Leading the leaders of the teaching of numeracy Peter Sullivan Literacy and numeracy national partnerships

Overview A task for you The context Your assets Planning action Literacy and numeracy national partnerships

Part 1: Some mathematics We are selecting furniture but we want to be flexible You are in the shop so the expectation is that you will do this by imagining. If we choose trapezoid seats, can we make a regular hexagon? Literacy and numeracy national partnerships

Can we make an irregular hexagon? Literacy and numeracy national partnerships

How can we make an equilateral triangle using three seats? Literacy and numeracy national partnerships

What other shapes can be made using trapezoid seats? Literacy and numeracy national partnerships

Part 2: The (South) Australian context Literacy and numeracy national partnerships

The Shape Paper(s) All Australian governments have committed to the goals of the Melbourne Declaration, Australian schooling promotes equity and excellence; and that all young Australians become successful learners, confident and creative individuals, and active and informed citizens. (p. 5) Literacy and numeracy national partnerships

This is even described as an entitlement … of each student to knowledge, skills and understandings that provide a foundation for successful and lifelong learning and participation in the Australian community. (p.10) Literacy and numeracy national partnerships

What are you hoping for? Creativity, imagination, adaptability, willingness to think and make decisions, persist, … … and life long learners … … or correct answers, compliance, acceptance of place in life, … Literacy and numeracy national partnerships

SA vs Aust Year 9 over 6 years Literacy and numeracy national partnerships

We know that many students - forget what they have learnt from one year to the next, - are unwilling to engage with challenging tasks, - develop negative attitudes to mathematics early. We also know that there are too few students choosing middle and high levels of mathematics study … The current context Literacy and numeracy national partnerships

The experience of many students in the middle years is described predominantly as boredom Too many students are excluded (structurally) too early from the opportunity to learn mathematics All students can do work that is more challenging, and the challenge helps them to make connections Literacy and numeracy national partnerships

“More of the same” is not a desirable option It is not just improvement but CHANGE that is needed In other words... Literacy and numeracy national partnerships

Some myths that need to be addressed Instruction followed by practice is the only way to teach Complex problems are OK but students need to be shown how to work them out Students become more disengaged when they are challenged Mathematics concepts are best taught one at a time Only some students can learn mathematics Students prefer to be shown what to do Literacy and numeracy national partnerships

What do you see as the most critical aspect of being a powerful learner of numeracy and literacy? Powerful learners connect ideas together, they can compare and contrast concepts, and they can transfer learning from one context to another. They can devise their own solutions to problems, and they can explain their thinking to others. Literacy and numeracy national partnerships

If, as a teacher, I wish to build more powerful numeracy and literacy learners among my class/es, what, in your opinion, would be my first step? First, establish the classroom culture that is needed Next, find out what students know – (as distinct from what they do not, which seems to be the focus of many commonly available assessment tools in current use). Then build on what they know to create connected and challenging learning experiences – (learning one idea at a time is disabling, but connecting ideas together is powerful) At the same time, take actions to both model persistence, affirm persistence when you see it, and explain the importance of persistence. Never criticise failure, but affirm failure as a step on the path to powerful learning Literacy and numeracy national partnerships

In the Australian curriculum Understanding – (connecting, representing, identifying, describing, interpreting, sorting, …) Fluency – (calculating, recognising, choosing, recalling, manipulating, …) Problem solving – (applying, designing, planning, checking, imagining, …) Reasoning – (explaining, justifying, comparing and contrasting, inferring, deducing, proving, …) Literacy and numeracy national partnerships

How is this represented in the AC? Literacy and numeracy national partnerships

Part 3: Your assets The collective energy of the teaching teams The coaches and other innovators Literacy and numeracy national partnerships

Teams can focus on the six principles as the basis of sustainable improvement Literacy and numeracy national partnerships

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Key principle 1: Identify important ideas that underpin the concepts you are seeking to teach, and communicate to students that these are the goals of your teaching, including explaining how you hope they will learn Literacy and numeracy national partnerships

goals

Implications for leaders Create opportunities for discussions of: – goals for the year – unit goals – lesson goals And processes for articulating and communicating those goals to each other and the students (and their parents?) Literacy and numeracy national partnerships

Key principle 2: Build on what the students know, both mathematically and experientially, including creating and connecting students with stories that both contextualise and establish a rationale for the learning Literacy and numeracy national partnerships

goals readiness

What are implications for leaders? Encourage teachers to – Find out (or at least assume) what students are interested in – Create a rationale for learning – Relate the topic to past and future topics – Link learning to other domains Literacy and numeracy national partnerships

