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- there are many foundations that lead up to understanding
- it's important to understand the progression of where they have coming from and where they are going
- it's great to see a simple developmental continuum
- Do the skills need to match the conceptual understanding?
- your previous experince can help ypu conceptual understanding

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Students from where the educator was from seemed to be locked into a very concrete progression.

The markers for progression seemed very developmentally appropriate.

Use of manipulatives throughout the grade levels

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Fractions - through the grade levels students need to know that fractions are part of number not a seperate entity.
number talks important
move away from teaching so many strategies - teach number sense and fluency and not strategies
always use concrete models ALSO draw visual representations
using the term Unitising
great that he gave us a sequence for teaching number

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- having a flexible and transferable understanding
-  having a visual understanding that can be manipulated
- being able to use logic
- being able to reason
- understanding the process/ the how
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- The ability to understand a concept. (A big idea and not only remember steps that need to be followed)
Being able to apply their learning in different context. Recognizing general patterns.  Making connections between previous learning and new learning.
Multiple representations of any concept.

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Understanding how numbers are made up not just the name of a number
working towards how to reconstruct and reconstruct numbers and see purpose.

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The ability to transfer knowledge and understanding.

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- Is accessible for all
- Provide opportunities for students to move forward in their understanding
- Supporting students to see math through many ways and in everyday life

- Use the tools THEY (the students) need to solve math problems
- See math as a process and that process is valued as it supports mathematical understanding
- To see students as individual mathematicians

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Cultivating a safe environment
Finding out what students are capable of to determine next steps
Talking about maths in different contexts.
Differentiating learning for different students.

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Engage student interest and maintain motivation

Provide opportunities for authentic problem solving.

Prepare engagements that accomplish the above.

Ensure that students have a firm understanding of mathematical concepts.

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- Being in tune with new development on teaching
- Develop an enthusiasm for Maths
- Create a risk-taking environment where students don't be afraid of mistakes.
- Foster different approaches to problems (Strategies etc)
- Ongoing Formmative and Feedback
- Understanding the progression and its process/steps/stages. (Connected to Fletcher's video)
- Know how to demonstrate the flexibility with numbers to students. Elicit them to use it also.
- Give student's chance to talk and articulate Maths thinking
Be well prepared. (not winging it)

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-to teach the basics
-to get them to not be afraid of math
-to see math in context- real life applications
-providing a supporting environment/ safe space/ time
-provide necessary resources and hands on manipulatives

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See the purpose, make real connections, make it fun and engaging, target it at their level and not where they are suppose to be at, make them see the value  of it, make it inspiring and appeal to their curiosities, follow their interests, help them ask the right questions, understand  our students

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Consolidate each step before moving on. Each step matters, don't rush through.
Importance of grasping concepts that are applicable across math areas, eg. pattern. Being able to see patterns flexibly (eg. skip counting. Skip counting from any number and not just rote learned 2, 4, 5.)

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Five frames were something we weren't all familiar with, or haven't used much. Some of our learners would benefit from more experience decomposing and recomposing numbers in a concrete way. Schools need to support students with regular PD in Math. The PD should support teacher understanding of conceptual understanding/development in concepts such as place value, fractions/decimals, etc. Consistency in vocabulary is important. 

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Five frames were something we weren't all familiar with, or haven't used much. Some of our learners would benefit from more experience decomposing and recomposing numbers in a concrete way. Schools need to support students with regular PD in Math. The PD should support teacher understanding of conceptual understanding/development in concepts such as place value, fractions/decimals, etc. Consistency in vocabulary is important. 

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Conceptual development takes students from the concrete to the abstract. Students can transfer their knowledge and apply it. Concepts can be broken apart and put back together again. Representing and verbalizing in different contexts and different ways is evidence of conceptual understanding. It is not a linear progression from the concrete to the abstract - students go back and forwards. 

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Conceptual development takes students from the concrete to the abstract. Students can transfer their knowledge and apply it. Concepts can be broken apart and put back together again. Representing and verbalizing in different contexts and different ways is evidence of conceptual understanding. It is not a linear progression from the concrete to the abstract - students go back and forwards. 

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Deeper understanding of a system. Timeless, universal, transferable skill. Seeing connections. Applying skills: Use skills in a new context. Comprehension and good conceptual understanding are required to apply skills.

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We need to be accountable for what we are teaching the students. Teaching the right foundations is essential. Filling any gaps in understanding is crucial. Students can only apply Math they truly understand - therefore we need to make sure they do. Modeling a positive attitude and growth mindset is important. 

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We need to be accountable for what we are teaching the students. Teaching the right foundations is essential. Filling any gaps in understanding is crucial. Students can only apply Math they truly understand - therefore we need to make sure they do. Modeling a positive attitude and growth mindset is important. 

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1. keep a positive attitude, and be confident with the content.
2. Make sure it is happening every day in some form.
3. Be well prepared, even more so when you are not feeling great about it.
4. Know where the students will struggled (possibly really hard for a newer teacher).
5. Have multiple ways to show the same thing.

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Can't rush this - ensure the children have time to explore and play.

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Knowing and naming numbers does not necessarily mean the children understand quantity.

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Sequential - building on each other - this is when gaps may occur. Pushing them before they are ready or skipping steps.

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Flexible in your thinking and able to make TD connections helps to develop conceptual understandings.

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Able to make generalisations.

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What is conceptual understanding in math?

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What is conceptual understanding in math?

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-What concepts perfectly with math directly?
- Using different ways of data collecting.
- The connection between the context and process of thinking, order, collecting data, revisiting knowledge.
-The importance of reflecting using mathematical terminology when giving feedback to the children.

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Understanding a concept and be able to transfer and apply to a different context.

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Our responsibility to NOT project our mindset about maths (if it's negative) onto children)

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Up to date in our practice and literature.

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We need to know the levels of development - so the children are not having gaps in their learning. Concrete, hands-on learning.

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EY teachers can put maths in everything....we need to see the maths in each engagement and  to see and learn from what they already know to the next step.

This is the natural transdisciplinary connection between all subjects. The transdisciplinarity is in everything we do.

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Have an understanding of the 'big picture' - the continuum of learning - progression of learning.

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We all need to be onboard with understanding symbolic exploration and expression. Able to be fluent in the way we communicate this to our learning community.

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Start with what the children know...what they feel about mathematics. How do they make logic -  how do they make logic from what they know. We can see when we are observing. They way they look at things and observe things.
Look at the answer and see the logic....what is the thinking behind it...understand more deeply.
It's about making connections.

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Recognize, identify, understand who they are as maths learners.

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Making sure that children see that maths is all around us and connected to the real-world.

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Integrated in all areas of learning - indoor and outdoor - transdisciplinary.

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Help children connect with this part of their logical mind in a natural way. We need to make learning collaborative (with children and teachers). Start with prior knowledge.

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How it translates in what we do in the environment.

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We do feel comfortable with teaching and learning in maths.

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Discuss and demonstrate

Moving through stages

Apply and transfer knowledge and skills in different contexts

Being able to explain