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Consistency of Assessment

Mathematics 7-10

What is Assessment? Assessment is the process of identifying, gathering and

interpreting information about students' learning. The central purpose of assessment is to provide information on student achievement and progress and set the direction for ongoing teaching and learning.

“Schools are to undertake assessment to collect information about students’ learning. This will occur through both formal and informal activities.

Assessment of student learning will be undertaken for all learners, including students with disabilities: enrolled in regular classes; enrolled in special classes or in special schools; accessing life skills outcomes and content in Years 7-10 or

following life skills patterns of study in Years11-12.”Policy Standards for Curriculum Planning and Programming,Assessing and Reporting to Parents K-12

Assessment ‘for’ Learning

Assessment for learning acknowledges that assessment should occur as a regular part of teaching and learning and that the information gained from assessment activities can be used to shape the teaching and learning process.

Assessment for learning in the K-10 Curriculum Framework is designed to enhance teaching and improve learning. It is assessment that gives students opportunities to produce the work that leads to development of their knowledge, skills and understanding. Assessment for learning involves teachers in deciding how and when to assess student achievement, as they plan the work students will do, using a range of appropriate assessment strategies including self-assessment and peer assessment.

Teachers of K-10 students will provide students with opportunities in the context of everyday classroom activities, as well as planned assessment events, to demonstrate their learning.

Assessment ‘of’ Learning

Enables teachers to report on the status of student learning at various points in the teaching and learning program.

Involves teachers making professional judgements of student achievement, based on evidence collected from both formal and informal measures of each student’s performance, over time on a number of assessment for learning activities.

Collaborative planning and quality assessment processes In mathematics teaching we recognise that

assessment is a two-way mode of communication.

As well as gathering information about students’ learning, we know that it is through assessment that we communicate to students what it is that we value in mathematics.

Collaborative planning and quality assessment processes What kind of tasks provide students with an

opportunity to show what they have learnt, address significant mathematical content and provide quality feedback to the student on his or her learning?

A good assessment is valid and reliable. For example, it would not be valid to assess the topic of measuring length in such a way that students never actually measure length.

Collaborative planning and quality assessment processesIn practice, effective mathematics assessment

is characterised by tasks which: connect to prior learning provide adequate time for students to think

before responding engage students, are relevant and are valued

by them allow students to demonstrate their

mathematics skills in context

Collaborative planning and quality assessment processesStudents need to understand the standards

against which their work will be assessed. The criteria themselves are only the starting point. Students need to discuss the criteria in the context of their own work. Spending time looking at other students’ work, rather than producing their own work, may seem like ‘time off-task’, but the evidence is that it is a considerable benefit, particularly for ‘low-attainers’. (Frederiksen and White, 1997).

The Assessment Resource Centre supports assessing and

reporting student achievement relative to standards

Using Work Samples

Work samples aligned to grades assist teachers to have a clear understanding of the standards at each grade level. For each subject area in each stage, the samples of student work, together, show the standard of work typically produced by students performing at that grade level.

Teachers can use this information to assist them to consistently apply the Common Grade Scale to award grades to students.

Using Work Samples

Aligning a work sample to a particular grade indicates that the work sample is of a standard that would typically be produced by a student whose overall performance, on balance, best matches that grade description.

The samples of work for a subject area for a particular grade, when taken collectively, enable teachers to clearly see the quality of work typically produced by students who will be awarded each grade at the end of the stage.

Awarding Grades and Understanding Standards

Board of Studies Advice

Getting to know the standards (1)You become familiar with the standards by

reading: the descriptions for each grade the tasks and activities the work samples, and the grade commentaries.

Getting to know the standards (2) While reading, think of your experiences with

students you have taught who have produced work of a similar standard. This will give you a “mental picture” of the knowledge, skills and understanding represented by that grade.

Getting to know the standards (3) Discussions with your colleagues may also

be helpful particularly for

New teachers

Where a teacher is not experienced with that stage

Choosing the right grade (1) Reporting with grades requires teachers to

use their on-balance judgement in relation to standards.

This is a key professional skill.

Choosing the right grade (2) An on-balance judgement does not just focus

on a single piece of work. Teachers weigh up the assessment

information collected for a student up to that point in time.

This information will come from both formal assessment activities and informal observations and will be built up over time and in different situations.

Consistent teacher judgementsThe consistency of judgements about grades

within and between schools comes from: following teaching programs based on

common syllabuses using the common grade scale considering shared samples of student work discussions with colleagues

Common Grade Scale

Grade Grade Descriptions

A

The student has an extensive knowledge and understanding of the content and can readily apply this knowledge. In addition, the student has achieved a very high level of competence in the processes and skills and can apply these skills to new situations.

BThe student has a thorough knowledge and understanding of the content and a high level of competence in the processes and skills. In addition, the student is able to apply this knowledge and these skills to most situations.

