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New Senior Secondary Mathematics Curriculum

Design of Public Assessment

HKEAA

September 2006

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• First Consultation (2004): Direction of Public Assessment

• Second Consultation (2005): Framework of Public Assessment

• Third Consultation (2006): Design of Public Assessment

NSS Math CurriculumConsultations on Public Assessment

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NSS Math CurriculumDesign of Public Assessment

• Public Examination

• School-based Assessment (SBA)

• Standards-referenced Reporting (SRR)

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Public Examination

• Hong Kong Diploma of Secondary Education (HKDSE)

• Include questions of different types & levels so as to ensure a comprehensive assessment of abilities & skills, and to cater for the varied abilities of candidates

• The above guiding principle is already adopted in current HKCE & HKAL Mathematics examinations

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Schedule for Public Examination• 2007

Design sample papersConduct pilot testing on sample papers

• 2008Write descriptors for each levelSharing sessions on sample papers, descriptors for

each performance level and samples of student performances

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Public Examination (1)Component Weighting Duration

Compulsory Part

Paper 1 Conventional questions 65% 2¼ hours

Paper 2 Multiple-choice questions 35% 1¼ hours

Component Weighting Duration

Module 1 (Calculus and Statistics) Conventional questions 100% 2½ hours

Component Weighting Duration

Module 2 (Algebra and Calculus) Conventional questions 100% 2½ hours

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• All the questions to be attempted

• Two sections Section A: Foundation Topics of the Compulsory Part

together with the Foundation Part of the S1-3 Mathematics Curriculum

Section A divided into two parts: Section A(1) (35 marks): 8 to 11 elementary questions Section A(2) (35 marks): 4 to 7 harder questions

Public Examination (2) Compulsory Part

Paper 1 (2¼ hours) (65%)

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Section B: Compulsory Part together with the Foundation Part and the Non-Foundation Part of the S1-3 Mathematics Curriculum

Section B (35 marks): 4 to 7 questions

Public Examination (3) Compulsory Part

Paper 1 (2¼ hours) (65%)

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• Multiple-choice questions • All the questions to be attempted• Two sections

Section A ( 2/3 of the paper mark): Foundation Topics of the Compulsory Part together with the Foundation Part of the S1-3 Mathematics Curriculum

Section B ( 1/3 of the paper mark): Compulsory Part together with the Foundation Part and the Non-Foundation Part of the S1-3 Mathematics Curriculum

Public Examination (4) Compulsory Part

Paper 2 (1¼ hours) (35%)

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• One paper of 2½ hours’ duration

• All the questions to be attempted

• Two sections Section A (50 marks): 8-12 short questions Section B (50 marks): 3-5 long questions

Public Examination (5) Module 1 (Calculus and Statistics)

Module 2 (Algebra and Calculus) • The same as Module 1

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Public Examination (6) Conventional Papers

• Section A Emphasis on fundamental techniques and basic knowledge

and concepts Involves short questions which are standard and straightfor

ward• Section B

Assess problem-solving skillsMore emphasis on assessing higher-order thinking skills Involves long questions which have different levels of diffic

ulty In Section B, questions may be of different marks In Compulsory Part, Section B may involve short questions

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Public Examination (7) Sample question for reference

2005 CE Math Paper 1 Section B Question 16 Peter borrows a loan of $ 200 000 from a bank at an interest rate of 6% per annum, compounded monthly. For each

successive month after the day when the loan is taken, loan interest is calculated and then a monthly instalment of $ x is

immediately paid to the bank until the loan is fully repaid ( the last instalment may be less than $ x ) , where .

(a) (i) Find the loan interest for the 1st month.

(ii) Express, in terms of x , the amount that Peter still owes the bank after paying the 1st instalment.

(iii) Prove that if Peter has not yet fully repaid the loan after paying the nth instalment, he still owes the bank

$ .

(6 marks)

(b) Suppose that Peter’s monthly instalment is $ 1 800 ( the last instalment may be less than $ 1 800 ) .

(i) Find the number of months for Peter to fully repay the loan.

(ii) Peter wants to fully repay the loan with a smaller monthly instalment. He requests to pay a monthly instalment of

$ 900 . However, the bank refuses his request. Why?

(5 marks)

000200x

]1)005.1[(200)005.1(000200 nn x

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Rationale for introducing SBA

• Broaden the mode of assessment• Capture student performances at different points of

time

• Have a positive effect on teaching and learning

• Recognize the professional judgment of teachers in the assessment process: enhance the professional development of teachers

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Some International Experience of SBA

• Ontario in Canada & Queensland in Australia: 100%

WeightingNo. of Tasks

Duration Area of tasks

UK

(GCSE)20% 2

One week

(allowed to take home)

Mathematical investigation

Data Handling

IBO

(Standard & Higher Levels)

20% 21 hour classwork +

2 hours homeworkMathematical investigation Mathematical modeling

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Local Experience of SBA (1)HKALE

Subjects Year Implemented Weighting

A Chemistry 1978 20.0%AS Chemistry 1994 20.0%A Biology 1995 20.0%AS Chinese Language & Culture 1994 10.0%AS Liberal Studies 1994 20.0%AS Design & Technology 1994 33.3%AS Electronics 1999 20.0%

