Diagnostic Testing in Mathematics

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Diagnostic Testing in Mathematics

• A stepwise process to ease the school /
  university interface
• Dr CDC Steele
• School of Mathematics

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Why ?
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Why ?

• Give individual students an idea of strengths and
  weaknesses

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Why ?

• Give individual students an idea of strengths and
  weaknesses
• Build up profile of classes as a whole, tailor
  courses etc.

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Why ?

• Give individual students an idea of strengths and
  weaknesses
• Build up profile of classes as a whole, tailor
  courses etc.
• Use to assign students to most appropriate
  lecture course

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Why ?

• Give individual students an idea of strengths and
  weaknesses
• Build up profile of classes as a whole, tailor
  courses etc.
• Use to assign students to most appropriate
  lecture course
• Identify students most in need of extra help

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When ?
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When ?

• August Students sent mock test

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When ?

• August Students sent mock test
• Freshers Week Students sit actual diagnostic
  test

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When ?

• August Students sent mock test
• Freshers Week Students sit actual diagnostic
  test
• Week 1 (Monday) Students assigned to lecture
  courses

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When ?

• August Students sent mock test
• Freshers Week Students sit actual diagnostic
  test
• Week 1 (Monday) Students assigned to lecture
  courses
• Week 1 Schools sent information regarding
  performance on topics

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When ?

• August Students sent mock test
• Freshers Week Students sit actual diagnostic
  test
• Week 1 (Monday) Students assigned to lecture
  courses
• Week 1 Schools sent information regarding
  performance on topics
• Week 2 Students get followup programme

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When ?

• August Students sent mock test
• Freshers Week Students sit actual diagnostic
  test
• Week 1 (Monday) Students assigned to lecture
  courses
• Week 1 Schools sent information regarding
  performance on topics
• Week 2 Students get followup programme
• Week 4 Submission of followup programme

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Who ?

• 2004
• Test A
• Aero Eng, Civil Eng, Elec Eng, Chem. Eng
• Maths, Mech Eng,
• Optometry, Chemistry
• Test B
• Building, Foundation
• Textiles

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Who ?

• 2004
• Test A
• Aero Eng, Civil Eng, Elec Eng, Chem. Eng
• Maths, Mech Eng,
• Optometry, Chemistry
• Test B
• Building, Foundation
• Textiles

• 2005
• New additions ?

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What ??
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What ??

• Well, I hope that this point will come out anyway
  !!

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The mock Test
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The mock test

• Questions similar to those to come up in
  Diagnostic Test
• Answers to these question
• Description of a wider range of potential
  questions
• References to these questions

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Questions similar to these to come in diagnostic
test
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Answers to these questions
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Wider Range of Potential Questions
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References to sources
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The Real Test
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The Real Test

• Takes place in week 0 (freshers week)
• 80 minutes for test A
• 40 minutes for test B
• Tests divided into sections of 4 questions on
  similar topics
• Profile of marks across sections more important
  than total mark
• Students informed that mark does not count.

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Test A

• Section A H. Pre-A-level and P1,P2 (C1,C2,C3)

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Test A

• Section A H. Pre-A-level and P1,P2 (C1,C2,C3)
• A Algebra
• B Trig and Geometry
• C Series
• D Functions
• E Polynomials
• F Logs / Exponentials
• G Differentiation
• H Integration

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Test A

• Section A H. Pre-A-level and P1,P2 (C1,C2,C3)
• A Algebra
• B Trig and Geometry
• C Series
• D Functions
• E Polynomials
• F Logs / Exponentials
• G Differentiation
• H Integration

• Sections I L
• P3 (C4)

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Test A

• Section A H. Pre-A-level and P1,P2 (C1,C2,C3)
• A Algebra
• B Trig and Geometry
• C Series
• D Functions
• E Polynomials
• F Logs / Exponentials
• G Differentiation
• H Integration

• Sections I L
• P3 (C4)
• I Further Algebra
• J Further Differentiation
• K Further Integration
• L Vectors

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Answer Grid 2004
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Possible Change 2005

• Multiple-Choice ??
• Options for
• I knew this once but I have forgotten
• I have never known this
• Marked by optical reader

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Output

• Mark (correct or wrong) for each question
• Mark out of 4 for each section
• Profile of marks for various section
• Number of sections A-H 3 or 4 out of 4
• Number of sections I-L 3 or 4 out of 4
• Total mark A-H
• Total mark A-L

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Destination Courses Test A

• 1P1 most advanced
• 1Q1 (1M1) intermediate
• 1R1 most basic
• Allocation done on basis of previous results,
  diagnostic tests, student opinions
• Allocation on web-page . Monday week 1

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To qualify for 1P1

• In combination with previous results
• Large number of 3 or 4 out of 4 sections across
  A-L
• Threshold totals A-H and A-L

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To qualify for 1Q1

• In combination with previous results
• Reasonable number of 3 or 4 out of 4 sections
  across A-H
• Threshold total A-H

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The QR borderline

• Students with decent previous qualifications but
  poor performance on diagnostic test
• Attend 1Q1 for weeks 1-3 , take another test in
  week 4

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Tutorial Groups

• Students placed in small group tutorials with
  students of similar ability / progress.
• Sometimes specifically selected by being strong /
  weak on particular topics.
• Diagnostic test returned at first tutorial session

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General Profiles

• Profiles of classes built up from diagnostic test
  results.
• Sent to maths staff and staff in relevant
  schools. Useful for all 1st year teaching.

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The Followup Process
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The Followup process

• A student will
• Check sections allocated
• Look at references provided
• Ask at tutorials or elsewhere
• Do practice WebCT questions
• Do real WebCT questions

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Allocation of Sections

• Up to 2 sections chosen for students on 1P1 and
  1Q1.
• 1P1 may include A-L (early unlikely)
• 1Q1 may include A-H
• Sections and procedure shown on web-page

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Allocation of sections to students Individual
programme of work for each student
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References for followup work
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References for followup work

• References as in those for mock test
• HELM modules now also available
• Assistance also available in tutorials

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Practice WebCT Questions

• Computerised questions similar to those in real
  assignment.
• Sections A-H, I-L etc.
• Can be done as many times as desired
• Random questions / parameters etc.
• Feedback given
• Also, very simple practice questions as a guide
  to WebCT.

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Real WebCT Questions

• Questions on relevant topic (similar to practice
  questions)
• Enter a numerical answer or mutliple-choice
• Randomisation of questions / parameters
• Deadline, Friday of week 4
• Counts towards 1P1 or 1Q1 coursework

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Conclusions

• Students allocated to appropriate classes
• Students provided with profile of strengths and
  weaknesses
• Staff provided with appropriate profiles of
  classes
• Students directed to resources on weak topics