MPI - Create and Share in Mathematics

 Our last day of the Mathematics Practice Intensive for 2024!  I have to be honest and say that I will miss the sessions and all of the wonderful learning that has transpired.  My goal is to now use all of it in an absolutely amazing year of maths next year!

We learnt about another example of Maths Talks which was all around Images.  I can really see that my students are going to enjoy these activities and the chance to be detectives and really investigate all of the maths they can see in some really great images.  We were shared lots of great places in which to find these images.

An image that really resonated with me today was the brain image that really summed up being creative.  I actually think I will use it with my students too, it might even become our symbol for meaning Create.

I was also thinking that I want to have a visual presentation of all the different ways that students can create next year too.  Maybe as simple as having a section of wall where I add in the logos of the different sites etc. that they could use.  This could then ensure variety and choice in their Create Tasks.

When we are planning for these create tasks we also need to go through the process of:

• Active Verb
• Object Created
• Purpose
• Audience/End User
• Constraints

This will ensure we are creating opportunities for more genuine learning in our create tasks.

I am still working on the Sharing part of the equation.  I am leaving today's session with renewed focus on ensuring that my students' learning is shared in some way, this could be on their blog, this could be orally, but whatever it looks like, it is a very important part of the whole learning journey.

So, although it is the end of the MPI, I feel like it is only the beginning of my maths journey!!  I will leave for now with a quote that resonated with me:

Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.

— William Paul Thurston, American mathematician  

MPI - Statistics and Probability

MPI Day 8 was all about Statistics and Probability.  I really enjoyed today and it seemed to fly.  Statistics just seems so much easier to digest and teach than the likes of Geometry and Measurement which have so many parts to them.  

The Maths Talks focus was on Data Talks and I thought the examples shared with us were really great.  I can't believe I have never thought to add this into my programme before.  I really feel like I need to be smart about how I integrate all the Maths Talks examples into my daily programme and perhaps not just in maths time.  Keep it topical...there would be lots of data that could be shared at the moment about the US election, with summer heading our way there will be data about weather and temperatures and then perhaps Christmas present popularity data!

I also really liked the connections made with Critical Thinking.  Teaching students to take in the information or data with their smart critical thinking hats on.  Thinking about if the graph is a fair representation of what the data is actually telling us?

The CensusAtSchool site will definitely be getting a good look at for the beginning of next year.  From the Fabulous Feet lesson to Data Cards, lots of really great resources and ideas for teaching Statistics.

Right I am off to plan a few Probability lessons and hope that they become my most successful maths lessons ever that I can share in the next session!

MPI - Geometry

Day 7 of the Mathematics Practice Intensive was on the topic of Geometry.  There are many aspects of what qualifies as Geometry including 2D shapes, 3D shapes, angles, transformation, position and orientation.

We began as usual with a Maths Talk strategy.  Today's one was Quick Images or Subitising.  This is when you display an image of some sort (one that has items that can be counted) and then you take it away after about 3 seconds and the students work out how many objects were in the image.  The conversations are very interesting around how students saw the items and then how they worked out how many items there were.  The Jo Boaler video below was an excellent example of how you could carry out one of these Maths Talk sessions.

Just like I found with measurement, the strand of geometry is very vocabulary heavy.  This will mean ensuring I am using the TIP charts. lots of repetition and perhaps integrating some of it into my Literacy programme...just a thought!

Reading back over my last blog post about measurement I said that I was going to plan a week's worth of workshops and a rich task all about angles and teach it to the whole hub.  Success!  I did exactly that and so now because angles is also part of the geometry strand I am going to add onto that learning and cover the interior angles of triangles and quadrilaterals with my students.  

I was amazed by the amount of online tools that we can use while teaching geometry.  I had used a Maths Playground activity this week where the students used a virtual protractor to measure angles. I will be looking at what other tools I can use when we look at the interior angles learning next.

My mind is whirring away at the homework task where we need to bring an integrated maths lesson.  Do I link it to my angle teaching and learning somehow or go somewhere else entirely?!  Watch this space!

MPI - Measurement

Day 6 in the Mathematics Practice Intensive was all about Measurement.  I don't think I had connected how much you can use multiplicative thinking and working out during the Measurement topic.  This got me thinking about integrating strands (again!) and that perhaps this would be a great one to integrate into next term's teaching and learning because I want to go back over addition, subtraction, multiplication and division.  We have already 'done' measurement this year but how good to be able to cover it again and add new learning or consolidate the learning already covered.  The part that stood out to me was the perimeter and area part.  Perimeter is all about adding but also stepping it up if possible and using multiplication.  I will also make sure that I am making the connections between arrays and area.  Two birds, one stone, as they say!

