Space", 9.5 weeks in "Measures", and interestingly* 13 weeks improvement in "Multiplication Calculations".
*Actually on reflection this makes sense seen as most of the calculations over the past 5 weeks have been multiplicative.

However far more obvious in the classroom is the lift in confidence and use of vocab surrounding this topic when we work on anything related to it. There is technical and precise vocab being used by the learners to each other and in response to each other. 

Overall a really positive result and outlook for the success of this inquiry. Onto Fractions, Proportions and Ratios next :)

Thursday, 26 April 2018

Building Vocabulary through Context

Image result for Builders
Building Vocabulary

In a previous inquiry into reading I learned that new Vocab and understandings can be built up over time successfully, when the texts and learning content are themed around a similar context for consecutive number of weeks.

Therefore it is my hypothesis that this can also be applied to maths learning. My maths planning and teaching centres around a "topic" for 3-5 consecutive weeks. In most cases this will probably be a Strand focus and all the problem solving stories and questions will centre around that strand. The multiple part problem design of the DMIC questions, seems to work perfectly with Strand and Number combined problems i.e Unit Conversion and multiplication, or finding the area of shape then subtracting.

In doing this, I am hoping to build up a vocabulary knowledge base that will build over time and mean that they are capable of more complicated problems and stories. While also having a platform on which to build or gain more concrete understanding around unfamiliar maths vocabulary.

In Term One I felt like this worked really well in the two contexts that I chose. Instead of doing a whole week or 2-weeks on Measurement, we spent 5 weeks, but only focussed on specific measurement knowledge when it came up. Otherwise it was simply was just the context in which we solved our number problems.

Thursday, 19 April 2018

The launch

The Launch is an incredibly important part of the DMIC process.

The "Launch" refers to the launch of the problem solving question that the group is going to be attempting to solve. It should be done with a large group, rather than small groups to save time. I personally split my class of 34 into roughly half, however I pull other kids down or shift them around quite fluidly.

Unpacking and understanding the story of the problem takes up a huge chunk of time. It is important to allow the students the chance to figure it out, without giving it away. This was an issue I had in the beginning where I would rush the launch so that they could get started on the maths thinking. However understanding the story, is just as important for the DMIC process as unpacking the equation. I recently had my first observed session by a DMIC mentor. They told me that the launch involves just two questions; “What is the story about?/ What do we know from the story?”  and  “What are we trying to find out?”

Once you have introduced the problem and taken a few ideas from students about what the story is about, get the large group into smaller groups of 4. Together they will figure out what they think the story is about, and whether they can agree on a strategy they could use to solve it. It is important to make sure that none of the students have a maths book in their hands at this point, and that all the discussion is verbalised amongst the group. The teacher then goes around and assesses how the group discussions are going, but does not sit and work with any one group yet. When the group has agreed on a strategy, choose one student to be the 'recorder' and let them use that persons (at only that persons) maths book and pencil.

In these groups the learners will solve the problem together and then report back, and continue with the rest of the DMIC process. To read these notes we were given in full see the document here.

An example problem that I used during my observed lesson was this:


  • Teacher (T) to read problem in full.
  • T) Question group about the problem
    • Who knows who Roger Tuivasa-Sheck is?,
    • Who watches League?
    • Who knows what the Full back does?
    • What are running meters?
    • What do you think the phrase "clocked up" means?
  • T) ask students to think about what the "story" is
    • What is the story asking us to do
The idea is that all the learners will understand what this story is about, and that they are thinking about whether or not Roger Tuivasa-Sheck will be able to run enough meters each game to meet his goal. This is crucial that they understand the story, before they start thinking about the maths. Therefore when they start thinking about the maths strategy to use they will be able to eliminate some strategies that wound't fit the problem.

Saturday, 17 March 2018

More than a hunch

My hunch for this inquiry was that the DMIC approach could help to raise maths achievement and language acquisition with priority learners in the classroom. 

This hunch was based on previous years experience, where I had noticed that many of my learners working 'Below the National Average' would fail on questions not because of the maths itself, but their lack of understanding of what the maths was asking them to do.  Rather than wrangle with the problem, these learners would too often jump into what they thought (or guessed) the equation was and in doing so work it out incorrectly. Yet when given the equation directly they almost always had a far higher rate of success at answering the problem correctly. 

I believe that the launch aspect of the DMIC process will greatly help these learners. In particular their understanding for what each maths problem is asking them to solve, i.e. what is the story of the problem about, and what are you trying to do with it. Working in groups with learners at a higher level, and watching and listening to their strategies for unpacking the problem will hopefully help as well.

A secondary aspect to this inquiry that I wish to implement, is a stronger focus on language acquisition of technical maths language. The graphs below show that there is a larger gap for this group between the national average in Literacy than in their Maths* (*with the exception of a couple of outliers). My belief is that by increasing their arsenal of "Maths language" they will have greater success at comprehending the maths problems they are faced with. 

The Graphs

These graphs show my target group of 9 Year-Six learners working "Below" or close to "At" in maths at the End of last year. The red line shows the national average. I thought it would be interesting and revealing to show the Maths data alongside the Literacy data to see if there were any trends that I could spot. Not too surprisingly, the most obviously trend was that almost all of these 9 learners were falling behind in their literacy more than in their maths.

