Tag: Mathematical Practice Intensive

MPI 9: Creating and Sharing with Mathematics

Learning is forever evolving. As a lifelong learner, I ensure to give myself the tools to help me further develop my understanding with what I am learning and the world around me. So, how do I replicate this for my learners.

This year we have worked towards understanding how Maths fits in whichever curriculum we use. I have spent the time agonising about how I am going to amplify learning from 9 days across the 3 terms. Not only that, but with the curriculum changes, what that look like for our school, our learners?

MPI has been ‘RATE’ Kaupapa all in one; where I have been challenged in my thinking and how I would reflect this as evidence for all of my students. Every session has been a challenge for the mind and interestingly enough, I have ensured that I have been able to identify the components I can challenge my students and their learning with and expose them to Mathematics in Our World.

What did I learn that increased my understanding of the kaupapa and pedagogy of the Manaiakalani Mathematics Programme ? 

  • How Maths can be digital with sharing and creating? It does not have to be just different sites to engage. How the pillars are pivotal but also how they work within the curriculum.
  • How my learning, and how my teaching practice can be amplified to engage student, colleague and whānau learning which aligns with the Pedagogy and kaupapa of the Manaiakalani Mathematics Programme.

In all honesty, I learned resilience, time management, patience and determination. All of which in some way talks about my context. My kaupapa and pedagogical knowledge of the Pillars of Mathematics and the tools I have gathered to enhance my kete have come from these 9 days. I have learned:

  • How Maths Talk can help the development and understanding of students and their thought processes. Thinking out loud is powerful.
  • How Maths can be digital with sharing and creating? It does not have to be just different sites to engage.
  • How the pillars are pivotal but also how they work within the curriculum.

One of the biggest takeaways I have learned is that for our students, opportunities to learn, empowerment, resilience and determination are needed. The key to unlocking the learning for my learners is enabling them to explore (tutu), engage (whakauru) and to ako, hanga and tohatoha.

For me, allowing the natural process of creating should enable my students to gain confidence and rigour in their Maths Learning. My explicit teaching, careful planning, better understanding of the new curriculum will also enhance my capability and confidence to teach this. Rewindable video or tracking through each component we’ve covered, should allow me to remember what was taught.

Our facilitators come from varying strength bases and are pivotal to the development of my learning. Mentorship is important as you need someone to observe, critique and help amplify your learning. At times, this became quite difficult, but I could call upon my peers to have professional conversations with. Thank you.

Elena, Georgie, and Donna – Thank you for being patient and motivating with your visible passion for Mathematics and Statistics.

MPI: Day 7 – Geometric Thinking

With the impending unknowns being implemented into our Curriculum, what do I need to teach?

Geometric thinking is what I call the creative and most culturally responsive strand of Mathematics and Statistics.  It is the strand we can make more connections with in terms of our Māori and Pacific patterning. Geometric Thinking has to be one of my strengths and definitely the strand that allows us to  be creative and identify the patterning and reasoning behind our thinking. However, as all strands connect, you have to allow growth in other strands like Measurement, but if we can’t make connections with Maths to everyday life, then we have to engage our students with what Math looks like in their world.

Whenever we have Geometry and Measurement, I automatically think of the fence line which surrounds our school and how in some cases it inhibits how we think and how we need to push past the boundaries (also with the fact that it is geometrical, is a running pattern, has parallel lines which are there to push past). This is what I teach and my students often talk about the shapes in our environments. We have to visualise and think about what any of our learning looks like through our own eyes. This will determine whether we will be successful or not. Our favourite geometrical task is that of Tukutuku, Māori and Pacific art as a means of expression.

Dorothy reminded me today of how the ‘Pencil and Paper’ is an important tool to assist us with reflection and notes (as it empowers us to speak), but it is the same case with our digital tools (in our case, our chromebooks). She reminded me that the simple tools I used before are just as valuable and perhaps even with the impending changes we are having, that we can still utilise the tools we have and simply Amplify.

