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Module 2 focuses on the teaching and learning cycle and effective pedagogy and practices in mathematics.
The effective teaching of mathematics results in students developing efficient numeracy strategies that they can apply within mathematics, across KLAs and beyond the classroom.
Overview of Module
This Module has a focus on professional readings. It is important that teachers make informed, evidence-‐based decisions on how to teach and what strategies to use in the classroom.
Overview of Module
Embedding the teaching practices explored in this module will allow teachers to see that this is
‘just the way we teach.’
It is not a numeracy program to be implemented in isolation from mathematics lessons. This is quality teaching for all students in all classrooms.
Overview of Module
Teaching students efficient numeracy skills forms one aspect of explicit mathematics teaching.
These skills can also be explored through, and developed in other KLAs.
This is a pedagogy, not a program
This is a pedagogy, not a program
purposeful questioning
practicing formative assessment
differentiating tasks
ongoing assessment
making connections
communicating efficient strategies
Examples of effective teaching strategies
Effective teaching strategies are the pedagogy that form how we teach, they are also underpinned by the teaching and learning cycle.
This is a pedagogy, not a program
Strategies that are used in a Year 1 classroom are transferable to a Year 5 classroom, the strategies remain the same. What changes is the content and students’ needs.
• The aim is for effective teaching strategies to be utilised in all mathematics classrooms from Kindergarten to Year 8 and beyond to assist students in becoming numerate.
• Developing numeracy skills mainly occurs in mathematics lessons.
• Strategies that teachers use should be embedded within classroom practice and not seen as extra to what is currently happening.
This is a pedagogy, not a program
• Some numeracy strategies can be practised and repeated throughout the day (generally in primary classrooms where the teacher has the same students all day, secondary teachers could possibly use the start of each lesson to reinforce).
• Any short, focused, frequent (SFF) activities used throughout the day need to be aligned to the concept students are currently learning and be based on the needs of the students being targeted.
This is a pedagogy, not a program
• Use the Participant's Activity Journal to complete this task• Choose either Option A or Option B for this reading task• Print out the two appropriate readings• Once read, complete the questions in the Activity Journal• If completing the course with another teacher or a small team, discuss the reflections on the readings as a group
Activity 1
The teaching and learning cycle represents the four stages that occur in the design and delivery of classroom tasks that incorporate an outcomes-‐based approach.
The cycle has no start or end point, with each step informing the next through ongoing evaluation. It is the process of gathering data and reflection that dictates where in the cycle you need to be operating.
The teaching and learning cycle
Students differ in many ways fundamental to learning: prior knowledge, ability, conceptions of learning, learning styles and strategies, interest, motivation, self-‐efficacy beliefs and emotion, as well in socio-‐environmental terms such as linguistic, cultural and social background.
[Our] challenge is to manage such differences, …within a shared education and culture.
The Nature of Learning: Using Research to Inspire Practice © OECD 2010
Teaching is a balancing act
‘Prior knowledge is one of the most important resources on which to build current learning as well as one of the most marked individual difference among
learners.’
The Nature of Learning: Using Research to Inspire Practice © OECD 2010
Prior knowledge
Using assessment for learning teachers can learn more about their students and their prior knowledge.Teachers should be able to answer these questions in preparation for planning:• What do my students already know and what can they do? • How do I know this? What is my evidence?• Which students require extension in particular areas? • Which students require support in particular areas?
Where are my students now?
The assessment data collected informsteachers of the numeracy skills and strategies students need to develop.
As teachers develop a unit of learning, they use the mathematics syllabus and a scope and sequence to determine allocated outcomes and content.
It is important to make connections between subtrands to assist in students’ conceptual understanding.
What do I want my students to learn?
