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Consistency of Moderation

Mathematics 7-10

What is moderation?

Moderation is a process where teachers compare judgements to either confirm or adjust them.

The process involves close collaboration to establish a shared understanding of what achievement of syllabus standards looks like and whether or not the student has demonstrated achievement of the syllabus standard. Teachers work towards making judgements that are consistent and comparable.

What is consistency of moderation?Consistency of teacher professional judgement

refers to the degree to which judgements about a student’s performance are independent of which teacher is assessing the student.

Why do we moderate?We moderate to: develop shared or common interpretations of

standards and expectations of what constitutes achievement of syllabus standards

develop shared understandings of what students’ achievements look like

develop accuracy and reliability in making judgements

ensure judgements are equitable in terms of implications for student learning

strengthen the value of teachers’ judgements inform well-targeted teaching programs

Moderation techniques in Mathematics

Some challenges

In studying children’s thinking we usually find all sorts of in-between patterns of performance: children who succeed on some versions of the task but not on others, and who thus seem sometimes to have the concept and at other times to not have it.

Cognitive Development (p. 321)

Flavell, Miller & Miller, 1993

Moderation techniques in Mathematics

Two componentsAll teachers’ judgements have two

components: the decision and the level of confidence in the decision

Sometimes you need more information to make a confident decision.

Examples of Professional Dialogue Discussion of syllabus framework Discussion of outcomes Share interpretations and understandings Collaboratively discuss work samples and

standards Shared understanding of student

achievement at a particular point

Teacher judgement How do you form your expectations of what your

students should achieve?

Sources of information:

- syllabus expectations

- shared professional expectations and discussion

Developing a shared understanding of syllabus outcomes

Informing judgement: What do you want the students to learn? What parts of the syllabus do you currently draw on to inform

your planning, teaching and assessing?

Knowledge and

skills

Students

learn

about

Working

Mathem

atically

Students learn to

Developing a shared understanding of syllabus outcomes

Why do students need to learn about measurement?

Why does the learning matter? Students need to make reasonable estimates

for quantities, be familiar with the most commonly used units for length, area, volume and capacity, and be able to convert between these units.

They should develop an idea of the levels of accuracy that are appropriate to particular situations.

Cylinder Configurations

Materials needed Three A4 sheets of paper Sticky tape Ruler

Outcomes MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders WMS4.2 Analyses a mathematical or real-lif e situation, solving problems using technology where appropriate

Task Working in pairs, you will need two A4 sheets of paper. With one sheet in the landscape orientation form a cylinder by joining the edges of the paper. With the other sheet in the portrait orientation form a cylinder by joining the edges of the paper. When made f rom an A4 piece of paper, which has the greater capacity: a cylinder formed by rolling along the length (portrait) or along the width (landscape)? J ustif y your answer.

Landscape

Portrait

What will the students do?

How well do you expect students to complete the task?

What is the expectation of student achievement at Stage 3, 4 and 5?

An understanding of the continuum of learning in the substrands of Area and Volume and Capacity will provide information on syllabus expectations for Stage 4 students.

What is the expectation of student achievement at Stage 3?Key ideas

Area Select and use the appropriate unit to calculate area Develop formulae in words for finding area of squares,

rectangles and triangles Volume and capacity

Select the appropriate unit to measure volume and capacity Estimate and measure the volume of rectangular prisms Determine the relationship between cubic centimetres and

millilitres Record volume and capacity using decimal notation to

three decimal places

What is the expectation of student achievement at Stage 4?Key ideas

Surface Area and Volume Find the surface area of rectangular and triangular prisms Find the volume of right prisms and cylinders Convert between metric units of volume

Perimeter and Area Convert between metric units of length Convert between metric units of area Investigate and find the area and circumference of circles Develop formulae and use to find the area and perimeter of

triangles, rectangles and parallelograms

What is the expectation of student achievement at Stage 5?Key ideas for

Perimeter and Area (Stage 5.1) Find the area and perimeter of simple composite figures

consisting of two shapes including quadrants and semicircles

Develop formulae and use to find the area of rhombuses, trapeziums and kites

Surface Area and Volume (Stage 5.2) Find the surface area of cylinders and composite solids Find the volume of pyramids, cones, spheres and

composite solids

Work sample 1

Cylinder Configurations

Materials needed Three A4 sheets of paper Sticky tape Ruler

Outcomes MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders WMS4.2 Analyses a mathematical or real-lif e situation, solving problems using technology where appropriate

Task Working in pairs, you will need two A4 sheets of paper. With one sheet in the landscape orientation form a cylinder by joining the edges of the paper. With the other sheet in the portrait orientation form a cylinder by joining the edges of the paper. When made f rom an A4 piece of paper, which has the greater capacity: a cylinder formed by rolling along the length (portrait) or along the width (landscape)? J ustif y your answer.

Landscape

Portrait

Work sample 2

Cylinder Configurations

Materials needed Three A4 sheets of paper Sticky tape Ruler

Outcomes MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders WMS4.2 Analyses a mathematical or real-lif e situation, solving problems using technology where appropriate

Task Working in pairs, you will need two A4 sheets of paper. With one sheet in the landscape orientation form a cylinder by joining the edges of the paper. With the other sheet in the portrait orientation form a cylinder by joining the edges of the paper. When made f rom an A4 piece of paper, which has the greater capacity: a cylinder formed by rolling along the length (portrait) or along the width (landscape)? J ustif y your answer.

Landscape

Portrait

Work sample 3

Cylinder Configurations

Materials needed Three A4 sheets of paper Sticky tape Ruler

Outcomes MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders WMS4.2 Analyses a mathematical or real-lif e situation, solving problems using technology where appropriate

Task Working in pairs, you will need two A4 sheets of paper. With one sheet in the landscape orientation form a cylinder by joining the edges of the paper. With the other sheet in the portrait orientation form a cylinder by joining the edges of the paper. When made f rom an A4 piece of paper, which has the greater capacity: a cylinder formed by rolling along the length (portrait) or along the width (landscape)? J ustif y your answer.

Landscape

Portrait

Work sample 4

Cylinder Configurations

Materials needed Three A4 sheets of paper Sticky tape Ruler

Outcomes MS4.2 Calculates surface area of rectangular and triangular prisms and volume of right prisms and cylinders WMS4.2 Analyses a mathematical or real-lif e situation, solving problems using technology where appropriate

Task Working in pairs, you will need two A4 sheets of paper. With one sheet in the landscape orientation form a cylinder by joining the edges of the paper. With the other sheet in the portrait orientation form a cylinder by joining the edges of the paper. When made f rom an A4 piece of paper, which has the greater capacity: a cylinder formed by rolling along the length (portrait) or along the width (landscape)? J ustif y your answer.

Landscape

Portrait

An initial sort

Look through the student work samples and, as a group, put them into three piles: At standard Below the expected standard Above the expected standard.

Discuss: What questions do you need to answer to be able to do this?

What is the basis for your decision?Below Stage 4 At Stage 4 Above Stage 4

Work sample # is at Stage 4 because…

Contacts / ResourcesRefer to the Curriculum Support website

www.curriculumsupport.education.nsw.gov.au