 Amplify:

For teachers, harnessing technology to amplify effective practice has TWO sides to it

  • Getting
  • Giving

Some of us do both! 

Continuing to amplify my practice in order to engage learning, but also inevitably encouraging this practice amongst our peers within our school and further a field to share our practice and our resources.

Within my learning today I need to give myself more time to unpack the learning and make it mine so I am able to amplify the learning. I am confident with teaching this strand, I just have to ensure that I take our students with me along the way and sometimes beware of the good ideas. There are many times where we can go too wide and I always think about ‘The T Shaped Literacy’ which always says wider and deeper.

Implementing Maths Talks as a warm up task resonates with me more as a warm up. This will allow our students to understand and clarify the questions in our PAT tests which inhibit their full understanding. I don’t understand why Maths suddenly becomes a Reading Test. 2D and 3D shapes are great, but I want to prepare my students for the PAT assessments too. How do you teach them the skills when they don’t have a clear understanding of what they are being asked to do?

Jo Boaler explains about Quick Image. This is a warm up task where you can identify how many objects there are with a simple glimpse. This task will allow the practise of imaging in your head. It encourages learners to find efficient strategies to determine the quantity of an object. Quick Image would be great to get our minds going and definitely encourage talking about our strategies. 

I think the small group workshop task would sit as another task following the first quick image.

I thoroughly enjoyed this task as it will engage my learners, however they will probably get side tracked with the digital tools, so I will definitely have to time the activity.

Angles are a part which I would like to focus on this time with a big workshop and drive on the use of vocabulary throughout Geometry. I am excited and my students are going to be excited when we explore and plan our next week together.

This strand will tie in well, with our number work and financial literacy inquiry.

Our wider community, will enjoy perhaps hearing our students talk about our project. Sharing their vulnerabilities when it comes to financial literacy and also how we can use Geometry in our Inquiry.

What a fantastic day of learning today! What a great week of Maths and Statistics we have ahead of us, especially with Financial Literacy and a snippet of Geometrical Thinking. There is much more to share so I will do so as it develops.

Thank you to the MPI Whānau.

Mā te huruhuru ka rere te manu. Adorn the bird with feathers so it can fly . This proverb reflects the idea that a bird cannot fly without feathers BUT if you give the bird what it needs, it can thrive.

MPI: Day 4 – Numbers

Within Literacy we talk about the importance of vocabulary. Explicitly teaching vocabulary in Maths ensures that we emphasise the importance of using and teaching the correct vocabulary and visual representations. Accordingly why do we need to focus on teaching vocabulary?

  • Students need to learn math terms because they are essential for understanding concepts, communicating ideas clearly, and solving problems effectively.
  • We need to connect math concepts with vocabulary and symbols to help students link abstract ideas with concrete representations.
  • It’s important to use visual representations so learners can see what it looks like.

Here’s an example shared to us by our MPI Team:

You can see here that this particular chart uses the term, brief information to explain and then a pictorial representation of its meaning.  I can see a few of these popping up when developed and not only in Maths.

Random side note: To Math or Not to Math – what is the answer? In NZ, we say Maths, some say Pāngarau, in US, they say Math. It can be confusing as it is confusing for students but how many of us use Maths or even Mathematics as a subject label?

In my opinion, our attitude towards Maths is always based on how we have either experienced it or have been taught it.

This would help with understanding how our students solve problems. I think that communicating our thought process should help this. It would allow our articulation of our thought process and give students opportunities to learn more vocabulary – so user friendly talking frameworks should help.

  • What did I learn that could improve my capability and confidence in teaching mathematics?

Encouraging to see that my content knowledge has not got lost and that I am achieving what my students need me to know. Place Value is tricky and interestingly enough I have a couple of students who use algorithms which is their ‘go to’ strategy  taught to them by their whānau. These students are also those at Stage 6 & 7 in Maths, but they have confusions especially when looking at decimals and place value.

