Mathematics pedagogy and practice
Implement professional dialogue about mathematics pedagogy and practice in your school or professional learning network using text-based protocols and core thinking routines for leaders.
Purpose of resource
The research snapshot and professional learning activity are part of the K-2 mathematics toolkit. This supports leaders to unpack research with teachers, that underpins the new syllabus.
Target audience
This resource can be used by school leaders to support teachers with effective syllabus implementation.
When and how to use
The research snapshot and the professional learning activity, ‘Unpacking the evidence base’ slideshow, complement each other and are focused on the same research article. Schools might use these:
- within whole-school professional learning sessions
- in stage meetings
- in professional learning groups.
These may take an hour to implement or can be modified as appropriate. The protocol used to help teachers unpack the evidence can be changed to suit the professional learning context.
Research base
The evidence base for this resource is:
- Sullivan, P. (2011) Teaching Mathematics: Using research-informed strategies (acer.edu.au) Chapter 5, page 24 to 30
- K-2 mathematics syllabus (2021) – research base identified in the syllabus (refer to the ‘About the English and Mathematics K-2 syllabuses support document)
- High impact professional learning (HIPL).
Contact
Email questions, comments and feedback about this resource to contactcurriculumreform@det.nsw.edu.au using the subject line ‘Re mathematics K-2 research toolkits’.
Alignment to system priorities and/or needs – School Excellence Policy, School Excellence Procedure
Alignment to School Excellence Framework – ‘Instructional leadership’ and ‘High expectations culture’ elements in the Leading domain as well as the ‘Learning and development’ and ‘Collaborative practices and feedback’ elements of the Teaching domain.
Alignment with the Australian Professional Standards for Teachers – 6.2.4 and 6.3.4
Consulted with – Literacy and numeracy team and principal school leadership representatives
Reviewed by – CEYPL director and CSL director
Created/last updated – 28 February 2022
To be reviewed: December 2022
Teaching mathematics: Using research-informed strategies Chapter 5
Research article – Sullivan, P. (2011) Teaching Mathematics: Using research-informed strategies (acer.edu.au) Chapter 5, page 24 to 30
‘…teaching mathematics well, in such a way as to make it count, is a worthwhile and reasonable proposition.’ page 24
Overview of research
The research moves to understanding what schools and teachers need to know and be able to do to improve student learning outcomes in mathematics.
This research outlines six key pedagogic principles for effective teaching of mathematics. They are:
- articulating goals – teachers identify key ideas from concepts to be taught and communicate with students that these are the goals of teaching and teachers explain to students how they will learn to reach the goal.
- making connections – teachers build on what students know by contextualising and establishing a rationale for the learning
- fostering engagement – teachers engage students through rich and challenging tasks that allow students time and opportunities to make decisions, and which use a variety of forms of representation.
- differentiating challenges – teachers interact with students while they engage in the experiences, encourage students to interact with each other and plan to support and challenge students appropriately.
- structuring lessons – teachers adopt pedagogies that foster communication and both individual and group responsibilities with teacher summaries of key mathematical ideas.
- promoting fluency and transfer – teachers understand that fluency is important, and it can be developed in two ways: by short everyday practice of mental processes; and by practice, reinforcement and prompting transfer of learnt skills.
Professional discussion and reflection prompts
- What would mathematics teaching and learning with the six key pedagogical principles look and sound like?
- What changes could you make in your classroom to address one of the pedagogical principles?
- What changes can we make as a school in light of this research?
Professional learning activity
Purpose of resource
The research snapshot and professional learning activity are part of the K-2 mathematics toolkit. This supports leaders to unpack research with teachers, that underpins the new syllabus.
Target audience
This resource can be used by school leaders to support teachers with effective syllabus implementation.
When and how to use
The research snapshot and the professional learning activity, ‘Unpacking the evidence base’ slideshow, complement each other and are focused on the same research article. Schools might use these:
- within whole-school professional learning sessions
- in stage meetings
- in professional learning groups.
These may take an hour to implement or can be modified as appropriate. The protocol used to help teachers unpack the evidence can be changed to suit the professional learning context.
Research base
The evidence base for this resource is:
- National Research Council (2001) ‘Adding it up: Helping children learn mathematics
- K-2 mathematics syllabus (2021) – research base identified in the syllabus (refer to the ‘About the English and Mathematics K-2 syllabuses support document)
- High Impact Professional Learning (HIPL).
Contact
Email questions, comments and feedback about this resource to contactcurriculumreform@det.nsw.edu.au using the subject line ‘Re mathematics K-2 research toolkits’.