AS Computer Applications 2000 30.0%

A Government & Public Affairs 1988 22.5%A/AS Physics 2004 15.0%A Engineering Sciences 2004 15.0%A/AS Art 2004 25.0%A Chinese Literature 2005 25.0%

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Local Experience of SBA (2) HKCEE

Subjects Year Implemented Weighting

Design & Technology 1980 33.3%Electronics & Electricity 1980 35.0%Design & Technology (Alt. Syl.) 2002 30.0%Graphical Communication 2002 30.0%Information Technology 2002 30.0%Technological Studies 2002 30.0%Ceramics 2004 35.0%Computer & Information Technology 2005 20.0%Integrated Humanities 2005 20.0%Science & Technology 2005 20.0%Visual Arts 2005 30.0%Chinese History 2006 20.0%History 2006 20.0%Chinese Language 2007 15.0%English Language 2007 15.0%

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• Aligns with the curriculum aims & objectives (Further Applications and Inquiry & Investigation)

• Adopts a pragmatic approach in implementing SBA

• Emphasizes quality rather than quantity

• Avoids unduly increasing the workload of teachers & students

Guiding Principles in Designing SBA in NSSMC

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• Assessment tasks will be more comprehensive and flexible that traditional exam questions:

TimeQuestion typeCoverage Use of open-ended questions Degree of assessing higher-order skillsTools can be usedWays of presenting answers

SBA: Assessment Tasks

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Year of Exam Implementation of SBA

2012 &

2013

Schools are not required to submit SBA marks. Public examination results constitute 100% of the final subject result. (x)

2014

&

2015

All schools have to submit SBA marks for feedback from the HKEAA on the outcomes of moderation. Public examination results constitute 100% of the final subject result. (O)

Starting from 2016, all schools have to submit SBA marks contributing 15% of the final subject results. ( )

The phasing in of SBA in Compulsory Part (1)

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S1 S2 S3 S4 S5 S6 Year of Exam

1st Cohort 2006 2007 2008 2009 2010x

2011x 2012

2nd Cohort 2007 2008 2009 2010 2011x

2012x 2013

3rd Cohort 2008 2009 2010 2011 2012O 2013O 2014

4th Cohort 2009 2010 2011 2012 2013O 2014O 2015

5th Cohort 2010 2011 2012 2013 2014 2015 2016

The NSS Math Curriculum has been gone through one cycle since July 2012

The phasing in of SBA in Compulsory Part (2)

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• Teachers design two assessment tasks (each student is required to complete one in S5 and the other in S6)one task on mathematical investigation or problem-solving one task on data handling

• Weighting of SBA: 15%

• Weighting of public examination: 85%

• Mainly be conducted in school under the supervision of teachers

SBA in Compulsory Part: Proposed Mode

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Resources for Setting Assessment Tasks (1)

Exemplars from HKEAA & CDI

2008 15 tasks

2009 15 tasks

2011 10 tasks

2013 10 tasks

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• Learning & teaching resources

• Textbooks & reference books

• Experience sharing among teachers

• Internet resources

• Others …

Resources for Setting Assessment Tasks (2)

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• Developmental StageDetailed guidelines & SBA handbooksExemplars, examples of student performancesTeacher training

• Implementation StageCo-ordinators to support schools & monitor the

implementationCommunication & experience sharing among teachers

• Post-exam StageModeration mechanism

SBA: Quality Assurance

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• Statistical method to moderate SBA marks with reference to students’ public examination scores

• Iron out possible differences among schools in marking standards

• The rank order of students in schools will be maintained

SBA: Moderation Mechanism

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• 2006Public consultation on Public Assessment (including the SBA

component)Review and finalize SBA design in view of school comments

• 2007Develop assessment criteriaConduct pilot testing on exemplary assessment tasksFurther develop exemplary assessment tasksSharing sessions with schools on SBA (assessment criteria,

detailed requirement and exemplars)

Schedule for SBA (1)

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• 2008Revise SBA design and requirement for trial out in 2009Conduct professional development courses and training on

SBA for teachers

• 2009-2013Publish SBA handbooks for trial outConduct a pilot study on SBA from 2009-2012Refine SBA design and requirement, if necessary, based on

the result of the pilot studyPublish finalized SBA handbooks for 2016 HKDSE in 2013Conduct professional development courses and training on

SBA for teachers

Schedule for SBA (2)

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Public Assessment in Extended Part

• There will only be a public examination, at least in the early stages

• Based on the experience of implementation of SBA in the Compulsory Part, consideration will be given to introducing an SBA component in the Extended Part at a later stage

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• Norm referenced: Report information on the relative performance of students

• Standards-referenced: Report information on the performance of students relative to fixed standards

• Standards-referenced Levels 1-5

• Use 5* and 5** to denote the highest performers

• SRR does not change the nature of the examination

• The levels awarded in the Extended Part will be reported separately from the Compulsory Part

Standards-referenced Reporting

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Thank you !!