I enjoyed looking at the different components of Number and finding other ways to teach fractions, decimals and percentages. How can you stick to one topic?

I was given more time to look at a plan and incorporate it, so time to unpack what was said, understand what was shared and think about how I might implement it with my class. Fantastic to see the examples and be able to use them to start my implementation or practice and then to create my own.

  • What did I learn that could be used with my learners? 

One reflection I have is that students identified themselves that you can see Maths in all activities we did at the marae and I’m grateful they are making connections with an authentic context. Our trips to the Marae and to the Museum made this connection to our learning, but the Maths development will be huge.

 

Learning is not easy for all and in my view, Maths needs a culturally responsive lens, therefore ensuring that our Rich Tasks and our Problem Solving Challenges are contextual and engage students by allowing them to make a connection to the task. Everything I learned today will help with student learning, but the application of it will enhance student engagement.

My rich task needed to be of multiple entry points with multiple ways to solve it, but my beginning rich task I created borders on an authentic problem solving task (which is fine), but it can be rejigged.

New learning means more reflection

 

 

 

  • What did I learn that could be shared within my wider community, with either colleagues, or whānau/aiga? 

The idea is once I understand and have a better idea of how it works for me, I will hope to develop it with others who may have done DFI, and RPI to further develop our own Pillars of Practice for our school. Then we can have an authentic learning hub which we have taken time and pride in.

Woah! what a lot of thought. Thank you to the MPI team.

Sitting in Draft

Who knew that there was another place to share my thoughts and edit them as needed they became a lot clearer? I think its called ‘my drafts’.  

The empty blog which seems to sit untouched except ‘in the magic space – my draft’, I can take my time to reflect, to think, to ponder and then to write some more. The task required us to reflect on the opportunities you afford to your learners to communicate their thinking and ideas (in the context of Mathematics) so what does this look like?

I think in most instances, I allow a lot of this to happen organically and this has developed over the many years of teaching, mentoring, collaboratively and also as a learner. As a learner, how would I process my thinking without reflecting, without understanding what was being taught and without having the opportunity to ask questions and to validate my thinking with my analogy or my interpretation of what is being talked about or taught? It would cause me confusion if I am not corrected, and it would cause me angst if I was not able to verbalise my thinking or the opportunity to validate my thinking. So, what opportunities would I afford my learners to communicate their thinking and ideas?

Ideally, affording our ākonga to articulate their thinking and ideas would be grown through what they do throughout all their learning. In the beginning, there were habits that needed to be unlearned, and new habits that needed to be enhanced. Talking frames helped at first, as well as open ended questions students could be given to build their ideas and to help direct their kōrero.  So, making sure we engaged students in helping to create a context of  Math problems helped with examples that were given a Māori and Pacific context, eg. Marae or art pieces like the Tivaevae patterns is one of the ways I try to give them time to make learning relevant for them.

How do they process their thinking or how are they given opportunities to communicate their thinking and their ideas? These are some ways:

We use the Talanoa /Manaaki Fono process (adopted from my experiences with Academy Ex). This is where we share any ideas in a safe space like our ako groups  where they are encouraged to explain their problem-solving processes and strategies, and then the speaker shares in our waka group.

The use of collaborative learning strategies is encouraged more to emphasise that Maths and learning in general is a means to collaborate in order to achieve a common goal.

Modelling my own problem-solving process by speaking (think aloud) shows students how to articulate their thought processes as they work through problems. This strategy I can encourage when students are solving problems independently or in groups. Recording an audio record of their thought process.

Having students articulate through pictures, numbers or by writing their strategies (recording) in a group modelling books or into their individual math books where they regularly write about their problem-solving strategies, thought processes, and reflections on their learning has helped. This practice helps them organise their thinking and provides a record of their progress.

