What is it?

NUMBAS is an automated maths assessment platform. Teachers can author questions and students’ responses are automarked by computer. Students can receive a worked solution or specific feedback on their particular answer, either immediately or on a set date. Randomisation of question variables can automatically generate a set of different questions, which allows students to practice questions and discourages answer copying.

NUMBAS is an open-source project created at the University of Newcastle, is free to use, has excellent documentation and continues to be actively developed.

How might I use it?

NUMBAS is a useful tool to help students enhance their maths skills through practice and is well suited to formative assessment: as it is able to provide detailed and timely feedback at scale.

It can support learning and teaching in the following scenarios:

• Regular practice – Proficiency in maths techniques is supported by regular practice.
• Closing the feedback loop. E-assessment leads to instant feedback and students the opportunity to act on the feedback and re-attempt a similar problem.
• Pre-assessment – to support students with varying experiences and abilities, e-assessment can be used to diagnose and improve their proficiency, then signpost students to additional support so they can access the course effectively.
• Bridging transitions – Maths in secondary education relies heavily on practice, feedback and intervention. To develop students towards independence needed in higher education, it could be useful to use maths e-assessment as a bridge to maintain these practices habits and as a reminder to keep up.
• Question randomisation – the randomisation of question parameters allows students to work on different instances of the same problems, which encourages discussion of approaches and supports academic integrity.
• Blended learning – Maths e-assessment can be paired with traditional approaches: where the feedback could focus on the approach to a solution, communication or the relevance of the expression, rather than the details and numerical solution.
• Flipped Learning – the opportunity for students to practice a question and receive feedback before a meeting can increase participation and make sure everyone is starting on similar footing.
• Supporting Remote Learners – e-assessment gives students off campus (e.g. on placement, distance learners, out of term time) access to assessment as learning and feedback.

How can staff use it effectively?

• Re-use or adapt questions from an existing question bank from numbas.mathcentre.ac.uk
• Offset the time needed to write a question bank through growing and improving the question bank over a number of years.
• When writing a question, start with the answer in mind and work backwards to form the question.
• Be aware of limitations: maths e-assessment is only able to give feedback based on the student’s final answer. Use NUMBAS to support students to solidify their maths techniques and fluency, which opens up contact time to build understanding and challenge in other areas (e.g. open-ended problem solving, proofs, etc.).
• Host your NUMBAS quizzes on Moodle using the External LTI tool for better reporting (contact the tel@bath.ac.uk for more information)

How can students use it effectively?

• Support good learning habits: time management and regular practice.
• Engage with feedback to reflect on approaches rather than the final answer.
• Build confidence and resilience.
• Identify areas of strengths and weakness.

What are the pros & cons?

Pros

• Allows formative assessment and consistent feedback to be delivered at scale.
• For students, repeated and low stakes assessment supports good student outcomes and avoids cramming.
• Instant feedback for the student and the opportunity for students to act on the feedback.
• Data from students can inform teaching practice.
• Supports a variety of teaching methods: flipped, blended, remote classroom, etc.
• Variable randomisation allows many a multitude of questions to be generated to support student practice and academic integrity.

Cons

• The student only inputs the final answer, so is not appropriate for all types of maths questions.
• Upfront time cost is needed to learn how to create maths e-assessment questions, as well as author questions and feedback for different student responses. This can be offset over time as the questions can be re-used.
• Complex questions and cases can be complicated to write.
• Summative assessment is not well supported because of the limitations of what maths content can be computer assessed and also IT security.

Case studies

Using NUMBAS for formative and summative assessment of Health students – University of Bath

TEAME – University College Cork and Cork Institute of Technology

The TEAME project looked at using the NUMBAS e-assessment platform to support formative e-assessment for approximately 500 first year Mathematics and Statistics students. Students were given unlimited access to practice questions and feedback a week before assessments. Staff reported good student engagement and participation, with students were positive about the instant feedback and usability of the tool.

Successes and Challenges of a NUMBAS trial – University of the West of England

Further reading and References

• NUMBAS Documentation
• NUMBAS training workshop recordings
• JISC Effective Practice with e-Assessment (2007) [pdf]