•Use the Participant's Activity Journal to complete this task along with an example lesson plan
• Print out and read the Capacity Building Series:Differentiating Mathematics Instruction reading
•Once read, annotate a current lesson plan focusing on how it could be differentiated:• e.g. open or parallel tasks, content, process or product
• If completing the course with another teacher or a small team, discuss reflections on the reading and the lesson plan as a group
Activity 2
Students will ‘get there’ through planned quality learning experiences. Teachers differentiate practice in response to students’ learning and support needs (identified in your initial assessments).Teachers modify lessons to cater for students’ needs.Content -‐ Change the range of numbers Process -‐ Use flexible grouping (ability, interest, mixed) Product -‐ Have students record in different ways
How will my students get there?
Teachers differentiate learning in ways that are responsive to students’ needs.
While units may be planned collaboratively and shared, teachers will need to differentiate units to cater for particular students.
Differentiation will be covered further in Module 5.
Developing units of learning
By monitoring and tracking through ongoing assessment, teachers can collect evidence of student learning, moment-‐by-‐moment. This informs teachers about what students currently understand and where to next in the learning.
How do I know when my students get there?
Effective and informative assessment and reporting:• has clear, direct links with outcomes• values teacher judgement• recognises individual achievement and progress• conveys meaningful and useful information.
• Use your Participant's Activity Journal to complete this task• Print out the Effective Pedagogy in Mathematics reading• Once read, complete the reflection task in the Activity Journal• If completing the course with another teacher or a small team, discuss reflections on the reading as a group and share ideas around the ten principles of effective pedagogy
Activity 3
Effective pedagogy in mathematics
Quality pedagogical approaches to
teaching mathematics are the building blocks for
numeracy.
‘The principles of practice identified by Askew1 and Clarke2 as being
central to effective teaching of numeracy were; making connections, challenging all pupils, teaching for
conceptual understanding, facilitating purposeful discussion, maintaining a focus on mathematics, and possessing and
instilling positive attitudes towards mathematics.’
Muir, Tracey. (2008) Principles of practice and teacher actions: influences on effective teaching of numeracy. Mathematics Education Research Journal, Vol. 20, No. 3, 78-‐101
1Askew, M., Brown, M., Rhodes, V., Johnson, D., & Wiliam, D. (1997). Effective teachers of numeracy. London: School of Education, King's College. 2Clarke, D., Cheeseman, J., Gervasoni, A., Gronn, D., Horne, D., McDonough, A. et al. (2002). Early numeracy research project final report. Melbourne, Australia: Australian Catholic University.
making connections-‐ connecting different areas of mathematics e.g. area and multiplication
challenge all pupils-‐ setting high but realistic expectations e.g. ‘your next step in learning is counting by tens off the decade’
teach for conceptual understanding-‐ awareness of conceptual connections between areas e.g. to understand
how to add and subtract, students must have a strong concept of ones, tens, hundreds
purposeful discussion-‐ use a range of question types to probe and challenge students’ thinking
e.g. How do you know when you have all the combinations?Muir, Tracey. (2008) Principles of practice and teacher actions: influences on effective teaching of numeracy. Mathematics Education Research Journal, Vol. 20, No. 3, 78-‐101
‘…teachers must see mathematics as a set of conceptual relationships between numbers and number symbols rather than as numbers that are manipulated by rules.
The questions we ask, the tasks we design, and the discussions we prompt can refocus students on discovering such relationships themselves.’
Teaching number sense, Sharon Griffin, Educational Leadership Vol. 61 (2004)
Habits of mind
The ten principles of effective mathematics pedagogy in the Anthony and Walshaw reading should not be taken in isolation but interpreted as part of a complex web of factors that can affect student learning.
The following presentation discusses a few of the key principles in more detail.
Effective pedagogy
Effective teachers provide opportunities for students to work both independently and collaboratively.
…teachers invite students to explain their solutions to others; they also encourage students to listen to and respect one another, accept and evaluate different viewpoints, and engage in an exchange of thinking and perspectives.