Facilitate regular waka or classroom discussions where students share their strategies and solutions. Use open-ended questions to prompt discussion and encourage students to explain their reasoning. Promote a culture of respectful listening and constructive feedback (Ground Rules for Talk)

Asking students to share their strategies with their peers and then blogs. This allows me to give our ākonga timely feedback and reflections. This would encourage them to reflect on their own and their peers’ explanations to identify areas for improvement and growth.

Students who are comfortable to do so will sometimes record themselves digitally showing how they solved the problem, this however is not consistent but is being developed.

I don’t know if there is a right way or a wrong way, but I am developing ways in which to encourage think aloud time and to give our students enough time to process their thinking with confidence and in a safe space.

I think though knowing my students and their quirks, that this is all I should introduce them too as we have been developing this all year round for all of our subjects. These students are not used to being asked their opinions, and they’re definitely not asked to communicate their thinking process or ideas because in their homes, some of our students are brought up to be seen, not heard! Cultural responsiveness needs to be considered but is not seen as only by ethnicity, but also by community norms or what society has deemed appropriate.

Talking the Whakaaro (Thinking)

He Whakaaro Noa Iho (A mere thought)

When does a kaitiaki not become a kaitiaki? An annoying thought has recently come to mind whenever someone asks me about what I do and where I teach. First and foremost, I need to clarify in my mind what I do … and recently my answer in the last week has been “I’m acting AP, but I’m caretaking a class of vibrant Y5&6 tamariki.” I do not know where it came from, but previously it has always been, “I am a kaiako at EHS kei Papakura.” The annoying thought is WHY? Why has it changed and why should it matter?

If we are truly Kaitiaki (Guardians) who and why does it matter who that is and what that entails. All that should matter is these children need us to be true to who we are and how what we do impacts on them and what they achieve. This is why whānau should be involved. Our knowledge as Kaitiaki is need in the guidance we provide and the opportunities we present.

MPI: Survey: What Type of a Mathematician are We?

Firstly, what an intense catch up couple of weeks it has been, but all tasks done and great conversations had. Recently, we had the task of surveying our class with a Survey to understand ‘What Type of a Mathematician are We? – I asked them some questions on what they thought might be in the survey. It was great, watching them both struggle and articulate what they thought the questions mean’t. I asked them to do the survey on their own, but after the weeks we spent talking about how we could collaboratively work smarter, harder and encouraging talk, they were suddenly asked to fill the survey out alone. “Oopsy!” – I allowed them to clarify the questions amongst themselves, and I also encouraged them to give examples of what the questions mean’t. Once they understood the scoring system, they were away.

                               Click on the image to find the Survey Results

 

So to the results: I found more value in the discussions about the results except, the whole experience with clarifying their understanding of what the questions were asking and what was mean’t also reminded me that for some the language in the survey or the need to comprehend what the question was asking them needed clarity. It also needed for the language to be considered as a global language. In the PAT Maths Test it asks you to consider prompts like 1 – like me and 4 – not like me or similar. Some students felt confused, but this is like what we need to do when thinking about assessments and the opportunity for students to ‘Talk the Whakaaro”.

We discovered that we do take into account that we all enjoy Maths and we are confident with this. Students felt Maths is a strong skill which we have been using in class and out in the playground, we just haven’t made the connection yet that Maths is everywhere. Our summaries seemed quite obvious, but I wanted to probe them more because it seemed too good to be true. I felt they were holding back and so we began looking at a padlet which allowed them to explore this more.

The validity of the data came to mind for me, and if this data was true then we have lots for me to worry about and nothing to do but to teach the skills and strategies as half the battle of confidence and engagement is already done. However when looking back at their PAT data and considering what our class went through at the time PAT testing was done, there were lots of thoughts and considerations I needed to address. One part in here which did concern me was the part I played in how I was perceived in the survey especially around whether I thought they were good at Maths and also about the feedback I gave them. Something for me to cover as a goal perhaps.

