# The House Cup: promoting qualitative grading in mathematics

Using qualitative instead of numerical grading in mathematics supports meaningful feedback that helps students improve the quality of their work, Jean-Baptiste Gramain explains

University of Aberdeen
3 Mar 2023
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Traditionally, mathematics assessments are graded numerically. This tends to favour the correctness of answers over their quality and can lead to poorly understood or non-constructive feedback.

Numerical grades are then converted, somewhat artificially, to alphanumeric grades (A3, B1, C2) in bands comparable to degree classifications (1st, 2:1, 2:2). In this way, assessments get linked to descriptors (A: excellent, B: very good, C: good) that may not reflect their quality.

By using descriptors to provide qualitative grading from the start, we can not only avoid grade inflation but also deliver meaningful feedback focused on the quality of the answers, which helps students improve their understanding and resulting work. This method can produce great results, but only if students are engaged from the beginning with qualitative grading.

## 1. Familiarise students with qualitative grading

To start, present your university’s grading system to students, in particular the grade descriptors, which detail precisely what is expected for each band. You can organise a short activity, where you present students with five solutions to a given exercise and discuss with them which band each solution falls into and why. Make use of formative assessment, for example by giving students the opportunity to submit their solutions to selected tutorial exercises and marking them alphanumerically.

## 2. Keep students engaged – the House Cup

A versatile way to keep students engaged with the course is to organise a House Cup, very much like at Hogwarts. At the beginning of the course, ask students to sit in groups of four or five and to choose a (mathematical) name for their “house”. I let students choose their fellow house members, but you could use a sorting hat.

Throughout the course, houses have to prepare and present solutions to chosen exercises that can be allocated randomly, using a sorting bag. Each solution presented is then discussed and graded qualitatively. Earning points for the quality of their solutions, the best house is eventually awarded the House Cup.

The House Cup facilitates group work, an essential skill rarely developed in maths courses, fosters friendly competition and stimulates the engagement of students with the course material in a fun and motivating way.

## 3. Use peer assessment

When a house presents a solution, get the other houses to discuss the grade it deserves. This will allow students to reflect on the grade descriptors and what makes a good answer, thinking about qualities such as clarity, completeness and concision. Most students will be grateful for this opportunity and will consider it a very helpful exercise. Some students, however, will be reluctant to “judge” their peers, so do ensure this remains constructive for everybody.

## 4. Keep it fun

To make sure students remain engaged with the House Cup and don’t feel you’re just “ranking them”, always keep things fun by adding nice twists.

• Use a sorting hat to allocate students to houses and a sorting bag to draw their assignments.
• Distribute bonus points for achievements such as asking or answering questions in class, being punctual, making progress between assessments.
• Allow houses complete freedom when they present, as some students will find it difficult to talk in public and shouldn’t be forced to do so.
• Organise an award ceremony at the end of the House Cup, including fun tie-breaking questions, where the winners are presented with an actual cup (or small plastic cups).
• Make sure all students are rewarded, if only with symbolic sweets or stationery.

Having engaged your students with qualitative grading, you are still left with the difficult task of marking their assessments. This can only be done if you are yourself familiar with the grade descriptors. This can take time at first, but you will soon find that, while it is sometimes difficult to decide whether to give an answer 1, 1.5 or 2 marks, it is usually fairly clear whether a solution is good, very good or excellent. Plus, having used formative assessments early on, you will have developed your skill and confidence, which will make further marking much easier.

Changing the way you grade assessments, or setting up a scheme such as the House Cup, can feel daunting, but don’t let that stop you. Using qualitative grading is unusual in mathematics and takes some getting used to, but it makes the feedback you give your students more meaningful and constructive. It encourages them to favour the quality of their submissions over “getting the answer right”. Students find the House Cup a fun way to engage with course material and deepen their understanding, a great opportunity to work in groups, and helpful motivator in producing high-quality mathematical answers. And you might finally get to shout: “Two points to Gryffindor!” during a lecture…

Jean-Baptiste Gramain is a senior lecturer and director of undergraduate pathways in mathematics at the University of Aberdeen.