Professional Learning
The Introductory Video provides an overview of the sequence of understanding that children go through as they learn about Addition and Subtraction and related concepts from Year 1 to Year 6. Freely available to all without subscribing.
Select Professional Learning to access:
CONCEPT SEQUENCE providing a down-loadable, written sequence of understanding of Addition and Subtraction and essential related concepts.
PROFESSIONAL LEARNING RESOURCE providing down-loadable written explanation of the sequence of understanding of Addition and Subtraction and essential related concepts.
LEADING A PROFESSIONAL LEARNING SESSION providing a script and agenda for a teacher to use to lead participants (including parents!) through the sequence of understanding of Addition and Subtraction and essential related concepts.
VIDEOS forming a complete sequence of understanding of Addition and Subtraction and essential related concepts.
Professional Learning
Professional Learning
GOOD NEWS EVERYONE! The professional learning resources at A Learning Place A Teaching Place are growing! Teacher Professional Learning is being developed to cover Grades, Concepts, Mathematics and Pedagogy.
Existing Professional Learning covers:
LEARN BY GRADE: Select Learn by Grade button above
* Each grade currently has a short video describing the concepts taught in that grade.
LEARN BY CONCEPT: Select Learn by Concept button above
* Early Counting and Grouping: Videos and Professional Learning Resource
* Place Value: Videos, Professional Learning Resource and Leading a Professional Learning Session
* Addition and Subtraction: Videos, Professional Learning Resource and Leading a Professional Learning Session
* Multiplication and Division, Fractions and Decimals, Patterns and Algebra, Money and Financial Mathematics: Overview Video
* Measurement and Geometry, Statistics and Probability: Overview Video
MATHEMATICS: Select Mathematics button above
* Problem Solving
* Algebraic, Additive and Multiplicative Thinking
* Instrumental vs Relational Thinking
PEDAGOGY: Select Pedagogy button above
* Explicit Learning
* Guided and Independent Learning
* Reflection
* Planning a Week's Lessons
* Using the Teaching Resources
* Differentiated Addition and Subtraction lessons
* Divergent Thinking
* Questioning
* Quality Mathematics Lessons
Mathematics is conceptually based, not skills based. Each concept has natural relationships to other concepts. Children only develop deep understanding of mathematical concepts and the relationships between concepts, through explicit teaching and investigation guided by teachers with deep understanding of the concepts and relationships developed through quality professional development.
At A Learning Place A Teaching Place, you will find professional learning resources that will deepen your understanding, empowering you to develop and enhance your students’ mathematical understanding. Browse now and discover our year-specific Scope and Sequences, and concept-specific Concept Sequences, current Mathematics and Pedagogical research, with related professional learning resources including videos, and agenda and notes to lead a professional development session. The grade Scope and Sequences and Concept Sequences explicitly cover the content descriptions and outcomes of the Australian Curriculum and NSW Mathematics Syllabuses for each grade and concept, and provide teachers with explicit relationships to other concepts.
The research and evidence-based spiralling curriculum within the grade Scope and Sequences, and Concept Sequences, and related professional learning resources accessed via these links, enrich the professional development of primary school teachers to provide children with the best opportunity to develop deep understanding of mathematical concepts and the relationships between concepts. Peruse our Learning resources today!
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in the first year of school.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 1.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 2.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 3.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 4.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 5.
Professional Learning
These resources provide detailed, research-based professional learning on the concepts and the relationships between the concepts in Year 6.
Professional Learning
These resources provide detailed, research-based professional learning on the Early Counting and Grouping number concepts.
The INTRODUCTORY VIDEO provides an overview of the sequence of understanding that children go through as they learn about Early Counting and Grouping concepts in Kindergarten / Prep / Reception. Freely available to all without subscribing.
Select Professional Learning to access:
CONCEPT SEQUENCE providing a down-loadable, written sequence of understanding of Early Counting and Grouping concepts.
PROFESSIONAL LEARNING RESOURCE providing down-loadable written explanation of the sequence of understanding of Early Counting and Grouping concepts.
