Actual Models in Different Contexts

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Actual Models in Different Contexts

• 28 April 2009

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What is tiering?

• Tiering refers to the provision of more than
  one level of question papers to students. One
  difficulty inherent in all single-level structure
  is that they may discourage a student from
  developing a center of interest among a large
  number of subjects. So it may be desirable to
  introduce more than one tier of examinations to
  students. For the ease of discussion, we shall
  concentrate on cases in which an additional level
  of examination is introduced. In reality,
  multi-level structures may be used, depending on
  the availability of resources and degree of
  acceptance by the general public at large.

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The Basic Proficiency Tests

• Tests in Chinese, English and Mathematics at S3
  level.
• Offered to the general public
• Taken on an optional basis

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Candidature for Basic Proficiency Tests

• The Chairman of the School Examinations
  Board said that the small candidature was mainly
  due to the failure of Government to give formal
  recognition to the tests. He pointed out that
  schools and students would not take the tests
  seriously as they were aware that the BPT
  qualifications would not serve any practical
  purpose. A member opined that the BPT
  qualifications would have little value for
  employment purposes and that the tests should be
  abolished with immediate effect.

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Special Papers

• Special papers (commonly known as S levels)
  provide a means of extending intellectually able
  students by offering them the opportunity to
  demonstrate and be assessed on more complex
  intellectual skills and to have their
  achievements recognized. Discussions indicate
  that the majority of the able young people who
  take special papers find them a rewarding
  experience. Many teachers also find it highly
  rewarding to teach these courses to small groups
  of able young people.

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Concerns

• Nevertheless, special papers have been
  declining rapidly in popularity. Numbers of
  students sitting them have fallen from 17 400 in
  1989 to 9 500 in 1994. The fall has been
  particularly steep in Mathematics, where the
  take-up is less than a third of its previous
  level. Reasons for this general decline include
  the following
• Some centers are reluctant to encourage
  specialization and prefer to offer breadth rather
  than depth.
• Some centers (particularly in the further
  education sector, where special papers do not
  carry funding units) find it difficult to provide
  extra tuition for small numbers of pupils in
  individual subjects.
• A lack of credit given to special papers by
  institutions of higher education, who see
  achievement as measuring the strength of the
  teaching institution as much as that of the
  pupil.
• Some feeling among universities that at this
  stage students might benefit more from other
  forms of development.

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The Use of Graded Tests

• Offers tests at different levels of difficulty

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Examples

• ABRSM Tests
• Language tests

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Two Tests, Two Scales

• Serves practical purposes
• Provides progression
• Dependent on demand

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Tailored Syllabus

• Refraction of light
• Laws of refraction
• Path of a ray being refracted at a boundary
• Definition of refractive index of a medium n
  sin i / sin r
• Application of Snells law to solve problems
  involving refraction at a boundary between vacuum
  (or air) and another medium
• Total internal reflection
• Conditions for total internal reflection
• Problem solving involving total internal
  reflection and critical angle at a boundary
  between vacuum (or air) and another medium

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The Use of the Tailored Curriculum in Mathematics
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Core-competence Approach

• Performance on the core part graded separately
• Two grades provided

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Core-competence Approach

• The grade on the core part serves the
  certification purpose
• The grade on the whole subject serves the
  selection purpose

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The AS Model
AS
Paper 1
AL
Paper 2
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• AS candidature still small compared with the
  main AL subject.

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One Test, One Scale

• Not always possible to divide a syllabus into
  different parts
• Content may be over fragmented
• Special methods needed to aggregate scores in
  subparts

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Syllabus A and Syllabus B

• Two different syllabuses offered
• A linkage is made with effect from 1997

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Syllabus A and Syllabus B

• Since then the candidature jumps rapidly

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Differentiated Paper Approach

• In this option, students are required to sit
  two papers from the three offered with one of the
  papers being a common paper undertaken by all
  students. This common paper would span the range
  of difficulty in the subject except for the
  extremes of the difficulty scale. It would not
  include questions which are so difficult that
  only the most able students could successfully
  answer the question. It would not include
  questions that were easy enough that all students
  would answer them correctly.
• There is a second paper which is designed
  with a range of difficulty to challenge the most
  able students undertaking the subject. The third
  paper will have a limited range of difficulty and
  focused on the likely achievements of the less
  able students. This paper is likely to offer
  little challenge to the more able students.
• Once the choice has been made, it will have
  implications for the grades attained. Examination
  boards usually set limits on the attainment of
  students if they take the lower tier examination.

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Differentiated Papers

• Practised in GCSE examinations

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Addition of an Extra Paper

• Mathematics
• Additional Mathematics

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Candidature for the subject of Mathematics and
Additional Mathematics in the HKCEE
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Two Levels, One Scale

• Equating techniques required (horizontal /
  vertical equating)
• Levels of attainment at bottom end not recognized
• No unified design

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Tiering Conditions for Success

• Forward looking
• Flexible arrangements
• Financially viable

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• What can we do next?

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What can we do next?

• The formative use of summative assessment
• The summative use of formative assessment
• Adopt tiering methods as appropriate

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The Formative Use of Summative Assessment

• 2007 CE Maths p110

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The Summative Use of Formative Assessment

• Use SBA marks for summative assessment
• But for reliable assessment, as required for
  summative purposes, there must be certain
  conditions on the use of this information,
  specifically that
• It is reviewed strictly against the criteria
  of what students are expected to achieve at
  certain ages / stages. The criteria are applied
  holistically, using judgements as to the best
  fit. There is some way of ensuring that the
  judgements of one teacher are comparable with
  those of other teachers.
• Harlen James

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Tiering

• Two Tests / Two Scales
• E.g. HKDSE Mathematics
• One Test / One Scale
• E.g. HKDSE Combined Science
• Two Tests / One Scale
• E.g. HKDSE English Language

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• A progressive society counts individual
  variations as precious since it finds in them the
  means of its own growth.
• John Dewey (1916)
• Democracy and Education