Lead Teacher MeetingsWhangarei

Term Two 20112 & 3 June

Dianne Ogle

Overview of Day

• Feedback from Meeting One – what have you tried

• Effective Pedagogies in Mathematics• Moderation – National Standards examples,

features of moderation process.• Key Ideas – continued• Update on What’s happening – ALiM, SMT• Where to next.

Effective Pedagogies in Mathematics – Anthony & Walshaw• BES findings have been summarised in a

booklet published by International Academy of Education. Will be sent to schools.

• It is intended to be a catalyst for systemic improvement and sustainable development in education.

• 10 principles – that are not stand-alone indicators – of best practise.

Beliefs that inform the principles

• Look at page 6 of Effective Pedagogy in Mathematics

• Think about each of the beliefs mentioned and what are the implications of each one.

• Work collaboratively to unpack what each belief implies.

Effective Pedagogy in Mathematics

What does it look like, sound like, feel like?

Effective Pedagogy in Mathematics• In groups of three, become familiar 3 of the

principles. • What does each principle look like, sound like

and feel like in action?

• What are the common threads - next steps:– As a teacher– As a Lead Teacher of Mathematics

Effective Pedagogy in Mathematics – Challenges• Alton-Lee has identified key challenges that

exist for each of the Principles. • What are they – summarise the ones you

worked on before

• What are the common threads - next steps:– As a teacher– As a Lead Teacher of Mathematics

Where to from here?• What do you feel are the key challenges facing

your school with regard to effective pedagogies?

• Where might you start? Identify one action you

will take.

Clear the Decks• You need a pack of cards, picture cards removed.• Decide on the target and discard any cards that are

equal to or greater than the target number.• Layout an array of cards face up so that the number of

cards on show is one less than the target number. • Play by clearing away any two cards that add to the

target number. • Replace the cards as soon as they are chosen. • Aim is to clear the whole pack of cards. • Read the number sentence as the cards are cleared

away.

An array if the target number is 6

Moderation/Teacher Judgment

• Three Elements:– Teachers attending to the learning students produce– Appraising this work against a reference framework– Making an explicit response such as feedback or

judgment on the learner’s work

Overall teacher judgment has an added complexity in that the judgment process is applied to a range of data.

Overall Teacher Judgment

• According to the Ministry of Education fact sheet (MOE, 2010) on overall teacher judgment,“An OTJ draws on and applies the evidence gathered up to a particular point in time in order to make a judgment about a student’s progress and achievement. Using a range of approaches allows the student to participate throughout the assessment process, building their assessment capability.... No single source of information can accurately summarise a student’s achievement or progress. A range of approaches is necessary in order to compile a comprehensive picture of the areas of progress, areas requiring attention, and what a student’s progress looks like.”

What is moderation?

The process where teachers compare judgments to either

confirm or adjust them

The Process

• Involves close collaboration to establish a shared understanding of what achievement of an outcome looks like and whether or not a student has demonstrated achievement of the outcome.

Underlying assumptions

• Reflective, secure professionals; open minded • Well developed interpersonal skills• Deep content knowledge• Strong pedagogical and assessment

knowledge/skills• Understandings of curriculum; progressions• Provision of exemplars• Understanding of standards• School culture of ongoing professional learning

A framework for moderation

What makes moderation easier?• Planning (the process and content)• Teachers familiar with curriculum/standards• Agreed criteria• Start with the same tasks, aims and criteria• Explicit easy criteria to judge• Sufficient samples of student work• Open-ended tasks• Providing context of tasks• Time and trust to fully discuss student samples

What makes moderation more difficult• Teachers having different interpretations of

curriculum, standards, underlying concepts• Culture of blame, mistrust, resistance to

change or ongoing learning• Insufficient evidence of achievement• Setting a range of different tasks, aims,

criteria• Poorly set tasks• Limited time

Engaging with the Standards through a rich task

Figure It Out Geometry Level Three

Pages 14 & 15 ‘Fun Run ’

Using your NZC, and the mathematics standards what type of responses would you expect to hear from students who meet the standard at year 5, 6, 7 or 8?

Geometry – Position and Orientation

• End of Year 5: describe locations and give directions, using grid references and points of the compass.

• End of Year 6: describe locations and give directions, using grid references, turns, and points of the compass.

• End of Year 7: describe locations and give directions, using grid references, simple scales, turns, and points of the compass.

• End of Year 8: describe locations and give directions, using scales, bearings, and co-ordinates.

