Diagnostic Testing : only the beginning A component in a longer process CDC Steele University of Manchester.

Diagnostic Testing : only the beginning

A component in a longer process

CDC Steele

University of Manchester


• Dates back as far as 1824 by several different routes but took its present form in 2004.

• 35 000 students

• 29 000 Home/EU

• 6 000 Overseas

• 26 000 UG

• 9 000 PG


• 11 500 staff

• 4 000 academic

• 2 000 research

• 341 Buildings


• Four Faculties– Engineering and Physical Sciences– Life Sciences– Medical Sciences– Humanities


• School of Mathematics– 90 academic staff– 400-500 mathematics students per year

Service courses to ~ 1000 students in various parts of the University.– Aerospace

Engineering– Civil Engineering– Mechanical

Engineering– Chemical

Engineering– Electrical

Engineering

– Chemistry– Optometry– Computer Science– Materials Science– Foundation Year

Entry Profiles of Maths Students

• A-levels– C1, C2, C3, C4– 2 more modules from Mechanics (M1, M2 etc,)

Statistics (S1, S2 etc), Decision (D1, D2 etc)– Many students students AS- or A-level in

Further Maths– Generally require A+ in maths A-level

Entry Profiles of Service Students

• A-levels– C1, C2, C3, C4– 2 more modules from Mechanics (M1, M2 etc,)

Statistics (S1, S2 etc), Decision (D1, D2 etc)– Some students AS- or A-level in Further Maths

Entry Profiles of Students

• A-levels. Most Engineering schools ask for Grade B in maths (part of ABB etc)

• Other UK Qualifications

• International or European Qualifications

• University of Manchester Foundation Year

Degree Structure

• Most Students : 3 year degree. (BSc, BEng etc)

• Some able students : 4 year undergraduate masters, M Math, M Eng etc

• Each year : 2 semesters : Sept – Jan and Feb – June. 12 weeks teaching plus exams at end of semester.

The streamed system for Engineers : 1996-2009

• Engineers in several schools ‘streamed’ into P-stream, Q/M-stream, R-stream.

• Streaming follows diagnostic test but not only outcome of diagnostic test

Q/M – stream. ‘Standard’

R – stream. ‘At Risk’

P – stream. ‘Elite’

Typical P-stream student

• A at A-level or equivalent

• Strong on sections C1, C2, C3

• May be weak on some C4 material

• May also be weak on a little earlier material.

Typical Q-stream student

• B,C at A-level or equivalent

• Reasonable on sections C1, C2,

• May be weak on some C3 material

• Not terribly good on C4 material

• May also be weak on a little earlier material.

Typical R-stream student

• May not have officially satisfied entry offer

• May have large areas of maths which are causing difficulty.

The diagnostic and followup programmes

• A means to measure weaknesses and concentrate efforts of students in the early weeks towards areas where they may have underachieved in the diagnostic test– Rusty– Not time for teaching– Genuine difficulty with topic.– May not have been taught certain material

Pre-diagnostic mailshot

• Mock diagnostic posted to prospective students mid-August including– Mock test paper– Answers– Other possible questions– Links to paper and web-based resources

describing the topics.– Computerised Practice Questions

Diagnostic Test

• A test in Freshers’ week designed to measure student profiles across various mathematical topics.

Diagnostic Testing at UMIST/Manchester

• Carried out since 1996

• 1997-2001 : 24 questions (6 sections) in 40 minutes

• 2002-2009 : 48 questions (12 sections) in 80 minutes

• Change following curriculum 2000.

• Total mark less important than series of ‘mini-marks’ for various sections.

Diagnostic Testing at UMIST/Manchester

• Carried out since 1996

• 1996-2004 Short answers

• 2005-2008 Multiple-choice (optical reader)

• 2009 Multiple-choice (manual entry)

• Carried out in Freshers’ week (week 0). Different times for different schools etc.

Questions and Answer box 1996-2004

Questions 2005-2009

Diagnostic Test : Sections

• A : Arithmetic and Algebra

• B : Geometry and Trig• C : Sequences• D : Functions and

Algebra• E : Polynomials• F : Logarithms and

Exponentials

• G : Simple Differentiation

• H : Simple Integration• I : Rational Functions• J : Further

Differentiation• K : Further Integration• L : Vectors

A-H : C1, C2, C3 Material : I-L : C4 material

Diagnostic Followup Programme

• For students on P- and Q- streams.

