Mathematics and Statistics Leaders Symposium September 2011 Waipuna Conference Centre Overall Teacher Judgments and Moderation Christine Hardie

Purpose To explore the multiple sources of evidence teachers can use to make overall teacher judgments in mathematics To exemplify a moderation process To examine the key principles of moderation within and between schools

Effective Assessment – NZC – p.40 Benefits students Involves students Supports teaching and learning goals Is planned and communicated Is suited to the purpose Is valid and fair

Overall Teacher Judgment (OTJ) What is an overall teacher judgment?

Overall teacher judgment An overall teacher judgment involves drawing on and applying the evidence gathered up to a particular point in time in order to make an overall 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. (MOE – fact sheet 2010.)

Overall Teacher Judgment Standards based assessment – shared benchmarks of expected performance, supported by exemplars. Summative judgment – a point- in- time description of student achievement and as such should be based on evidence that is relevant at the time the judgment is being made. Holistic judgment, defensible judgment, on-balanced judgment Part of the knowledge building inquiry cycle

Evidence All schools have data about student achievement. To make the most of these data to improve learning, we need to be aware of the evidence that describes our students’ wider learning environment. Demographics Student achievement Perceptions School processes Other practice

Evidence for overall teacher judgments in mathematics What evidence are you collecting to inform your overall teacher judgment in mathematics? Are these sources of evidence adequate?

What might count as evidence: GloSS tool – assesses the strategy number framework which aligns with the National Standards - (Use of tool needs be moderated) PAT E-asTTle School designed tests and questions ARB’s NEMP tasks

What might count as evidence: Modelling book evidence –work alongside the teacher Students books/worksheets as well as models, graphs and diagrams Learning conversations Student profiles – nzmaths Numeracy planning sheets – used as a working document Rich tasks – diagnosis Post it notes – anecdotal notes Self and peer assessment

Overall teacher judgment How do you use the multiple sources of evidence to make an overall teacher judgment?

Assessment Key Messages (pages 10-12) Meeting a standard depends on the nature of a students response to given problems, not just their ability to solve the problems. (p.10, paragraph 6) When assessing a student’s achievement and progress, the teacher needs to make an overall teacher judgement (OTJ) about the student in relation to the whole standard. (p.12 paragraph 1) The expectations for Number are the most critical requirement for meeting a standard” (p.12. paragraph 5) Number knowledge is for facilitating problem solving, just demonstrating number knowledge e.g. basic facts, is insufficient to meet a standard. (p.10, paragraph 3) independently and most of the time. (p.12 paragraph 4).

Student C

Reference materials The New Zealand Curriculum (NZC) The NZC Mathematics Standards Number Framework – Book 1 Mathematics Poster Exemplars – mathematics illustrations

Exemplars How can you use exemplars like the mathematics illustrations to support teachers to make overall teacher judgments?

Mathematics Illustrations The main purpose of the illustrations is to show how a task and a student’s response can demonstrate what it means to meet some aspects of a specific standard. Because the same task can allow students to demonstrate aspects of the expectations for more than one standard, some of the illustrations compare students’ responses to the same task at different year levels.

Questions / Discussion How do we determine if a student is ‘early’ or ‘at’ in stage 5 and stage 6?

Level 2 Stage 5: Early Additive Differentiating Between Early and Late Stage 5 Which problems, if solved correctly using part-whole thinking, would indicate late stage 5 thinking, e.g. End of Y4 83 –

Additional Stage 5 questions

Level 2 Stage 6: Advanced Additive How would you differentiate between Early and Late Stage 6?

Students place in the process How are you including the student in the process of evidence collection and analysis?

Students place in the process Ability to articulate their learning and their next steps. Teachers need to consider how their practice supports students to discuss their learning, and to explain and justify their mathematical thinking.

School-wide systems to collect evidence As a leader of mathematics what school-wide processes and systems have you put in place to support the collection and analysis of evidence?

Summary: Consistency of overall teacher judgment is developed by… Discussing what sources of evidence you currently collect to inform teaching and learning decisions Critiquing whether these sources of evidence are adequate Developing a process/template for the school (or areas within the school – e.g. junior and senior school) so that teachers are using similar types of evidence to inform OTJs.

The big picture -Moderation Moderation is the process of teachers sharing their expectations and understandings of standards with each other in order to improve the consistency of their decisions about student learning and achievement. The process where teachers compare judgments to either confirm or adjust them.

Moderation processes require I nterpersonal/social skills Theoretical and content knowledge and pedagogical content knowledge Familiarity with the agreed frame of reference or standard Staff culture-disposition towards, and systems for on- going professional learning

Teachers need to be safe to: express and clarify thinking ask questions explore solutions adapt thinking after listening to informed ideas of others tolerate and appreciate differences in perspectives view differences as opportunities to deepen knowledge base

Each teacher from a team/syndicate brings evidence of one of those students Select the children whose evidence is conflicting or who sit on the cusp. The team selects one student’s results for which they have come to agreement and take to whole- school (vertical) moderation. Teachers compare independent OTJs and come to an agreed judgment for each student using evidence / NS / resources. An example of a moderation process Each teacher uses evidence/ NS/resources to make an independent OTJ for each student

Moderation What moderation processes are you leading in your school?

Whole school moderation and between schools moderation How can we moderate across the whole school? How can we moderate between schools?

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