C The student has a sound knowledge and understanding of the main areas of content and has achieved an adequate level of competence in the processes and skills.

D The student has a basic knowledge and understanding of the content and has achieved a limited level of competence in the processes and skills.

EThe student has an elementary knowledge and understanding in few areas of the content and has achieved very limited competence in some of the processes and skills.

A-E Grades

At the beginning of a reporting period, teachers will consider what students are expected to learn. That is, the knowledge, skills and understanding that is typically spelt out in the syllabuses and the teaching/learning programs developed by schools.

At the end of the reporting period, teachers will consider how well students have achieved. This is addressed by using the common A-E grade scale which summarises the degree to which students have demonstrated their achievement of the knowledge, skills and understanding they have had the opportunity to learn. How well takes into account the breadth and depth of their learning.

Course Performance Descriptors (CPDs) Course performance descriptors have been developed by the

OBOS for each course. They describe the main features of a typical student's performance at each grade measured against the syllabus objectives and outcomes for the course.

You will make the final judgement of the most appropriate grade on the basis of available assessment information and with reference to the course performance descriptors.

The grades awarded should reflect the relative emphasis placed on the assessable objectives of school programs and the syllabus. For example, where a school has placed considerable emphasis on the development of research skills, that emphasis should be reflected in the assessment program.

CPDs for Mathematics

Previous syllabus 3 courses (Advanced, Intermediate,

Standard) and 3 sets of course performance descriptors (A,B,C,D,E in each course)

Current syllabus One course, with multiple pathways for

students, reported using one set of 9 course performance descriptors (A10, A9, B8, B7, C6, C5, D4, D3, E2)

CPDs for Mathematics Download a copy of the Stage 5 Course

Performance Descriptors for Mathematics from the NSW Board of Studies website at http://www.boardofstudies.nsw.edu.au/syllabus_sc/index.html#mathematics

CPDs for MathematicsCPDs are: standards achieved by Year 10 students at

the end of Stage 5 not intended to be a checklist or a

comprehensive description of student performance

Using AE Grades and CPDs

Year 7

Semester 1 A-E reporting scale used

to make judgements on student

achievement related to

the syllabus outcomes

and content taught

during that semester

only.

Semester 2

Year 8

Semester 1

Semester 2

Year 9

Semester 1

Semester 2

Year 10

Semester 1 BOS CPDs used to make

judgementSemester 2

Making Judgements Assessment ‘for’ Learning Identify where

students are on the K-10 mathematics continuum and design learning activities that will move them along the continuum

Allocating GradesAssessment ‘of’ Learning

The Assessment Program1. Establish an assessment program that consists of a

number of assessment activities2. Ensure the assessment activities cover the full range of

outcomes3. Provide opportunities for students to display their

achievements in different ways and to work in a range of situations

4. Decide on the relative importance of each assessment activity

5. Collect performance information on each student from assessment activities

Allocating Grades Assessment ‘of’ Learning

Option 1 Assemble the information on each student

from the assessment activities to provide an overall picture of the student’s achievement

Match the overall picture of each student’s achievements to the most appropriate CPD to allocate the grade

Allocating Grades Assessment ‘of’ Learning

Using linked tasks The trigonometry linked task illustrates the

type of questions students should be able to answer as you move across the CPDs

In tasks 1 to 6 students are given the trigonometric ratios, whereas in tasks 7 to 11 they must know the ratios

Each task is linked to a CPD and syllabus content

Allocating Grades Assessment ‘of’ Learning

Trigonometry linked task

Allocating Grades Assessment ‘of’ Learning

Option 2 Use the information from the assessment

activities to determine the order of merit for the group

Use the information from anchor assessment activities developed from the CPDs to relate the order of merit to grades awarded

Allocating Grades Assessment ‘of’ Learning

Using anchor tasksA percentages anchor task Suppose that you included a question on

comparing discounts as part of one of your assessment tasks

Is a discount of 15% followed by a discount of 10% the same as a discount of 25%?

Justify your answer, giving examples and reasonsWhat is the difference (if any) between the two

discount situations?

Allocating Grades Assessment ‘of’ Learning

Using anchor tasksWhich grade level would (at least) be indicated

or suggested by a student who could correctly answer this task?

E D C B A

Allocating Grades Assessment ‘of’ Learning

Using anchor tasks

C6 B7

B7C6

Class 1

Class 2

Helping New Scheme TeachersIt is important for all teachers and particularly

for new scheme teachers to: share interpretations of syllabus expectations

and understandings with colleagues or teacher networks

use student work samples collaboratively to make judgements

have a shared understanding of student achievement at a particular point

Contacts / ResourcesRefer to the Curriculum Support website

www.curriculumsupport.education.nsw.gov.au