{"id":79765,"date":"2026-03-05T00:42:10","date_gmt":"2026-03-05T05:42:10","guid":{"rendered":"https:\/\/world.edu\/?p=79765"},"modified":"2026-03-05T00:42:10","modified_gmt":"2026-03-05T05:42:10","slug":"teaching-mathematical-statistics-one-lecturers-way-of-testing-what-students-understand","status":"publish","type":"post","link":"https:\/\/world.edu\/teaching-mathematical-statistics-one-lecturers-way-of-testing-what-students-understand\/","title":{"rendered":"Teaching mathematical statistics: one lecturer\u2019s way of testing what students understand"},"content":{"rendered":"

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\nIt\u2019s getting tougher to assess how much university students have learnt. In his work as a Mathematical Statistics lecturer, Michael von Maltitz has tried a\u00a0new way<\/a>\u00a0of getting students to learn, and of assessing what they\u2019ve absorbed and retained. Students have to show and discuss how they arrived at their understanding of the subject. They can\u2019t just rely on cramming, because he interviews them as if they were applying for a job.<\/em><\/p>\n

What prompted you to try something new?<\/strong><\/h4>\n

\u201cWe understand, but how will it be asked in the test?\u201d 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.<\/p>\n

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.<\/p>\n

What did you then do differently?<\/strong><\/h5>\n

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.<\/p>\n

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 \u201cstudy notes on steroids\u201d.<\/p>\n

Assessing the portfolio would be an exercise in evaluating the learning process, rather than a memorised product.<\/p>\n

The process was challenging but offered a reward for me and my students \u2013 that of discovery. Students seemed to be\u00a0genuinely learning<\/a>.<\/p>\n

Besides checking their portfolios, I needed a way to assess progress that didn\u2019t fall into the old habits of memorisation and \u201cteaching to the test\u201d. 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.<\/p>\n

I decided to test this form of deep learning using a workplace method \u2013 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.<\/p>\n

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\u2019 creators the next day. Feedback was immediate, and the interview assessment became a learning experience, for me and the student.<\/p>\n

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.<\/p>\n

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\u2019s. In doing so, the students themselves could moderate my assessment practice.<\/p>\n

What results did you observe?<\/strong><\/h4>\n

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 \u201cstatistics\u201d communication and they had better time management and self-reflection skills.<\/p>\n

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.<\/p>\n

How did you confirm these results?<\/strong><\/h4>\n

To formally test the developments I had noticed in my students, I conducted research on the class in 2022, which was published in\u00a0conference proceedings<\/a>\u00a0and an\u00a0article<\/a>.<\/p>\n

This study showed that students experienced significant learning in every facet of an educational framework known as\u00a0Fink\u2019s taxonomy<\/a>:<\/p>\n