Key principle 2: Arranging for learning
There are times when teachers group students by ability so students can work alongside peers at the same level of understanding.
Allowing teachers to work with one specific group at a time while the other groups work independently.
At other times, mixed ability groups are important. Students can share efficient strategies and different ways of working to find varied solutions to tasks.
At times, when explicit teaching occurs, the whole class may work together or as individuals.
In the mathematics classroom: Flexibility in the learning environment
Effective teachers support students in creating connections between different ways of solving problems, between mathematical representations and topics, and between mathematics and everyday experiences.
The ability to make connections between apparently separate mathematical ideas is crucial for conceptual understanding and numeracy development.
Key principle 5: Making connections
For students to be able to: • develop the formula for the volume of prisms by considering the numbers and volume of ‘layers’ (base area x height) Volume Stage 4, NSW mathematics K-‐10 syllabus
We need to first make the connections for students between the concepts (links to Aspects 1, 3, 5 and 7 on the Numeracy continuum)
Key principle 5: Making connectionsIn the mathematics classroom
Skip counting Repeated addition Multiplication Area Volume
Students' numeracy and underlying mathematical understanding will be enhanced through engagement with a variety of applications of mathematics to real-‐world situations and problems in other learning areas.
NSW mathematics K-‐10 syllabus
Key principle 5: Making connectionsOutside the mathematics classroom
Key principle 5: Making connections
The Improving Mathematics Education in Schools (TIMES) Project 2009-‐2011
Example of linking Multiplication and Division and Ratios and Rates in the syllabus, aligned to Aspect 5 Multiplication and division as operations and Aspect 3 Number properties of the numeracy continuum, to real life problems involving money.
Effective teachers use a range of assessment practices to make students’ thinking visible and to support students’ learning.
Moment-‐by-‐moment assessment of student progress helps them [teachers] decide what questions to ask, when to intervene, and how to respond to questions.
Key principle 6: Assessment for learning
Example of questions to ask during an activity as part of formative assessment (example Make 100 activity from Counting On activities, NSW DET, 2004)
Key principle 6: Assessment for learningIn the mathematics classroom
Questioning1. After two rolls the teacher asks students to name all possible scores. (In the sample game the possible scores are 5, 23, 32, and 50.) Note: If the first two numbers rolled are the same, there are only three possible scores, e.g. rolls of 3, 3 produce possible scores of 6, 33, 60.
2. When there are two rolls to go, ask students to stand if it is still possible for them to score exactly 100. Ask their scores and check as a whole class activity.
3. When there are two rolls to go, ask students to announce their scores and say what they would like the next two rolls to be, e.g. a student with a score of 88 could score exactly 100 with 2 sixes. The same result could be achieved with a 1 and a 2 (12).
Effective teachers develop and use sound knowledge as a basis for initiating learning and responding to the mathematical needs of all students. They understand:• the big ideas of mathematics• mathematics as a coherent and connected system• how to extend and challenge student ideas• how to adapt and modify their routines to fit student
needs
Key principle 10: Teacher knowledge
The numeracy continuum K-‐10 needs to be viewed not as separate aspects to teach, but as interrelated concepts that build on each other to assist students in developing efficient numeracy strategies.
Understanding the big picture of how being able to identify and count numbers leads to understanding patterns in mathematics is vital.
Teachers also need to understand the links between additive and multiplicative thinking, flexibility with numbers and the commutative property of addition and multiplication.
Key principle 10: Teacher knowledgeIn the mathematics classroom
End of Module 2: This is a pedagogy, not a program
For accreditation please ensure all activities for this module have been completed.
All activities are to be completed in the Participant Activity Journal, the annotated lesson from Activity 2 also needs to be attached for this Module.
This is Module 2 of 5, all five modules must be completed to receive the 12 hours of registered professional learning.
Once all five modules are completed, the principal/delegate will sign off on the deliverables and the participant’s completion in the MyPL@Edu event that was scheduled by the school.