MPI - Day 7: Statistics and Probability

Today's focus was understanding Statistics and Probability. We looked at the following areas:

1. Data Talks
2. What is Statistics?
3. Statistical Investigations
4. Lies, Lies and Statistics - Statistical Literacy
5. Census at School
6. Take a Chance - Probability

Today's session has got me thinking about how I can make teaching statistics more engaging and meaningful for our learners. Today really highlighted the importance of understanding variability and using statistical enquiry to explore real-world problems—and I want my learners to feel that statistics isn't just about numbers, but about making sense of the world around them. One idea is to get the kids more involved in collecting and interpreting data that matters to them. Maybe they could do investigations on topics they care about, like tracking how much recycling we do at school or comparing their favourite sporting events. 

I also want to help them get comfortable with different types of data—categorical, numerical, multivariate, and time-series—in a hands-on way. I’m thinking about activities where they can sort and compare data from the class or observe changes over time, like in a science experiment. Making it practical and connected to their everyday lives could really make these concepts stick.

I really enjoyed the Lies, Lies, and Statistics session. It is so true that data can be misused to mislead the intended audience. As teachers we need to lead learners to develop a healthy skepticism when it comes to interpreting data. We talked about evaluating data, spotting errors, and understanding how different visualisations can sometimes be misleading—skills that I think are crucial for our learners, especially in today’s information-heavy world - especially when viewing this type (or any data for that matter) on social media!

I want to bring more opportunities for critical thinking into our statistics lessons. We could look at some real-life graphs and discuss whether they’re accurate or if they might be misleading. Questions like, "What is the graphic trying to show?" and "Is there anything about the graph that could mislead someone?" could be great prompts for group discussions. Or even have the kids create misleading data and see if their friends can pick it?

I'm looking forward to diving deeply into Stats in the next few weeks!

MPI - Day 7: Geometric Thinking

Today's focus was understanding Number through Measurement. We looked at the following areas:

1. Quick Images (Subitising)
2. What is Geometry?
3. 2D Shapes and Angles
4. 3D Shapes
5. Transformation and Symmetry
6. Pathways: Position and Orientation

Today was a great hands on session. I was reminded just how fun geometry can be, especially with all of the online tools that are available. If I was teaching this subject now I would be diving deep into the interactive activities. Getting learners involved by measuring angles and identifying shapes is a great way to make learning more engaging. It helps them not just understand the theory but also apply it, which ties in nicely with the curriculum's emphasis on building thinking and problem-solving skills. I also like how these tools give learners the chance to work independently, which is perfect for catering to different learning speeds and styles. Plus, they offer variety, so I could see myself using them to mix things up in lessons. As always I’d probably add some real-world examples to make these ideas even more relatable for learners, especially since as an adult its rare to use protractors, triangle angles, etc on a daily basis.

The thing that strikes me the most during today's session is the vocab that is used in Geometry. Geometry involves many specific terms, e.g., vertices, edges, faces, polygons, prisms. These will be new to many learners and may seem abstract without proper introduction. As a teacher, it’s important to ensure that learners not only memorise these terms but also understand them in context. This means I would need to use key vocab consistently during lessons, ensuring that definitions are clear, and constantly reinforcing these words through repetition, visual aids, and hands-on activities.

Side Note:

How cool is tessellation art?!

  

MPI - Day 6: Number through Measurement

Today's focus was understanding Number through Measurement. We looked at the following areas:

1. Beginning multiplicative thinking
2. Multiplicative Thinking: Fractions and Decimals
3. Exploring length, perimeter and area 
4. Measurement: Volume and Capacity
5. Measurement: Triangles and Angles 

Today's learning reminded me how much fun measurement is to learn but especially to teach! The last two sessions of today's learning is what interested me the most. 

Today's 4th session centered around volume and capacity, focussed on how learners can measure the space objects take up (volume) and how much containers can hold (capacity). I reflected that this is really about helping learners make the jump from 2D to 3D thinking, which for some of our learners is a really tough progression to make. Once again (and this has been a reoccurring theme during the MPI sessions) we need to constantly make connections for our learners to everyday situations—like in this session, measuring liquids or figuring out the capacity of containers. This keeps the maths learning practical and easier to visualise, especially when using manipulatives - which is a must!

Today has really got me thinking about what our learners need to help them pass the PAT tests (short term) and the prerequisites (long term). It was really interesting to see what questions seemed to stump our year 8 learners. It’s clear that many students find measurement challenging. The key reminder yet again is to keep it interactive—use manipulatives, get students visualising their work, and always tie it back to things they know from the real world! As teachers, it’s up to us to keep building on this and ensure students not only understand the mathematical concepts but also see how maths applies to their everyday lives.

Today was full of great reminders. I'm looking forward to helping learners grapple with measurement next term!

MPI - Day 5: Algebraic Thinking

Today's focus was understanding Algebra. We looked at the following areas:

1. Early algebraic thinking
2. Symbols and Expressions
3. Number Properties
4. Equations, Patterns and Relationships
5. Variables and Linear relationships

Today's learning highlighted for me the importance of developing algebraic thinking in learners, guiding them from basic pattern recognition to more complex generalisations and equation solving.

This got me thinking about how important it is to use a scaffolded approach - where learners progress through stages and can deepen their understanding of patterns and relationships. This gradual progression is crucial in helping learners transition from concrete to abstract mathematical thinking, just like in other maths domains, but in my opinion it's even more important. This is because algebra can be so much more scary for learners who aren't used to the vocab or used to the notation of algebra.

