The introduction of CAS into assessment in mathematics at the IBO Aspects of item design and student performance

International Baccalaureate Organization (IBO) International Examination curriculum –Offered in over 2000 schools in 125 countries All students must complete 2 yrs of mathematics 3 Mathematics courses, Math HL used for CAS Pilot CAS Pilot first examinations in 2006

Institutional impacts on Pilot Prestigious university entrance examination IBO has less influence on student acceptance into university than a national examination authority. Schools concerned about impact of student CAS use on university entrance International context can slow progress 2000 first year of graphics calculator required examinations

Institutional impacts on Item Design Constraints –The examination represents the values of the system –New program with minimal change to graphics calculator required mathematics curriculum –Modified questions from the concurrent graphics calculator examinations –High degree of commonality preferred –Questions set were accessible to by hand techniques –Questions largely context free and conservative in nature

John’s view as external advisor I saw the draft Higher Level papers (non- CAS and CAS) and wrote a report. Here is a summary of my thoughts for Paper 1.

NB This was a JOB for the IBO – it would not have been proper for me to start making value judgements as to what to do and what not to do – but I should provide opinion for THEIR consideration. Research issue – ‘players in the game’

20 questions – one to be decided Of the 19 questions 13 CAS questions were identical 1 CAS questions was almost identical 4 CAS questions were based on non-CAS 1 new CAS question replaced a non-CAS

Issues Identical questions - anything wrong with this? Various arguments ♦ Keep them all the same – we use the tool but assess the mathematics ♦ Totally new paper - celebrate what CAS can do And lots of other views: ♦ conservative ‘celebration’ ♦ conservative ‘care’ for old skills

However, imagine you are a student who has used a CAS for 2 years in class. You see the first question In an arithmetic sequence the second term is 7 and the sum of the first five terms is 50. Find the common difference of this arithmetic sequence. Do you expect to use your CAS?

Issues – complex input/output In a complex number question switching between complex formats potential for error in keying in potential for unusual output, e.g.

Overview of Paper 1 CAS calculators do no more than GCs (including no help) 2b, 6, 7, 8a, 10b, 13, 15, 16, 19, 20 Question posed so that CAS will not assist in the solution 1 CAS can help but this is minor with regard to the whole question 3, 4, 5, 11, 17, 18 CAS can help but CAS use complex and/or error-prone 2a, 2c, 10a, 14b CAS provides considerable help 8b, 14a

CAS impact on Item Design Shift in mathematical abilities assessed Explosion of student methods expected Potential “trivialisation” of questions Reasoning from an output versus by hand calculations

Observations of student performance Effective mathematics communication lacking Minimal use of CAS noted Reluctance to use CAS led to examples of students erroneous use of by hand techniques Question involving parameters were not well done Students performance was comparable to non CAS examination.

Observations for the future Students require more practice with questions involving parameters Students need to become more comfortable with using CAS Structure of CAS outputs