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On the risk of misinterpreting statistics

13 Apr 2022

In her capacity as Professor of Mathematics Education, Karin Binder primary focus is on problems surrounding the incorrect presentation and communication of statistical information, especially in social contexts that are fraught with risks.

Professor Karin Binder | © @v.zign

In her capacity as Professor of Mathematics Education, Karin Binder has been lecturing and conducting research at LMU since October 2021. Her primary focus is on problems surrounding the incorrect presentation and communication of statistical information, especially in social contexts that are fraught with risks.

Data play a prominent role in today’s society. But they can also cause considerable confusion if they are not interpreted properly, or if analytical findings are not communicated correctly. The coronavirus pandemic serves as a good example: “At the start of the pandemic, when there were suddenly lots of positive test results, many of which turned out to be false positives – such as in schools, where large numbers of tests were performed – this came across in media coverage as dramatic, because most of the positive tests were incorrect,” Binder explains. “But the main reason was that there were not yet many infections in the population, which created a very high probability that false positive results would occur in cases – such as in schools – where testing was widespread. The media impact was huge, but it was not really justified.” In research, this phenomenon falls into a category known as Bayesian reasoning, a subject that has occupied Binder since her time at the University of Regensburg – and that she resumed work on in October of last year at LMU. “My concern is to develop a set of tools that will enable statistical data about risks to society, for example, to be presented in a readily comprehensible form.” Given the often faulty presentation of data and incorrect communication of findings, she adds, that is often not the case today.

The same is true even for professional groups among whom one would generally expect to find better statistical evaluation capabilities. In the context of medical issues, Karin Binder has been working for some years with medical and medical education colleagues at LMU. “As part of a German Research Foundation (DFG) project, I am also collaborating with people from the Mathematical Education Group to investigate how to ensure that correct diagnoses and verdicts are derived from the available data and are properly understood by doctors.” Ultimately, she notes, “we repeatedly encounter situations where unnecessary operations are performed because of an incorrect medical diagnosis, and where innocent people are imprisoned because statistical information was misinterpreted in court.”

Data expertise is imperative

Binder and her colleagues have developed digital materials for training courses whose aim is to help significantly improve the data skills of medical and legal professionals.

“The good thing,” Binder says, “is that this kind of training can also be adapted relatively easily for school tuition.” That is because, as a mathematics educator, she is obviously concerned to optimize what schools regularly deliver in terms of data skills within her subject area. “We ask ourselves how statistical information can be integrated in classroom teaching in such a way that schoolchildren are taught how to approach it from an early age,” she says. Binder acknowledges that a lot has already happened over the past 20 years – that a lot more material on data and chance has been built into the curriculum, for example, especially in elementary schools. Nevertheless, the mathematician still sees plenty of room for improvement.

In this context, she also recognizes the importance of research into professional skills. “Before the PISA shock, we generally looked at the performance of schoolchildren,” Binder notes. “But most major studies of school performance gave less attention to the fact that there are also teachers who have to teach the material and who are important to the performance and motivation of the children.” As the professor emphasizes, the professional skills of teachers are exceptionally important, particularly in subjects such as math, which people tend to either love or hate.


© @v.zign

“What was known as the COACTIV study was launched in 2003 to also factor in the skills of the teachers,” she recalls. In the COACTIV study, math teachers from the 2003/04 PISA classes were quizzed and tested, above all with regard to their knowledge of the subject and their ability to teach their specialist discipline. At the same time, the study was built around mathematical assignments done in the classroom, as well as homework and test assignments. “The study produced a vast treasure trove of data that we could not yet fully analyze with the methods available at the time. Today, we want to apply machine learning methods to analyze the data again and draw new conclusions about how the qualities of teachers affect the performance of their pupils.”

Although Karin Binder started out by training as a construction draftswomen and only later completed her Abitur (German higher education entrance qualification), she had always known that she wanted to be a math teacher. She studied mathematics and physics at the University of Regensburg, where she also earned her doctorate after writing Promoting Bayesian reasoning – Effects of different tree diagrams in different Bayesian situations, which won her the Kulturpreis Bayern (Bavarian Culture Award) in 2018. She was then engaged as a research associate at the University of Regensburg and has also conducted research under Professor Gerd Gigerenzer at the Max Planck Institute for Human Development in Berlin. After a brief stint as a part-time math teacher at a high school in Regensburg, she initially took up a professorship at the University of Paderborn before moving to LMU in October 2021, where she was appointed professor in February of this year.

Karin Binder is looking forward to wide-ranging contact with colleagues from different disciplines that should result from her activities at LMU and will extend her research work into other fields.

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