LEADING A PROFESSIONAL LEARNING SESSION providing a script and agenda for a teacher to use to lead participants (including parents!) through the sequence of understanding of Early Counting and Grouping concepts.
VIDEOS forming a complete sequence of understanding of Early Counting and Grouping concepts.
Professional Learning
These resources provide detailed, research-based professional learning on the Multiplication and Division concept and essential related concepts.
Professional Learning
The Introductory Video provides an overview of the sequence of understanding that children go through as they learn about Place Value and related concepts from Kindergarten/Prep/Reception to Year 6. Freely available to all without subscribing.
Select Professional Learning to access:
CONCEPT SEQUENCE providing a down-loadable, written sequence of understanding of Place Value and essential related concepts.
PROFESSIONAL LEARNING RESOURCE providing down-loadable written explanation of the sequence of understanding of Place Value and essential related concepts.
LEADING A PROFESSIONAL LEARNING SESSION providing a script and agenda for a teacher to use to lead participants (including parents!) through the sequence of understanding of Place Value and essential related concepts.
VIDEOS forming a complete sequence of understanding of Place Value and essential related concepts.
Professional Learning
These resources provide detailed, research-based professional learning on the Fractions and Decimals concept and essential related concepts.
Professional Learning
These resources provide detailed, research-based professional learning on the Patterns and Algebra concept and essential related concepts.
Professional Learning
These resources provide detailed, research-based professional learning on the Money and Financial Mathematics concept and essential related concepts.
Professional Learning
These resources provide detailed, research-based professional learning on the Statistics and Probability concept and essential related concepts.
Professional Learning
These resources provide research-based professional learning on the Measurement and Geometry concept and essential related concepts.
Professional Learning
Number and Algebra are investigated together. As children investigate number concepts, they are investigating properties and relationships.
Professional Learning
Statistics and Probability (Chance and Data) are intrinsically linked - without information (data) we cannot identify the chance of an event occurring. Attempting to identify the chance of an event occurring without information may lead to inappropriate and unnecessary risk.Through the investigation of Statistics and Probability, children develop their understanding and capacity to assess risk.
Professional Learning
Measurement and Geometry are investigated together. Children investigate features and properties of shapes and objects, then apply of their understanding of these features and properties to measure their length, area, volume and capacity and mass.
Mathematics
Mathematics is conceptually based... not skill based. Understanding of one concept is needed to understand another concept, and another concept, and another concept….
Existing Professional Learning covers:
* Problem Solving
* Algebraic, Additive and Multiplicative Thinking
* Instrumental vs Relational Thinking
Many children (and indeed adults) have gaps in this relational understanding of mathematical concepts and so their learning plateaus.
Children in the first three years of school think additively - this means thinking in terms of Addition and Subtraction.
Following these years, children begin to think multiplicatively about Place Value, Multiplication and Division and Fractions - this means thinking in terms of Multiplication and Division.
As Jacob and Willis, pointed out at the MERGA Conference 2001 'Unless teachers consciously help children develop multiplicative thinking, which goes well beyond repeated addition, it may not happen for many children.'
To teach for deep understanding requires the teacher to have deep understanding. This is particularly true when teaching mathematics.
The Mathematics professional learning resources, and the Teaching resources at A Learning Place A Teaching Place, will deepen teacher understanding as the teacher is developing their students’ understanding.
Mathematics involves much more than computation and calculation. Mathematics involves explicitly and intentionally thinking algebraically, additively and multiplicatively in appropriate situations. We think algebraically as we look for patterns in relationships in our world. Additive thinking involves thinking in terms of addition. Multiplicative thinking involves thinking in terms of multiplication - in orders of magnitude.
Mathematics may be taught and learned instrumentally or relationally. Instrumental learning involves possession of a rule and the ability to use it. Relational learning involves knowing both what to do and why.
