[Insert faculty Banner] 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. Examples of assessment for learning activities linked to school teaching programs can be found on the Curriculum Support website at http://www.curriculumsupport.education.nsw.gov.au/secondary/mathematics/years7_10/programming/index.htm Schools to look at include Dapto HS with topic check ups; Coomealla HS with student checklists for topics; Northern Beaches Secondary College Manly Campus

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 processes In 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 processes Students 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 judgements The 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 B C D E 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. B The 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. E The 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 Mathematics CPDs 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 Year 9 Year 10 BOS CPDs used to make judgement

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 The continuum poster is ideal to display in your classroom and have students and teachers sharing a common understanding of syllabus expectations Place a copy of the Stage 5 mathematics CPDs beside the poster communicating to students the standards expected for particular grades at the end of Year 10 Display the continuum poster and the CPDs at parent teacher interviews communicating syllabus expectations to all stakeholders

Allocating Grades Assessment ‘of’ Learning The Assessment Program Establish an assessment program that consists of a number of assessment activities Ensure the assessment activities cover the full range of outcomes Provide opportunities for students to display their achievements in different ways and to work in a range of situations Decide on the relative importance of each assessment activity 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 The linked trigonometry tasks were developed to show the connection between the CPDs and the learn about and learn to points in the syllabus. Trigonometry was selected as the area of assessment because it is a new concept in the measurement strand for Stage 5 students, and many CPDs contain a reference to trigonometry. The tasks were designed to illustrate the type of questions that students should be able to answer as you move across the CPDs. The assessment task guide illustrates the link between the CPDs and the learn about and learn to points in the syllabus, giving appropriate examples. Developing the linked tasks is time intensive. It is recommended that the linked tasks only be used as a professional development activity to assist teachers in understanding the CPDs. The trigonometry linked tasks may be used in their current form or adapted for different cohorts. Four schools used the tasks and provided feedback on the appropriateness of the content and manageability. Teachers identified the tasks they would use to assess their students. In tasks 1 to 6 students are given the trigonometric ratios, whereas in tasks 7 to 11 they must know the ratios. In the trial schools, students studying the MS5.3.2 outcome were only given tasks 7 to 11. Students and teachers were asked for feedback about the tasks. Comments included: Easy to understand (student) The set out and diagrams were a positive (student) It was interesting that the test went from easy to hard (student) I liked how you made it hard and you helped along the way (student) Good range of questions (teacher)

Allocating Grades Assessment ‘of’ Learning Trigonometry linked task Page 1 of the Teacher copy of the trigonometry linked task. A full version of the task is available on the Curriculum Support website for download. Description of activity Students will be asked to demonstrate what they understand and can do in relation to their work in trigonometry. Students complete the relevant linked tasks. Context Measurement, Working mathematically The eleven tasks assess the right-angled and non right-angled trigonometry syllabus content from Stage 5.1 to 5.3. Each task is linked to a CPD and syllabus content. Students may attempt the tasks either throughout a unit or at the end of the unit.

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 tasks A 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 reasons What is the difference (if any) between the two discount situations?

Allocating Grades Assessment ‘of’ Learning Using anchor tasks Which grade level would (at least) be indicated or suggested by a student who could correctly answer this task? E D C B A The student typically can calculate the result of successive discounts is part of the course performance descriptor for grade B7 If a student correctly answers this question it could be one discriminator that indicates the student’s performance as at least a B7. They could be a higher grade but this item is only discriminating at least a B7 for a correct response and below a B7 for an incorrect response.

Allocating Grades Assessment ‘of’ Learning Using anchor tasks C6 B7 Class 1 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 for different class groups. Class 2

Helping New Scheme Teachers It 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 / Resources Refer to the Curriculum Support website www.curriculumsupport.education.nsw.gov.au