Teaching mathematical statistics: one
lecturer’s way of testing what
students understand
Published: March 4, 2026 5.27pm SAST
Author: Michael Johan von Maltitz Associate Professor, Mathematical Statistics
and Actuarial Science, University of the Free State
-------------------------------------------------------------------------------------------------------------It’s getting tougher to assess how much university students have learnt. In his work
as a Mathematical Statistics lecturer, Michael von Maltitz has tried a new way of
getting students to learn, and of assessing what they’ve absorbed and retained.
Students have to show and discuss how they arrived at their understanding of the
subject. They can’t just rely on cramming, because he interviews them as if they
were applying for a job.
What prompted you to try something new?
“We understand, but how will it be asked in the test?” This is the question that was
posed to me time and again in 2019 when I started lecturing a module in
mathematical statistics at second-year university level.
I knew I had to make a change. I already understood that students were stressed,
prone to memorising content and cramming before tests and examinations, and
using short cuts to attain a good grade, rather than to learn anything.
What did you then do differently?
The module was unfamiliar to me so I decided to allow the students to approach the
course content in the same way as I was: gathering information from different
sources and combining and collating it digitally, reflecting on how it helped to meet
certain objectives or learning outcomes.
These portfolios of learning evidence would contain course and outcome information,
content knowledge (including theorems and proofs), examples with solutions,
showpiece assignments, links to and discussions on online tutorials or videos, and
paragraphs of self-reflection. Readers might see these portfolios as “study notes on
steroids”.
Assessing the portfolio would be an exercise in evaluating the learning process,
rather than a memorised product.
The process was challenging but offered a reward for me and my students – that of
discovery. Students seemed to be genuinely learning.
Besides checking their portfolios, I needed a way to assess progress that didn’t fall
into the old habits of memorisation and “teaching to the test”. I needed to ensure that
a student had created their own portfolio and could defend the content in it. And I
needed an assessment method that would not take more time and effort than coming
up with a unique written test or examination, formulating a typeset memorandum,
and marking more than 100 answer scripts, giving feedback that the students might
never look at.
I decided to test this form of deep learning using a workplace method – the interview.
In a 30-minute online interview with each student, I asked questions about their
understanding of the module content, as well as questions concerning their own
portfolios. Each student had to defend the information collected and reflected upon.
The interview worked perfectly when paired with the portfolio. I assessed a set of
portfolios in an evening, gave typed feedback, and then interviewed those portfolios’
creators the next day. Feedback was immediate, and the interview assessment
became a learning experience, for me and the student.
They were able to defend their portfolios if I made any errors on the portfolio
assessment, and I could give the correct answer immediately to any interview
question they were stumped by.
Afterwards, the recording of the interview could be given to the student, and if they
felt I was being unfair at all, they could compare their interview with another
student’s. In doing so, the students themselves could moderate my assessment
practice.
What results did you observe?
After a year or two of teaching and assessing like this, I noticed my students seemed
to understand more of the content. They retained more into their final year, they were
fluent in “statistics” communication and they had better time management and selfreflection skills.
Students told me that they were asked the same questions in their first job interviews
as I had asked in my modules, and that they felt much more at ease in those first few
job interviews.
How did you confirm these results?
To formally test the developments I had noticed in my students, I conducted research
on the class in 2022, which was published in conference proceedings and an article.
This study showed that students experienced significant learning in every facet of an
educational framework known as Fink’s taxonomy:

foundational knowledge

application and communication

integration of content into other areas

self-reflection

interest

learning how to learn.
Thus, the method of learning and assessment could formally be called a success
within Statistics.
Can this approach be used in other courses?
Yes. One might argue that if this method can be employed for a mathematical
module, it can be utilised anywhere. Mathematical modules contain theorems,
proofs, definitions, theoretical and practical problem solving – items that might seem
difficult to assess through verbal communication. But it is the understanding of the
ideas behind the theorems, the stories of and the tricks used within the proofs, the
application of the theoretical problems, that are so important in an age where your
favourite AI can provide content knowledge.
Mathematical proofs and worked calculations, both of which take time in practice,
can be assessed by looking at a portfolio containing these items with the student’s
annotations and reflections. The understandings of these concepts are assessed in
the interview.
Likewise, in other subjects, a portfolio could be used for assessing knowledge-based
content, while the interview could be used to gauge a student’s understanding of
what was put into the portfolio, why they chose that content, why the content is
important, and how that content is used in practice.