Developing the WACE Mathematics Exams

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Developing the WACE Mathematics Exams

• Michelle Östberg

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The Starting Point

• CC prepared sample questions from past TEE papers
  for each unit pair grouped into Section1 and 2
• MRG provided feedback on unsuitable items for
  Section 1 (calculator free)
• Subcommittee met to structure details about why
  items were unacceptable in order to develop the
  exam design brief

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Questions rejected

• Numerical/algebraic work unnecessarily
  cumbersome, ie prevented assessment of the
  intended concept
• Artificial questions that are not truly assessing
  the concept, e.g. chance and data questions that
  really only test the manipulation of formulas

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Section 1

• The criterion that motivated the decision to have
  a calculator-free section was to test procedures
  that could be carried out on a calculator but
  that students should be able to do without a
  calculator

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Section 1

• Numbers to be nice, and complex questions for
  which the cognitive load would be excessive are
  to be avoided
• Questions can test procedures only or be
  applications

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Section 2

• All questions for which the use of a calculator
  is expected

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Calculator neutral questions

• Calculator-neutral questions can be included in
  either section

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Design Brief MAT/MAS

• Time allowed
• Reading time for Section One five minutes
• Working time for Section One 50 minutes
• Changeover period no student work approximately
  15 minutes
• Reading time for Section Two 10 minutes
• Working time for Section Two 100 minutes

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Design Brief MAT/MAS

• Permissible items
• Section One
• Standard items pens, pencils, pencil sharpener,
  highlighter, eraser, ruler
• Section Two
• Standard items pens, pencils, pencil sharpener,
  highlighter, eraser, ruler
• Special materials drawing instruments,
  templates, notes on up to two unfolded sheets of
  A4 paper, up to two approved CAS calculators, and
  one other
• non-CAS calculator (graphics or scientific)

2010 2011 only
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Design Brief MAT/MAS

• Additional information
• Section One and Section Two are printed
  separately with a different coloured front cover.
  
• Section One has a perforated page of formulas
  particular to that examination, which is retained
  for possible use in Section Two.
• Calculator memory does not need to be cleared.
• Instructions to candidates indicate that for any
  question or part question worth more than two
  marks valid working or justification is required
  to receive full marks .

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Design Brief MAT Stage 2

• The marks assigned to content areas in the
  examination are within the following ranges

These weightings apply to the whole examination
rather than individual sections
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Design Brief MAT Stage 3

• The marks assigned to content areas in the
  examination are within the following ranges

These weightings apply to the whole examination
rather than individual sections
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Design Brief MAS Stage 3

• The marks assigned to content areas in the
  examination are within the following ranges

These weightings apply to the whole examination
rather than individual sections
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Section 1

• Calculator-free
• 40 marks
• 510 questions with subparts
• Reading time 5 minutes
• Working time 50 minutes

• This section contains questions that examine
  procedures that can reasonably be expected to be
  completed without the use of a calculator.
• It contains a variety of question types which
  require both open and closed responses.
  Open-ended questions typically call for
  high-level reasoning.
• Questions require candidates to demonstrate
  knowledge of mathematical facts, conceptual
  understandings, use of algorithms, use and
  knowledge of notation and terminology and
  problem-solving skills. Selected questions could
  require candidates to investigate mathematical
  patterns, make and test conjectures and
  generalise and prove mathematical relationships.

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Section 1

• Calculator-free
• 40 marks
• 510 questions with subparts
• Reading time 5 minutes
• Working time 50 minutes

• Questions may require the application of the
  concepts and relationships to unfamiliar
  problem-solving situations, choose and use
  mathematical models with adaptations, compare
  solutions and present conclusions.
• Stimulus materials may include diagrams, tables,
  graphs, drawings, print text and data gathered
  from the media and are organised around scenarios
  or concepts relevant to the units.
• Candidates answers may include calculations,
  tables, graphs, and interpretation of data,
  descriptive answers, and conclusions.

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Section 2

• Calculator-assumed
• 80 marks
• 813 questions with subparts
• Reading time 10 minutes
• Working time 100 minutes

• This section contains questions that examine
  content and procedures that may require the use
  of a calculator.
• Candidates answer a variety of question types
  which require both open and closed responses.
  Open-ended questions typically call for
  high-level reasoning.
• Candidates demonstrate knowledge of mathematical
  facts, conceptual understandings, use of
  algorithms, use and knowledge of notation and
  terminology and problem-solving skills. Selected
  questions could require candidates to investigate
  mathematical patterns, make and test conjectures
  and generalise and prove mathematical
  relationships.

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Section 2

• Calculator-assumed
• 80 marks
• 813 questions with subparts
• Reading time 10 minutes
• Working time 100 minutes

• Questions may require the application of the
  concepts and relationships to unfamiliar
  problem-solving situations, choose and use
  mathematical models with adaptations, compare
  solutions and present conclusions.
• Stimulus materials may include diagrams, tables,
  graphs, drawings, print text and data gathered
  from the media and are organised around scenarios
  or concepts relevant to the course.
• Candidates answers may include calculations,
  tables, graphs, and interpretation of data,
  descriptive answers, and conclusions.

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Design Brief

• Not clear enough, so examples
• whats in
• whats out

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2ABMAT Whats In

• 2AMAT
• 1.2.4 linear relationships
• (a) (i) Complete this table, using the rule y
  2x 3
• (ii) Plot the points from your table on the
  Cartesian axes provided, and use them to graph
  the line y 2x 3.
• (b) On the same axes, draw the graph of
• x y 3.

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2ABMAT Whats In

• 2BMAT
• 1.1.5 convert numbers to and from scientific
  notation
• The distance from the earth to the sun is about
  150 000 000 kilometres. Write that number using
  scientific notation.

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2ABMAT Clarification

• 2BMAT
• 1.3.1 without a calculator solve equations with
  one algebraic term such as 2x2119, 3x324
• The examples in the syllabus entry are suitable
  for Section 1, but 2x2120, is not as surds are
  involved in the answer

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3ABMAT Whats In

• 3AMAT
• Reciprocal functions
• The pitch of a pipe in a musical organ (in cycles
  per second) is
• modelled by the equation where l
  is the length of the pipe (in metres).
• (a) Describe in words how P varies with l.
• (b) What would be a suitable domain for l?
  Justify your choice.
• (c) Graph the function P, using the axes below
• (d) What is the pitch of a pipe with a length of
  3 metres?
• (e) (i) Is P increasing or decreasing as l
  increases l 3?
• (ii) What units would the rate of change of P be
  measured in for the relationship?

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3ABMAT Whats In

• 3BMAT
• 1.3.4 use differentiation to determine tangent
  lines at a point for polynomial functions.
• Show that the equation of the tangent to the
  curve
• , at the point where x 1 is
• Comment
• Answer is built into the question, and numbers
  are nice so emphasis is on demonstration and
  understanding of calculus and algebra techniques

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3ABMAT Clarification

• 3AMAT 1.3.2 Solve algebraically . . . exponential
  equations would be suitable for Section
  1(nice numbers), would not be
  suitable.
• 3BMAT 1.1.1 formulate and solve one-variable
  equations and inequalities . .
• would be suitable for Section 1,
• is too hard.

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Questions???