• R-stream could itself be considered as a followup

• Allocates up to 2 sections from A-L for P-stream, up to 2 sections from A-H for Q-stream.


• Allocates up to two sections based on marks of 0/4, 1/4, or 2/4.

• Sections A (Arithmetic and Algebra) and D (Functions and Algebra) allocated preferentially, then in alphabetical order.

• Students told of relevant sections via web-site towards end of week 1 of semester.


• Students informed of– Relevant section(s)– References to relevant materials– Includes HELM Resources– Pro-active and re-active sessions in

Mathematics Resource Centre.– Practice ‘tests’ on computer.

– Leading up to


• Computerised test in week 4 of semester on relevant topic(s)

• Similar to practice tests.

• Exercise counts 20% towards coursework for relevant course unit (itself worth 20% of unit assessment).


• HELM Resources

• HEFCE FDTL4 project 2002-2005

• Workbooks on various mathematical topics.

• Workbooks on mathematical topics

Example

Engineering Application


• Manchester Mathematics Resource Centre. – Support Centre for students to drop into with

Mathematical Enquiries.– Also runs pro-active sessions centring on

material on Diagnostic Followup.– Centre is within an Engineering

Building but open to ALL students.


• Computer-assessment

• Use of STACK, developed by Dr Chris Sangwin, University of Birmingham

• Accepts mathematical input

• Gives specific feedback

• Varies coefficients sensibly



Results 2007

Students

Diag Test

Followup

G 3 89 53

H 12 69 83

I 18 49 88

J 24 49 87

K 29 87

L 69 92

Students

Diag Test

Followup

A 75 83 90

B 114 67 84

C 184 38 90

D 163 65 89

E 41 70 93

F 24 60 95

Results 2008

Students

Diag Test

Followup

G 62 76 88

H 47 70 74

I 117 46 67

J 84 43 68

K 67 32 53

L 45 62 88

Students

Diag Test

Followup

A 58 89 78

B 166 70 84

C 179 65 87

D 181 82 89

E 66 78 80

F 117 64 86

Diagnostic Results 2002-09

Longer Consequences of Diagnostic Test

• Practice Tests, HELM Materials, Resource Centre all there for further use etc.

Purposes of Diagnostic Test

• Used to assign students to lecture course groupings (until now)

• Used to assign students to tutorial groups

• Used to inform staff of entry profiles of students

• Used to assign each student an individualised programme of work

Diagnostic Followup for Maths Students

• Same procedure up to diagnostic test i.e. mailshot, practice questions,

• Followup made available to maths students but not feeding into coursework.

• Students told of weaker sections and encouraged to take part in followup on these.

• Can be used as ‘indicator’ of students who may or may not be engaging with the course.

Other Diagnostic Tests

University of Manchester Foundation Year

• Students from countries with an educational system which stops slightly short of level for entry to 1st year

• Students desiring a change of direction

• Students not quite reaching the level for entry to 1st year

University of Manchester Foundation Year

• Test B

• 40 minute test.

• Three sections from Test A plus 3 sections on more basic work

• Practice questions provided in advance plus opportunities to try questions electronically.

• Used to inform staff, to allocate students to lecture courses and tutorial groups etc.

Materials Science

• Cannot ask for Mathematics A-level or equivalent. Major variations in arrival mathematics profile

Materials Science

• Test D : 50 minutes. 8 sections i.e. six from Test B test plus two more from test A.

• Used to decide which students need to go in group for more intensive sessions.

Late arrivals

• Can be a problem with compulsory followup.

• Test session a week or two later etc.

• ‘Envelope’-based test system.

Conclusions

• Students arrive with potential weaknesses in some areas.

• Take Diagnostic test and weak areas are identified

• Diagnostic Followup addresses areas of weakness

• Students can continue to access materials after exercise officially finishes.

Diagnostic Testing : only the beginning A component in a longer process CDC Steele University of Manchester.

Documents

maths slide

students students

level slide

chemnitz slide

buildings slide

pg slide

elite slide

c4 material slide