The Teaching and Professional Learning resources here at A Learning Place A Teaching Place, provide Scope and Sequences and Concept Sequences, allowing teachers to teach children to think mathematically, and to learn maths relationally. The resources will not only enhance your students’ mathematical thinking and understanding, but yours too! Browse now!
Mathematics
Mathematics
Mathematics
Pedagogy
Pedagogy can be defined as the way something is taught and learnt.
Existing Professional Learning covers:
* Explicit Learning
* Guided and Independent Learning
* Reflection
* Planning a Week's Lessons
* Using the Teaching Resources
* Differentiated Addition and Subtraction lessons
* Divergent Thinking
* Questioning
* Quality Mathematics Lessons
There has been much research into effective pedagogy for teaching maths for deep understanding, over a long period of time, highlighting the importance of using strategic questioning rather than telling.
Richard R Skemp believed that children could learn intelligently from a young age. He defined two ways of teaching and learning which he called Instrumental Understanding and Relational Understanding.
Lev Vygotsky's Zone of Proximal Development demonstrates that learning with people who are close to our own level of understanding accelerates learning and deepens understanding. Vygotsky’s research into the role of talk in learning also concluded that talk is vital to deep understanding. Questioning rather than telling allows children to engage in talk using and developing mathematical meta-language.
Sir Ken Robinson observed, children become less creative, rather than more creative due to shallow teaching. Divergent thinking can be defined as thinking of all possibilities.
Many of us were taught Maths through telling. Our teachers told us how to 'do' maths and then we 'practised' until we could 'do' it independently. The learning theory was that if we were told how to 'do' it and 'did' it enough, understanding would follow...
The problem was that in many cases, understanding never followed, whether or not we could 'do' the mathematics. However it was thought we 'understood' if we arrived at the correct answer. If we didn't arrive at the correct answer, we were simply 'told' how to 'do' it again!
We now know that this is not an effective way to learn Maths. Maths is conceptually based, not skills based. Understanding of one concept is needed to understand another concept, and another concept, and another concept.... Children need to develop understanding of concepts, and the relationships between concepts, and not merely 'do' maths.
Telling children about Maths allows us to know what we understand. Teaching maths using a pedagogy of questioning, allows us to know what children understand. Asking children about Maths allows both the teacher and the child to identify their current understandings and to build on them. This also allows the teacher to correct misconceptions, build on incomplete understanding and teach every child from their leading edge. Teaching maths using a pedagogy of questioning has the added benefit of deepening teacher understanding, as they engage in substantive communication about mathematical concepts with their students!
If you would like to enhance your understanding and practice of the pedagogy of questioning, browse our resources now!
Pedagogy
Pedagogy
Pedagogy
Pedagogy
Pedagogy
At A Learning Place A Teaching Place, you will not find resources that dictate what you teach in a lesson. We recognise that you are the expert in your classroom. The teaching resources allow you to plan terms and weeks of lessons, differentiated using the levels of understanding demonstrated by the children in your class.
Pedagogy
Pedagogy
Quality Maths lessons involve 3 aspects:
– Explicit Learning
– Guided and Independent Investigation
– Reflection
Explicit learning is different to explicit instruction. Explicit instruction involves giving children instructions which they follow. Explicit learning involves asking strategically planned questions, designed to allow children to construct and develop understanding and meta-language. The explicit learning aspect of the lesson prepares children to investigate mathematical concepts independently. The Teaching Plans contain all of the Explicit Learning for each concept.
Pedagogy
Quality Maths lessons involve 3 aspects:
• Explicit Learning
• Guided and Independent Investigation
• Reflection
Reflection allows children to identify and explain their current understanding of mathematical concepts. To reflect, children think about, discuss and record their response to, a specific reflection question. Recorded responses to reflection questions allow teachers – and the child – to see growth in each child’s understanding!
Pedagogy
Quality Maths lessons involve 3 aspects:
– Explicit Learning
– Guided and Independent Investigation
– Reflection
It is during independent investigation that children develop their deep understanding and meta-language. During guided investigation the teacher guides the children through the process they will use to investigate the concept independently.