News, Teaching Stories

Assessing Authentically: Mathematical Investigations

BILT Student Fellow Dominique Duff interviewed colleagues from four units across the University to share their authentic assessment practices in this blog miniseries.

This is a first-year unit designed to foster independent study skills and support the transition to university by proving an opportunity to work with other students. In this unit students work in teams on three mini-projects and explore in workshops topics related to their studies. This unit is well integrated with the rest of their course as the topics of the investigation projects and workshops are closely linked to other units in the curriculum which provides students with the opportunity to explore the material beyond what is covered in their other units and understand how the ideas and theories they cover can link. 

The Teaching

Investigation projects: Students have weekly meetings in small groups with their personal tutor to discuss the three mini-projects that they are working on over the year. For each investigation project they break up in small teams and produce a short report using software that will be a utilised throughout their degree. These weekly meetings are used to support the students allowing them to give updates on their progress and report on problems. Some sessions will focus on skills building such as how to write mathematics, how to prepare a presentation and how to assess a project report.

Investigation workshops: There are also weekly workshop sessions where students meet for a 2-hour block supported by a teaching assistant. For the first hour students self-organise into small groups to work through the steps of that week’s investigation workshop, with the teaching assistant on hand for guidance. This is not designed to teach new maths but instead to support the rest of their course by teaching students how to read and write maths. Students then have the opportunity to engage in further discussions, either about the topic that they just studied or about questions related to current homework problems. These workshops allow students to build learning communities and give them time to digest their course material in a supportive environment. 

The Assessment

Students must attend the workshops in order to pass the unit though they do not count as part of their summative assessment.

Students write a report and deliver a presentation for each of their three projects. Project 1 is formative and is designed to give students feedback to support their later summative efforts. Project 2 is summative with 30% of the unit grade being based on the report with 10% for the group presentation and another 5% for peer marking reports. This is repeated with Project 3 though 35% is from the report and 10% for the presentation. Individual marks on the report are derived from a group mark weighted by peer moderation surveys. 

The final 10% of this unit’s assessment comes from career sessions in weeks 21-24. This involves two sessions of taught content about career skills assessed by peer-marking cover letters and a CV they wrote in response to a real job advertisement in the field (5%) and a mock interview with their peers (5%).

The Student Voice

Overall students seem to enjoy this unit and see the value of the skills taught. Students agreed that the assessment method was not the ‘traditional’ way used on their course and ¾ of students thought that it was authentic to what might happen in their future career. 

Pie chart with 70.2% Agree, 8.5% strongly agree, 14.9% disagree

“This assessment method felt authentic”

This would suggest that the majority of students on this unit feel like this style of assessment was different to their normal mathematical problem sets and something they are more likely to utilise later in their career. This should not be taken to mean that the ‘traditional’ assessment methods do not have their place, but these results indicate that alternative assessment styles that focus on transferable skills might also be a great tool for producing quality graduates and improving the student experience.

I think mathematical investigations was probably one of my favourite units because you felt engaged, maybe because it was actually in person and you were working with other people. It was good, I really enjoyed it”

Transferable Skills

Students reported that they feel like the unit was well integrated with the rest of their program and teaches skills that will be useful later on in their degree such as presentation skills, group work and specialist software skills. 81% of students thought that they were assessed on the transferable skills taught in this unit. 

Pie chart with labels 71.7% Agree, 10.9% strongly agree and 15.2% disagree

“I think the teaching on this unit taught me transferable skills”

We wrote it in LaTeX [specialist software], which is quite good. It was a really good skill to have developed becausealmost all mathematical and scientific reports are written in something like that. There’s definitely skills to be developed from in this unit and, depending on which topic you were given, it could be quite useful if you did want to go on to do something in that area of maths again. So if I’m doing more modules like that in later years, I know what I have to do and stuff in this unit could be quite helpful.”

Students also felt like the unit integrated well with the rest of the first-year curriculum and allowed them to consolidate the teaching from their other units while developing skills that are under-utilised in other aspects of their course

It’s like less sort of conceptually challenging, I think because generally what they got us to write about was stuff that we were quite confident in from other units so that the actual challenge was producing the report. That was good because none of us do stuff like that on a regular basis.”

Group Work

Students saw the value of group work in building a learning community and seemed to agree that the groups were of a “good size”. 

It was valuable regardless of the actual content because I think it was the only opportunity in first year to really meet other people on the course.”

Like always with group work, there was the age-old question of how to deal with group members who didn’t pull their weight. Students still expressed frustration with this despite peer-review practices but felt that overall the benefits outweighed the drawbacks

“Between each project the tutor tried to change up the groups to make sure that no one was being significantly impacted by certain team member or anything…I do think that doing it as a group is like a good idea”

The peer review was helpful, but I think in the end some of us still feel like we did more work than others yet we get a pretty similar score…. but I mean it wasn’t disastrous”.

Career Skills

There was a generally mixed view on the final weeks of the unit covering career skills such as CV and interview techniques. While some students saw the benefit of the sessions in supporting summer internship applications most believed that the timing of these sessions didn’t work.

I know plenty of people just did not show up because it was only worth 10% and it was 3hour sessions. That felt like a lot of time that you could be spent revising cause it’s in the weeks just before your exams.

“I would say that it was like relatively useful, and I definitely would do it, but I think it wasn’t at the best time to convince many people to do it.”

“I think for lots of people because it was their assessments, they didn’t really engage with it in a sensible way. Most the time I think people just ended up saying stuff that they wouldn’t really have in real life to get it over with. I think that that part of the unit wasn’t really taken very seriously.”

Staff Comments

Designing this unit is fun but challenging. Most of the work in the design is done the summer period, so that the unit self-runs itself over the course of the academic year (with a few points needing more work from us such as moderating projects or running the career activities). We love to share our experience with this unit, but we find it is something easier to communicate via a conversation rather than a written statement. So we would welcome anyone who want to contact us at or to discuss any aspects of this unit.


This unit is very well integrated into the rest of the program and allows students to develop an understanding of their whole discipline and the way it links together. There is great focus on skills building through group work and presentations which will be useful throughout the degree. It is clear that the staff feel strongly about the student experience and encourage the development of a learning community even in a large cohort of around 230 students. 

Overall, this is a thoughtfully designed unit which students feel adds considerable value to their degree. They appreciate the transferable skills developed here and believe that the group work is a great way to build relationships and ease the transition into university studies. Students agree that the final sessions of the unit focus on career skills may be better received at a different time but on the whole the unit is well-structured and well-paced. 

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