Key Principle 3 Engage students by utilising a variety of rich and challenging tasks, that allow students opportunities to make decisions, and which use a variety of forms of representation Literacy and numeracy national partnerships

_math_curriculum_makeover.html Today's math curriculum is teaching students to expect -- and excel at -- paint-by-numbers classwork, robbing kids of a skill more important than solving problems: formulating them. In his talk, Dan Meyer shows classroom- tested math exercises that prompt students to stop and think. Literacy and numeracy national partnerships

Why challenge? Learning will be more robust if students connect ideas together for themselves, and determine their own strategies for solving problems, rather than following instructions they have been given. Both connecting ideas together and formulating their own strategies is more complex than other approaches and is therefore more challenging. It is potentially productive if students are willing to take up such challenges. Literacy and numeracy national partnerships

This is a paddock in the shape of an L. The area is 1 hectare. How many metres wide is the top part of the L? (A square 100 m x 100 m has an area of 1 hectare) (Diagram not drawn to scale) 6020 cohort

AnswerPre-TestPost-Test I prefer tasks I work on in class to be much harder than the paddock question 16% I prefer tasks I work on in class to be about as hard as the paddock question 62%61% I prefer tasks I work on in class to be much easier than the paddock question 22%23% 100% 6020 cohort

AnswerPre-TestPost-Test I prefer to work out tasks like the paddock question for myself 31%32% I prefer to work on tasks like the paddock question with other students 54%58% I prefer to be told what to do by the teacher 15%11% 100% 6020 cohort

First do this task On a train, the probability that a passenger has a backpack is 0.6, and the probability that a passenger as an MP3 player is 0.7. How many passengers might be on the train? How many passengers might have both a backpack and an MP3 player? What is the range of possible answers for this? Represent each of your solutions in two different ways cohort

Starting from the content descriptions 6020 cohort

Reading the content description(s) to identify the key ideas Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) (ACMSP292) 6020 cohort

Reading the content description(s) to identify the key ideas Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) (ACMSP292) 6020 cohort

Reading the content description(s) to identify the key ideas Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) (ACMSP292) 6020 cohort

Reading the content description(s) to identify the key ideas Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) (ACMSP292) 6020 cohort

Reading the content description(s) to identify the key ideas Represent events in two-way tables and Venn diagrams and solve related problems (ACMSP292) (ACMSP292) 6020 cohort

Literacy and numeracy national partnerships goals readiness engage

What are the implications for leaders? Encourage teachers to – acknowledge different learning styles and to use a variety of types of experiences – give students opportunities to make decisions – see challenge as part of learning – allow Students to explain and justify their thinking Literacy and numeracy national partnerships

Key teaching principle 4: Interact with students while they engage in the experiences, and specifically planning to support students who need it, and challenge those who are ready Literacy and numeracy national partnerships

goals readiness engage difference

Literacy and numeracy national partnerships achievement ability

8 strategies for dealing with difference Literacy and numeracy national partnerships

Common to all 8 approaches The intention is to foster the sense of a classroom community to which all students contribute The experience of engaging with the task happens before instruction The classroom pedagogies are explicit – The grouping – Expectations for individual work – Modes of assessment Literacy and numeracy national partnerships

Few rather than many tasks All students are given time to engage sufficiently to participate in the review Asking students to solve problems in more than one way Different ways of responding to the experiences, and the different approaches are themselves educative Literacy and numeracy national partnerships

Key teaching principle 5: Adopt pedagogies that foster communication, mutual responsibilities, and encourage students to work in small groups, and using reporting to the class by students as a learning opportunity Literacy and numeracy national partnerships

goals lesson structure readiness practice engage difference Collaborative teacher learning

Part 4: The role of the leader of the leaders Literacy and numeracy national partnerships

My summary of the challenge for you The mechanism for sustainable improvement is effective collaborative planning teams and any barriers to this should be removed The focus of these teams needs to be on improving the experience of students when learning mathematics Many current approaches to teaching mathematics need to be questioned, and the expectation of improvement made explicit Literacy and numeracy national partnerships

If you have resistant teachers, use collaborative planning as a starting point Support your innovators Communicate your expectation of change and, at least, trying new ways Literacy and numeracy national partnerships

Selecting and sequencing tasks including adapting them for your students Examining curriculum content descriptions to identify the important idea(s) Planning the teaching and assessment including differentiating for particular students Drawing on experience (self and colleagues) Drawing on “own assessments” Checking school or web documents, teacher resources and/or student texts Establishing specific learning goals, writing assessments, etc Literacy and numeracy national partnerships