There appears to have been a period roughly during the 1980s when multiple choice questions (MCQ) featured prominently in A-level exam papers. Precisely when or why they appeared and, indeed, when or why they disappeared again is a mystery to me at the moment. Moreover, the only textbooks I’m aware of that include MCQs are those authored by Bostock and Chandler. (There are also a couple of exam preparation books by Shipton and Plumpton that include them: Multiple Choice Tests in Advanced Mathematics, and Examinations in Mathematics.)
In the new A-level
MCQs do get a cameo role in the new A-level assessments from AQA. Each of their Specimen papers includes a couple of MCQs worth a single mark each. Here’s an example from Paper 1:
In the document The Thinking Behind Great Assessment by Dan Rogan (Chief of Examiners), is the snippet
positioning MCQs as one of four features “at the heart of our aims for the qualification”. Later in the document comes some elaboration:
Aside from ease in assessment terms, I’m keen to focus on the pedagogical value of MCQs and the potential for their use in teaching. The above example feels similar to those offered on the Diagnostic Questions site although I would suggest different potential answers if I wanted to uncover misconceptions (for example, including 2 as an option to identify students who simply observe the coefficient of x).
Indeed, here is such an MCQ on gradient from the Diagnostic Questions site [sign-in required when following that link]:
One of the excellent features of the Diagnostic Questions is the “insights” where you see students’ explanations for their answers. For example, this student offers their reasoning for (incorrectly) choosing option B:
It’s an MCQ, Jim, but not as we know it
In the 1980s A-level papers, MCQs were a much more serious affair. For a start, there were five different types of MCQ. Even interpreting the instructions is no mean feat. I’ll describe each type and then include an example. [Photos from Plumpton & Shipton.]
Section I (multiple choice)
There is a single correct answer among five options.
Section II (multiple completion)
Three responses are given (1, 2, 3) of which one or more are correct. The letter representing the student’s answer depends on which are correct:
Section III (relationship analysis)
These questions comprise two statements (1 and 2) and the student has to determine the logical relationship between them:
Section IV (data necessity)
A problem is followed by four pieces of information and the student must determine which (if any) piece of information could be omitted and the problem still be solvable:
Section V (data sufficiency)
These comprise a problem and two statements (1 and 2) in which data are given. The student has to decide if the given data are sufficient for solving the problem. Brace yourself…
Just a couple more variants…
In Core Maths for A-level, Bostock & Chandler simplify things down to three types:
- Type 1: exactly as Section I above
- Type 2: akin to Section II above but students simply write the letters corresponding to which items follow from the information in the question.
- Type 3: true/false
In their Further Pure Mathematics book, they have:
- Types 1 and 2 as in their other text
- Type 5 is true/false (as Type 3 in their other text)
- Type 3 corresponds to Section III above
- Type 4 is an amalgamation of Section IV and Section V: a problem is introduced followed by a number of pieces of information. Either all the information is needed (answer A); the total information given is insufficient (answer I); or some information can be omitted without affecting the solution of the problem (the letters for these items must then be specified)
Use of MCQs in Teaching
I think there is good potential for the use of these more sophisticated MCQs in A-level teaching, although I fear students will either need simplified instructions (for example those used in Bostock & Chandler, rather than the London board papers of the 1980s) or significant training in how to respond. In particular, I agree with Plumpton & Shipton’s comments about Sections III – V:
These items enable coverage of topics which are difficult or unfair to examine by longer structured questions. Indeed, these more sophisticated item types are a far better test of mathematical understanding than some longer questions in which candidates may be applying a method or technique which they have learnt but not have properly understood.
Time to begin building a usable bank of these questions so that I can try them out next year!