Once again, the integration of real-life applications and visual aids are needed (even more so than basic number examples) to help enhance comprehension and making abstract ideas more tangible for learners.

I have also been reflecting during this afternoon on teaching variables to kids here at PES. It got me thinking on the struggle they may have with the shift from arithmetic to algebraic thinking, so patience and continuous reinforcement will be key here. Especially breaking down the idea that a variable is just a symbol that can represent different values and why we might need this or find it helpful.

We'll also need to encourage learners to explore and experiment with variables in different contexts, allowing them to see how this might be used in their real life. 

If I was teaching this to a group of kids for the first time again I would be making sure to regularly assess understanding through discussions and practical examples in order to see if I could break down misconceptions or confusion. 

Today was thought provoking, especially the last 2 sessions and I look forward to helping teachers to teach algebra with their learners!

MPI - Day 4: Number

Today's focus was on knowing and understanding our learners as Mathematicians. We looked at the following areas:

1. Maths Talks
2. Understanding Place Value
3. Fractions as a Number
4. Fractions as Operators
5. Decimals and Percentages
6. Integers - Positive and Negative Numbers

Here are some of my reflections from today:

1. "Use materials and manipulatives to help develop a conceptual understanding."

Teaching place value is essential to ensuring the mathematical success of our students at PES. The slide on the right served as a valuable reminder for me, particularly when mentoring fellow educators in mathematics, of the critical role that materials and manipulatives play in helping students grasp complex place value concepts.

2. I found it extremely beneficial to revisit some of the fundamental concepts involved in teaching fractions. One key takeaway for me is to remind teachers to not only approach problems from whole-to-part but also to ensure that students frequently engage with part-to-whole problems as well.

3. Teaching fractions and percentages in authentic learning contexts is important because it allows students to connect abstract mathematical concepts to real-world situations, making the learning experience more meaningful, relevant and most importantly, fun!

Today provided me with valuable reminders into the key elements of effective place value instruction!

MPI - Day 2: Know your learners as Mathematicians

Today's focus was on knowing and understanding our learners as Mathematicians. We looked at the following areas:

1. What makes a confident maths teacher?
2. Assessment 101
3. Keeping track of learning
4. Assessment Data and Planning 
5. Developing assessment capable learners 
6. Tracking Maths Profiles

The most impactful part of today was thinking about, "What makes a confident maths teacher?" As a mentor and a maths teacher myself, this is an important question to ask when thinking around the development of a teacher's pedagogy. 

This got me thinking around what dispositions I would need to have to be an effective teacher (or what items to focus on when helper others to develop in their teaching of maths). We need to work on:

Acquiring a deep understanding of maths knowledge:

We need to have a deep understanding of mathematical concepts ourselves. This will allow us to explain ideas clearly and answer student questions effectively. It's also critical for us to be able to guide learners through their next steps and provide them with effective feedback.

A growth mindset:

If we truly want maths to be enjoyable (which evidence suggests that learners produce the best outcomes when enjoyment is part of the learning), then we as teachers need to portray maths as an interesting and engaging subject. We need to foster a love of learning and reflect this in out teaching style in such a way that allows learners to enjoy the challenge that maths can provide.

Create a supportive environment:

We were encouraged today that we need to create a safe space where mistakes are seen as a natural part of the learning process, encouraging students to take risks and persevere.

Assessment as a means to track and build next learning steps:

We were given a teacher workbook to use for planning and tracking of learners current/next steps. This is a great resource. It has led me to think around how this could neatly fit into what we are already doing as a school and how we can adjust to fit in with the HERO learning intentions, etc...

Today was very thought provoking and an excellent reminder of what we can do to become the best maths teachers for our amazing learners.

MPI - Day 1: Mathematics is Core

Today's first MPI session was a really impactful day looking at the following areas:

1. What Characterises a ‘Good Mathematician’? 

2. The Idea of Teachers as Mathematicians

3. Mathematics Across the Curriculum

4. Using extended discussion in maths

5. How to Grow ‘Good Mathematicians’

A Good Mathematician

 Some of the following things have stuck out for me today. Firstly, thinking deeply into what makes a 'Good Mathematician' was challenging. As teachers we often think that it's those kids who can answer questions quickly and correctly is what makes a good mathematician. However, today we were challenged that it's our learners ability to think creatively and critically and logically. Also, it's their ability to enjoy an intellectual challenge and to relish the struggle of finding a solution; both individually and as part of a group. 

Something that was impactful to me was the concept of finishing quickly. "Many people incorrectly believe that being good at maths means being fast at maths. It doesn’t - and we need to disassociate maths from speed." This is so true. Often it is in the quiet, slow wrestle of a problem that gold can be found!

 

Maths is a Visual Subject

Secondly, the idea that maths is a visual learning area really hit home! "Maths is to think visually and creatively and make connections. Not just about calculating" Teachers help students become mathematicians when they believe everyone can learn maths at high levels and that the maths is visual. 

I read a small research paper called, "Seeing as Understanding: The Importance of Visual Mathematics for our Brain and Learning: by Jo Boaler, Lang Chen, Cathy Williams and Montserrat Cordero. This explains that visual processing is an important part of how our brains learn maths, even at higher levels. Using visual aids and manipulatives can help students of all ages understand maths concepts more deeply. It argues that the old approach to teaching maths (an abstract approach) can make maths more difficult for students to learn and can discourage them from pursuing maths further. This is incredibly freeing for teachers to know that it's not just for struggling learners or for younger aged learners. This is for all learners and all topics!

Really looking forward to the next session!