I think this helps to support my hypothesis that language acquisition in maths will ultimately help lift maths achievement levels, as it supports my own observations where success has been blocked due to comprehension of the problem.
* I thought it was worth noting that I don't usually consider a "Overall Gloss score" or "Global score" as it can provide quite a warped view on the individual learner if their scores aren't streamlined across the 3 fields. However for this graph it was the best way to show results.

Friday, 2 March 2018

Talk moves

crucial aspect of the DMIC approach is the successful dialogic discussion and argumentation involved in exploring the the different ways of looking at, or solving a maths problem. A useful resource for developing this culture amongst the class is through the use of Talk moves.

If you Google Talk Moves it will produce about 198,000,000 search results. The majority of the links on the first 3 search pages are useful, and will get you on the right track. However, here are 2 links that I found were really helpful for my own understanding.

First Link: What are talk moves?
A summary of the 5 Talk Moves outlined by Chapin, O'Connor, & Anderson (2003).
- Link to PDF

Mathematical Discourse
Five Talk Moves

The teacher tries to repeat what a
student has said, then asks the
student to respond and verify
whether or not the teacher’s
revoicing is correct.
“So you’re saying…”

Asking Students To Restate
Someone Else’s Reasoning
The teacher asks one student to
repeat or rephrase what another
student has said, then follows up
with the first student.
“Can you repeat what he just said
in your own words?”

Asking Students To Apply
Their Reasoning To
Someone Else’s Reasoning
Students make their own reasoning
explicit by applying thinking to
someone else’s contribution.
“Do you agree or disagree and

Prompting Students For
Further Participation
The teacher asks for further
“Would someone like to add on?”

Using Wait Time
The teacher waits at least ten
seconds for students to think before
calling on someone for an answer.
“Take your time… we’ll wait.”

Second Link: Useful cards for the classroom
Some print outs/ ideas to help develop the culture of using Talk moves and 'Talk move like' discussions by the Virtual Learning Network, Ministry of Education (2014). Copyright, Ministry of Education, NZ. 

Chapin, S. H., O'Connor, M. C., & Anderson, N. C. (2003). Classroom discussions: Using math talk to help students learn, grades 1-6. Sausalito, CA: Math Solutions Publications.
  • Miller, L. (2004). Talk Moves (Unpublished Resources), Virtual Learning Network: Ministry of Education, NZ.

Where do I start with half-class grouping??

As I already mentioned in a previous blog post, grouping my maths class into mixed ability groups was a difficult concept to get my head around. However the concept of also splitting my class into only 2 groups (i.e. half the class in each group), left me feeling pretty clueless about where to begin. This is what I did.

First go
I decided to start by finding out what it was like to teach half the class as one group. So, instead of worrying about how to group them, and who to group them with just yet, I simply asked to see the Girls and Boys as seperate groups. The learners absolutely loved it, but in hindsight (and what a beautiful thing it is) this may not have been the best decision... BUT, it did allow me to get a feel for what it would be like to have half the class down on the mat.

What I noticed:

  • We can fit - One of my main personal resistance's to this approach was the fact that I believed I would not fit a half-class group on the mat. Well we did, and it was easy. 
  • Some learners will shine - After the initial shyness wore off, there were some clear stand outs that loved being able to share their thinking, or their "way" of doing the maths. They loved having the attention of the whole group, and this was clearly their element.
  • Some learners will freeze - Even some kids who I know will happily share their thinking in a small group froze. I believe this must of come from a place of insecurity, i.e. knowing that they were in the same group as the "smart kids", and not want to get shamed for being wrong.
  • Confident kids will convince more capable kids they are wrong - Confidence is key! I had kids working at Early Stage 5 convincing other kids working at Late Six that they themselves were right with their "guesses", while and the mathematical reasoning and computational thinking was wrong. 
  • All of us were going to take some time to get used to this - I talk too much. Both myself and the kids are going to need more practice at this approach before we have any success.
  • It was fun - All of us left the lessons buzzing. 

Second go:
After a week and a bit of staying just the boys and the girls. I finally decided to regroup. Initially I asked each group of boys and girls to split into 2 groups and then combined them from there. I later read that social groupings does not necessarily (and in most cases does not) mean "friend groups". So I rejigged some of the kids around after that. After I had done this, I looked at their current achievement data, and found that the kids had organically done a pretty decent job at mixed ability grouping all on their own! The ability spread was pretty even across both groups, and I hadn't had to do any of the work, fantastic.

What I noticed:

  • It worked a lot better - Both the boys and girls worked together well, and took the lesson far more seriously now that the genders were mixed. However, I'm not sure if this was due to being mixed, or whether it felt more like an 'official' maths group, and therefore should be taken more seriously. Either way it was good news.
  • Confidence was improving - I started seeing less of the initial "hanging back" that I noticed, and more kids were piping up. I also noticed that my higher ability learners were now backing themselves a lot more. Instead of simply trusting the "loud" kids.
  • It was still fun - Aside from a small number of resistant and/ or very quiet kids these lessons are becoming a highlight of the day for everyone. 

I'm looking forward to learning more about the DMIC approach, and getting better at it. It's exciting, and the more I experiment with it, the more confident I feel. I just hope/ fear that I'm not wasting too much precious learning time figuring it all out too much..