Some thing else that really resonated with me was the teaching of angles.  I am going to create a one week whole class/hub sequence of lessons on this.  We will do learning around the vocabulary leading into actually measuring angles.  I am thinking I will plan four days of good explicit teaching lessons and then make the fifth day a rich task.  I am actually quite excited about this and think it will be a great first week back next term topic for maths.

Our new Maths Talks strategy was Number Strings.  The first one I have planned to try was actually one that was in a video shared with us today.  It fits so well with multiplication and arrays.  It's also a great one as a stepping stone for using place value to multiply numbers and using times tables we know to work out other equations.

So once again, leaving the MPI day armed with things to try and lots of resources to still explore!

Algebraic Thinking

 Day 5 in the Mathematics Practice Intensive covered all things algebraic!    

The biggest take away for me was the vocabulary.  This also linked with something that someone said today and I thought about how often I talk about this with my colleagues too - "Lots of students can do the maths, they just don't understand the vocabulary.  They don't understand what they are being asked to do in the question/maths problem"  I can see the value in using TIP charts a lot more regularly in my programme and a lot more revising of vocabulary.  

I also hadn't thought about the fact that all those symbols that we use daily in maths are actually crucial for algebra and also crucial for students to actually understand what they mean.  For example the good old equals sign not just meaning that something equals something else but that two sides balance, they are the same. 

I think it has been fair to say that Algebra has been a strand of maths that we teach but perhaps as a stand alone topic when it should be integrated throughout.  If you actually look at what algebra is, we are teaching it throughout our maths programme but I don't think we are being specific enough about it being algebra.  The changes I am going to make to specifically teach the vocabulary that goes with it and what it is, will hopefully stop students from feeling like algebra is a topic to be feared!  

The brilliance of algebra problems is that they can also be used to cover some choral counting, shared visual representations of what problems actually mean and number talk strategies.  

I am heading away to rethink my maths sessions.  Is there a way that I can include the choral counting, number talk strategies and algebraic concepts/vocabulary more regularly into my maths daily/weekly planning?

Number : Whole and Rational

Day 4 in the Mathematics Practice Intensive covered Number but more explicitly the parts of number that our students find to be their sticking points, those parts of number that students seem to struggle with.  So as you can probably guess this included Place Value, Fractions, Decimals, Percentages and Integers.

Dorothy's reminder of what RAT stands for was very timely and it is always great to refresh your knowledge of our Manaiakalani pedagogy.  Recognise Effective Practice, Amplify Effective Practice and Turbocharge Effective Practice.  I really thought about the Turbocharging part of our teaching and learning today and how I can really embed students reflecting on their learning through the use of our technology and also building up their confidence in their maths discussions.

Choral Counting was a great reminder...another one of those strategies that I used to do but has been lost along the way somewhere.  I can see that this will be brilliant to bring back as I start to teach my students about fractions and decimals.  

New learning for me today was something called a TIP chart.  I have used something similar but have never come across the TIP acronym before.  This will definitely be added to my teacher toolkit for weekly planning and not just in maths, I can see it being used very nicely in lots of areas.

My focus going forward is to complete some teaching and learning in the areas of fractions and decimals to see where my students' knowledge is.  I will be finding all of those manipulatives - physical and digital - to make this journey as clear as possible.

Planning a Maths Programme

Day 3 in the Mathematics Practice Intensive was all about Planning a Maths Programme.  Not, here is what you need to do, now go and do it but here are all the options and resources, choose what is best for you and your students and go and do it.  

It's amazing after each day of this intensive learning in maths how my thinking and reflecting on best practice is altering and my list of what I would like to change or freshen up, as we keep saying, is swirling around in my head.  I have that slightly annoying quality that really makes me want to freshen it all up immediately and be doing it as perfectly as possible (What would that look like...different in every teaching space around the country!)  I have to be sensible and change it bit by bit and mold it into a maths programme that I am happy with and is ensuring engagement and success for my learners.

Today we covered The Joys of Timetabling, Grouping, Planning for a Rich Task and Follow up Learning.  Structuring your maths week so you are fitting in workshops, oral language, rich tasks in flexible groupings and then some investigation tasks just seems to hit all the right targets for me.  

Moving forward I am going to continue to tweak my Task Board to include some more of the learning from today, mostly around the follow up tasks and basic facts resources that are available.  I will also move towards introducing a rich task and I like the idea of doing this on a Thursday because I could structure my workshops around the mathematical skills and strategies that could be useful to solve the problem.  Thank you to Sarah, who is on this journey with me, for suggesting that you could tell the group the problem and then the answer so it becomes about the best strategies to use to get to the answer, rather than the fastest person to solve the problem.  I am hoping that the injection of real contexts, rich tasks, more talking and investigations will switch my learners from feeling ok about maths to thinking it is pretty cool!

Right, I am signing off for now and will be checking out the resources above to create a Rich Task to share for homework:)