I have many thoughts and the discussions were rich, but let’s explore more with MPI first to look at what we can implement soon.

MPI – Day 1: Mathematics is Core to Learning

Mathematics is Core to Learning – Kaupapa and Shared Pedagogy 

Where do I begin? In Te Ao Māori, Mathematics and Numbers come naturally in all facets, but how do we teach it so we achieve the higher thinking order for both our students and within our learning as teachers?

Today MPI culminated what I had hoped is normalised teaching and learning in our environment, but also highlighted some of the ‘misunderstood’ habits I have attained since switching between the roles of Leadership and Classroom Teaching.

So, reflecting on the goals of MPI today gives me an opportunity to reflect and to think critically. I’d like to think that there is a purpose to my learning and then fill the gaps in my knowledge and thinking.

 

 

 

 

 

 

 

This is an important reminder that there is most certainly a purpose to our Professional Learning.

Dorothy Burt reminded us of the role teachers play in the innovation of Effective Teaching Accelerated Learning. In the early days of Manaiakalani, there were many early adopters who with the (Now) primitive nature of Technology still managed to find ways to engage students with Mathematical and Statistical learning.

During today’s session, my understanding of the kaupapa increased as I discovered more about Jessen’s (2013) point of ‘The notion of acceleration” in terms of increasing the pace of progress, but the part which resonated is the part of her quote which comes from “To achieve acceleration, your students need to learn at rates that are higher than average, so that they “catch up” Jesson, 2013. 

This inevitably comes from what we as learners, teachers and leaders expect from our learners. Our expectations need to be responsive, relevant and accelerated, but I also advocate that it needs to be contextual to allow growth in our learning communities too.

The Pillars of Practise has become common language, which I have heard about through those who are doing or have completed RPI (Reading Practice Intensive). I consider this an issue across the curriculum as there is no common language or framework. From school to school, we all have localised language or terms, and in some instances localised language which differs from class to class. How do we factor this in when students move on to other classes?  The Pillars will be the foundation of our learning along with the pedagogy of all of this. 

Following on from this, I think students can make huge gains over time, but it also needs to be consistent, applied, monitored and reviewed. The hard discussions need to be had and ownership of the learning needs to be clarified.

What does a ‘good’ Mathematician look like? 

According to BES (2007)   and according to my notes:
  • Think logically – have a process
  • Relate problem to known context
  • Know numbers
  • Have lots of strategies to solve problems with understanding

Each could argue the point, but what amazes me is the fact that this could also be applied across the other curriculum areas.

What Makes A Good Mathematician?  

Learners also need to be engaged with what they are learning. Making this contextual and interesting will become a highlight.

With reflecting on today’s session, I’ve often thought of myself as a confident and capable Mathematician until one year whilst having Professional Development imposed on me without the grounding of getting to know me or what I had been doing prior to this professional development. I think making a connection and expressing Maths visually would have been a much better way to make the learning relevant for me and most certainly my practice. I feel I am strong in my capability with Maths, but now it will be my confidence to teach this that will be a core part of my learning here.

There are many resources found today that will be useful to implement, but for my own development,  I’m taking some much needed reading from Kazemi, E. et al. (2016) ‘Listening to and Learning from Student Thinking’ which talks about how I need to give students time to voice their understanding and their strategy to allow me to better understand their thinking and their confusions. It also prioritises gathering data about and with students to ensure equity occurs.

Growth Mindset – As with all the learning we have previously learned, I have always taken what resonates with me or what makes me connect to deepen my understanding and with my cultural lens implement it into our context, with the understanding that students will critically think and ask questions to understand it themselves. This means … sometimes we have to unlearn stuff and then learn new habits. Speed is not Important, so learners have time to clarify, understand, process and articulate their learning. 

Wharehuia Milroy, “Tuwhitia te hopo, mairangatia te angitū!
                                                  Feel the fear and do it anyway!