Alignment to system priorities and/or needs – School Excellence Policy, School Excellence Procedure
Alignment to School Excellence Framework – ‘Instructional leadership’ and ‘High expectations culture’ elements in the Leading domain as well as the ‘Learning and development’ and ‘Collaborative practices and feedback’ elements of the Teaching domain.
Alignment with the Australian Professional Standards for Teachers – 6.2.4 and 6.3.4
Consulted with – Literacy and numeracy team and principal school leadership representatives
Reviewed by – CEYPL director and CSL director
Created/last updated – 28 February 2022
To be reviewed: December 2022
Adding it up: Helping children learn mathematics
Research article – National Research Council (2001) ‘Adding it up: Helping children learn mathematics’.
'Mathematical proficiency is not a one-dimensional trait’, page 116
Overview of research
This research outlines five strands of mathematical proficiencies. These five strands are interwoven and interdependent in the development of proficiency in mathematics.
It highlights that mathematical proficiency has five components, or strands:
- conceptual understanding – comprehension of mathematical concepts, operations and relations
- procedural fluency – skill in carrying out procedures flexibly, accurately, efficiently and appropriately
- strategic competence – ability to formulate, represent, and solve mathematical problems
- adaptive reasoning – capacity for logical thought, reflection, explanation, and justification
- productive disposition – habitual inclusion to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy.
Professional discussion and reflection prompts
- What do the five components of mathematical proficiency currently look like in your classroom?
- Which of the five components would you like to enhance your understanding of and why? How will this impact student learning?
- How can you further build students’ adaptive reasoning?
Professional learning activity
Purpose of resource
The research snapshot and professional learning activity are part of the K-2 mathematics toolkit. This supports leaders to unpack research with teachers, that underpins the new syllabus.
Target audience
This resource can be used by school leaders to support teachers with effective syllabus implementation.
When and how to use
The research snapshot and the professional learning activity, ‘Unpacking the evidence base’ slideshow, complement each other and are focused on the same research article. Schools might use these:
- within whole-school professional learning sessions
- in stage meetings
- in professional learning groups.
These may take an hour to implement or can be modified as appropriate. The protocol used to help teachers unpack the evidence can be changed to suit the professional learning context.
Research base
The evidence base for this resource is:
- Sullivan, P (2011) Teaching mathematics: using research-informed strategies chapter 7, p 40-47. ‘
- K-2 mathematics syllabus (2021) – research base identified in the syllabus (refer to the ‘About the English and Mathematics K-2 syllabuses support document)
- High Impact Professional Learning (HIPL).
Contact
Email questions, comments and feedback about this resource to contactcurriculumreform@det.nsw.edu.au using the subject line ‘Re mathematics K-2 research toolkits’.
Alignment to system priorities and/or needs – School Excellence Policy, School Excellence Procedure
Alignment to School Excellence Framework – ‘Instructional leadership’ and ‘High expectations culture’ elements in the Leading domain as well as the ‘Learning and development’ and ‘Collaborative practices and feedback’ elements of the Teaching domain.
Alignment with the Australian Professional Standards for Teachers – 6.2.4 and 6.3.4
Consulted with – Literacy and numeracy team and principal school leadership representatives
Reviewed by – CEYPL director and CSL director
Created/last updated – 28 February 2022
To be reviewed: December 2022
Teaching mathematics: using research-informed strategies Chapter 7
Research article – Sullivan, P (2011) Teaching mathematics: using research-informed strategies chapter 7, p 40-47. ‘
Research snapshot
Mathematics teachers, arguably more than most teachers, find in every lesson that they must address the challenge that some students learn the current content quickly, while others require substantial support.’ page 40.
Overview of research
This research outlines how teachers can support differences in readiness so students can be successful in learning mathematics. It highlights that:
- Teachers face the challenge to support both students who need additional support and others who understand the work quickly.
- Research shows that grouping students by achievement has minimal effect on learning outcomes and profound negative equity effects (Hattie, 2009).
- Students should work on the same core task. To support this, teachers should offer support through differentiating the task on which students are working.
- Teachers should use differentiation to enable opportunities for all students to benefit from participation in common class discussions and shared experiences
- Teachers should plan ways to prompt students whenever students demonstrate a need for support or extension.
- Enabling prompts support students experiencing difficulty. Extending prompts extend the thinking for students who move quickly through the tasks.
Professional discussion and reflection prompts
- How do you currently support differences in readiness in mathematics?
- Why is it beneficial for all students to participate in the same core activities?
- What strategies foster a collaborative mathematics classroom community?