#MathsConf6- maximising the impact of multiple-choice questioning

At #MathsConf6 I attended a wonderful workshop delivered by @NaveenRizvi who works at Michaela Community School. She shared a number of valuable insights gained from visiting high-performing American Charter Schools and observing the practice of their best maths teachers. In this post, I’d like to share and then elaborate on an aspect of multiple-choice questioning, mentioned by Naveen, that was a real revelation moment for me.

Example 1- A poor multiple-choice question

Calculate the value of $\sqrt{\frac{36}{9}}$.

A. $\frac{10}{7}$

B. $2$

C. $x{^{2}}$

This is a poor multiple-choice question for many reasons. Firstly, there are few answers and so a complete guess has a 1 in 3 chance of being correct. Secondly, the two incorrect answers do not relate in any way to the question allowing the correct answer to be guessed by eliminating the ridiculous answers that are obviously wrong. Learning benefit- null.

I’m not suggesting anyone would give such a pointless multiple-choice question… (!) I’m just exaggerating to illustrate a point…

Example 2- A  better multiple-choice question

Calculate the value of $\sqrt{\frac{36}{9}}$.

A. $\frac{6}{9} = \frac{2}{3}$

B. $2$

C. $\frac{36}{3} = 12$

D. $\frac{6^{2}}{3^{2}}$

E. $4$

F. $\frac{18}{4.5}$

This is a better multiple-choice question for two main reasons. Firstly, there are more answers to choose from, decreasing the chance of a random guess being correct. Secondly, the wrong answers are based on common misconceptions; these can be used to inform your subsequent planning and teaching.

In the above example, the incorrect answers are based on the following misconceptions:

A. Square root the numerator only

C. Square root the denominator only

D. Confusion between the square root and the square of a number

E. Simplifying the fraction, but avoiding/ forgetting to square root

F. Halving rather than square rooting

The use of these distractor questions allows the teacher to be diagnostic in understanding misconceptions and gaps in students’ knowledge. They also prevent students from getting the correct answer through an intuitive process of elimination.

This approach has been put to highly effective use via Criag Barton’s www.diagnosticquestions.com website. Using misconception-based distractor questions is useful AFL, allowing you to take on identified misconceptions very early in instruction.

However, Naveen’s session opened my eyes to how multiple-choice questions can be levelled up even further in terms of their effectiveness…

Example 3- An even better multiple-choice question

Which of the following have a value equivalent to $\sqrt{\frac{36}{9}}$?

A. $\frac{6}{9} = \frac{2}{3}$

B. $\frac{\sqrt{36}}{\sqrt{9}}$

C. $2$

D. $\frac{36}{3} = 12$

E. $\frac{\sqrt{36}}{9^{\frac{1}{2}}}$

F. $\frac{6^{2}}{3^{2}}$

G. $4$

H. $\left ( \frac{36}{9} \right )^{\frac{1}{2}}$

I. $\frac{6}{3}$

J. $\frac{18}{4.5}$

In this example, the same incorrect distractors are included as in example 2 (A, D, F, G and J) which would give you information about misconceptions that students have. However, this time, through a slight rewording of the question I have included more than one correct answer. The question did not imply any particular number of answers; therefore a process of elimination is an entirely useless strategy. More importantly however, if students identify more than just one correct answer it tells you about the depth of their understanding. Rather than just identifying misconceptions, it tells you about the depth of their accurate-conceptions… Rather than diagnosing just what they can’t do, it diagnoses the strength and transferability of what they can do.

A student who submitted an answer of B, C, E, H and I has a much deeper understanding of the question/topic (links to fractional indices, simplifying fractions, rules of surds etc) than a student who submitted only one or two correct answers.

Multiple choice questions can be used to diagnose misconceptions. However, at MathsConf6 Naveen taught me they can also be used to diagnose the depth of students’ mastery of a topic too. Through the inclusion of more than one correct answer (by linking to other topics) you can also diagnose the depth and contextual transferability of students’ understanding/reasoning within the topic.

Thanks, Naveen for a fantastic session that included many other valuable insights! I would encourage readers of GMTI to check out her blog here: http://conceptionofthegood.co.uk.

first seen http://www.greatmathsteachingideas.com