Engaging with the Standards through a rich task

Building Borders – Figure It Out pages 12 & 13

Work through the activities in ‘Building Borders’

Using your NZC, the mathematics standards and Book one, what type of responses would you expect to hear from students who meet the standard at year 5, 6 , 7 or 8?

New Standards Illustrations

• New illustrations available on NZMaths.

• How do they add to the Standards document?

• How could you use them in your school?

Moderation Issues

• Dependability of evidence and that the assessment is consistent with teacher experience

• Moderation within and between schools

• Student Participation

• Reporting to parents, families and whanau

Where to next?

• What resources do you have available in school to support moderation, making judgments

• National standards examples• FIO/ARB tasks – deciding how to gather

evidence• Capacity building in/with schools

Brainstorm possibilities within your school

True or FalseAre the following statements true or false? Decide on your

answer – discuss with a partner and see if you agree.

93 - 38 = 91 – 40

Cain and Ryan went shopping at the $2 shop. Cain spent half of his pocket money, Ryan spent one quarter of his pocket

money. Cain spent the most.

True, False or Maybe

Key Mathematical Ideas

• Key strategies from last time

• Equations and Expressions – what are big ideas and implications

• Patterns and Relationships

Number Sense

• Having a good intuition about numbers and their relationships.

• Develops gradually as a result of exploring numbers, visualising numbers in a range of contexts, and relating them in ways that are not limited by traditional algorithms.

• Grows more complex as children learn more, eventually being able to think flexibly about fractions, decimals, percent and integers.

Big ideas

• Numbers are related to each other through a variety of number relationships - more than, less than, composed of

• “Really big” numbers possess the same place-value structure as smaller numbers. Best understood in terms of real- world contexts

• Whole numbers can be described by different characteristics, even and odd, prime and composite, square, understanding characteristics increases flexibility when working with numbers

Key Mathematical Ideas

Developing Meanings for the operations• Addition and subtraction are related. Addition names the

whole in terms of the parts, subtraction names a missing part

• Multiplication is related to addition• Multiplication involves counting groups of like size and

determining how many there are in all. Multiplicative thinking

• Multiplication and Division are related. Division names a missing factor in terms of the known factor and the product.

• Models can be used to solve contextual problems for all operations, regardless of the size of the numbers. They can be used to give meaning to number sentences.

Van de Walle & Louvin

Teaching Student Centred Mathematics,

Counting PrinciplesGelman and Gallistel (1978) argue there are fivebasic counting principles:• One-to-one correspondence – each item is labeled

with one number name• Stable order – ordinality – objects to be counted are

ordered in the same sequence• Cardinality – the last number name tells you how many• Abstraction – objects of any kind can be counted• Order irrelevance – objects can be counted in any order

provided that ordinality and one-to-one adhered to Counting is a multifaceted skill – needs to be given timeand attention!

Early Number relationships• Spatial relationships: children can learn to

recognise sets of objects in patterned arrangements and tell how many without counting.

One and two more, one and two less

• The two more than and two less than relationships involve more than just the ability to count on two or count back two. Children should know that 7, for example is 1 more than 6 and also 2 less than 9.

Anchors or “benchmarks” of 5 and 10

• An understanding of ten is vital in our numeration system and because two fives make up 10, it is very useful to develop relationships for the numbers 1 to 10 to the important anchors of 5 and 10

Part – Part – Whole Relationships

• To conceptualize a number as being made up of two or more parts is the most important relationship that can be developed about numbers.

Key Ideas – Equations and Expressions

Patterns and RelationshipsWhat important big ideas can you identify?

What links can you make to Effective Pedagogies and the Standards?

How could you help teachers to make connections – links to True/False activity?

Updates

• GLoSS sample – being moderated by NZCER – schools testing GLoSS in June – we are close to it being available

• JAM – going to Learning Media • ALiM projects• Leadership Consultation• ILC in PLD

References

Anthony, G., & Walshaw, M. (2007). Effective pedagogy in Mathematics/Pangarau: best evidence synthesis. Wellington: Ministry of Education.

 Kerry Mitchell, The Education Group & Dr Jenny Poskitt, Massey University New Zealand teachers’ overall teacher judgments (OTJs): equivocal or unequivocal? (Presentation)

Van de Walle, J. A., & Lovin, LouAnn. H. (2006). Teaching Student-Centred Mathematics Grades K-3 (Vol. One). Boston: Allyn and Bacon.