Many people assume mathematics is easy to assess.

After all, mathematics is all about precision and accuracy and so lends itself to short questions that have a single correct answer. Such questions lack ambiguity and are easy to mark consistently. Students need not worry that the subjectivity and idiosyncrasies of examiners will affect their marks. This is why short objective questions dominate school mathematics exams such as GCSEs, and even ostensibly longer questions are typically broken into smaller subparts.

We present a few example questions, complete with student responses, below.

To learn more, join us for our event for Maths teachers.

After all, mathematics is all about precision and accuracy and so lends itself to short questions that have a single correct answer. Such questions lack ambiguity and are easy to mark consistently. Students need not worry that the subjectivity and idiosyncrasies of examiners will affect their marks. This is why short objective questions dominate school mathematics exams such as GCSEs, and even ostensibly longer questions are typically broken into smaller subparts.

This is an impoverished view of mathematics.

We could easily take the same view of assessing language. Spelling and grammar are all about precision and accuracy and so lend themselves to short questions that have a single correct answer. And yet short objective questions do not dominate school English exams. Instead longer questions that require a sustained performance, such as writing an essay, are more commonly associated with languages. We can imagine the uproar if essay-style questions were removed from English GCSEs and replaced wholesale with short objective questions!

Students deserve opportunities to demonstrate sustained performance in mathematics, just as they do in languages and other arts subjects.

This would better align school mathematics with how people do mathematics in the real world, be it research mathematicians, engineers or someone doing their household budget. We need the mathematical equivalent of essay questions: that is, questions that are open-ended and allow a wide and unpredictable range of responses. Questions that are judged in terms of their mathematical quality, rather than their accuracy against predetermined answers.

At No More Marking we have recently been working on developing and trialling such open-ended mathematics questions. The results are consistently positive: from primary to university level we have found students engage fully with the questions, and the comparative judgement process enables their responses to be assessed validly and reliably.

We present a few example questions, complete with student responses, below.

To learn more, join us for our event for Maths teachers.

I completely agree with all that you say, and hope that teachers will be able to adapt the exams accordingly. But not only that, that they will be able to give more help to students so that the final result is not just right or wrong, but is a true test of their understanding of the mathematical principles behind the questions.

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Any system that will enable teachers to have more time to deal with students in a way that helps their understanding is going to be of great benefit. Too much reliance is being placed directly on right or wrong answers, instead of addressing the students' own ideas and methods to reach answers which, although not finally correct, show a degree of understanding of the process required to reach a correct answer, and this requires teachers to actually spend time with the student instead of all their time marking papers and leaving any feedback in the form of a final score.

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