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

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Manchester population Greater Manchester :

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Manchester Commonwealth Games 2002 Metrolink Town Hall Industrial Past Roman settlement but rose to prominence during Industrial Revolution Traditional Milling and Textiles Centre Twinned with Chemnitz

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University of Manchester Dates back as far as 1824 by several different routes but took its present form in students Home/EU Overseas UG PG

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University of Manchester staff academic research 341 Buildings

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University of Manchester Four Faculties –Engineering and Physical Sciences –Life Sciences –Medical Sciences –Humanities

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University of Manchester School of Mathematics –90 academic staff – mathematics students per year

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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

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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

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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

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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

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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.

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The streamed system for Engineers : 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

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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.

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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.

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Typical R-stream student May not have officially satisfied entry offer May have large areas of maths which are causing difficulty.

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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

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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

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Diagnostic Test A test in Freshers week designed to measure student profiles across various mathematical topics.

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Diagnostic Testing at UMIST/Manchester Carried out since : 24 questions (6 sections) in 40 minutes : 48 questions (12 sections) in 80 minutes Change following curriculum Total mark less important than series of mini-marks for various sections.

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Diagnostic Testing at UMIST/Manchester Carried out since Short answers Multiple-choice (optical reader) 2009 Multiple-choice (manual entry) Carried out in Freshers week (week 0). Different times for different schools etc.

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Questions and Answer box

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Questions

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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

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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.

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Diagnostic Followup Programme 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.

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Diagnostic Followup Programme 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

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Diagnostic Followup Programme 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).

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Diagnostic Followup Programme HELM Resources HEFCE FDTL4 project Workbooks on various mathematical topics.

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Workbooks on mathematical topics

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Example

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Engineering Application

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Diagnostic Followup Programme 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.

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Diagnostic Followup Programme Computer-assessment Use of STACK, developed by Dr Chris Sangwin, University of Birmingham Accepts mathematical input Gives specific feedback Varies coefficients sensibly

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Diagnostic Followup Programme

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Developments 2007 onwards Regime for Computer-assessment In 2007 explored use of packages analysing algebraic input –STACK –WeBWorK –Maple TA Used in practice version. Not yet in use for actual version (registration issues)

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Results 2007 Stud ents Diag Test Follo wup G38953 H I J K 2987 L 6992 Stud ents Diag Test Follo wup A B C D E F246095

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Results 2008 Stud ents Diag Test Follo wup G H I J K L Stud ents Diag Test Follo wup A B C D E F

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Diagnostic Results

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Longer Consequences of Diagnostic Test Practice Tests, HELM Materials, Resource Centre all there for further use etc.

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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

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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.

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Other Diagnostic Tests

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University of Manchester Foundation Year Students from countries with an educational system which stops slightly short of level for entry to 1 st year Students desiring a change of direction Students not quite reaching the level for entry to 1 st year

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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.

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

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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.

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Late arrivals Can be a problem with compulsory followup. Test session a week or two later etc. Envelope-based test system.

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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.

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