# New teaching materials improve statistical numeracy

## Frequently used histogram often misinterpreted

Data visualizations, including diagrams, are a frequent sight in the media. Histograms, in particular, are popular for their ability to present data concisely. Unfortunately, many people find these diagrams challenging to interpret. Lonneke Boels conducted an investigation into why this occurs, using artificial intelligence to analyse eye movements. Based on her findings, she has developed new teaching materials for secondary schools. Boels will defend her thesis at Utrecht University today.

Statistical errors can have a significant impact. In 2003, nurse Lucia de Berk was sentenced to life in prison for the murder of four patients and attempted murder in three cases, based on statistical analysis. However, in 2010, she was acquitted, thanks in part to statisticians who had refuted the statistical evidence used against her. She spent 6.5 years in unjust detention.

Misinterpreting histograms can lead to significantly incorrect conclusions

## Statistical numeracy

Not every statistical error has such far-reaching consequences. However, the ability to correctly interpret data visualisations, also known as statistical numeracy, is a prerequisite for full participation in society, according to Boels, who has been a math teacher for over twenty years. This includes histograms, which are often used but relatively poorly understood. A histogram is a specific type of diagram that represents the frequency of different classes of data, providing a good idea of the probability distribution of a particular variable.

## What goes wrong?

Boels' literature review, a part of her research, reveals several issues that arise when people interpret histograms. For instance, they struggle to determine how many statistical variables the histogram represents, what values of the variable were measured, and what the mean is.

Above, the histogram displays the distribution of annual income in the Netherlands. A common misunderstanding is that people believe the chart indicates that older individuals earn less or that earnings decrease later in the year. "Misinterpreting histograms can lead to significantly incorrect conclusions," Boels emphasised.

The subsequent eye movement study conducted by Boels demonstrated that students often confuse histograms with case histograms, which require a different approach. They read the histogram as if the measured values were along the vertical axis instead of the horizontal axis. The top figure on the right illustrates the eye movements of a student employing a correct strategy, while the bottom figure represents a student using an incorrect strategy. Fifty to sixty percent of the students tested applied an incorrect strategy.

## New teaching material

Based on her research findings, Boels has designed teaching materials to help secondary school students better understand histograms. The material includes exercises that are partly computer-based. The exercises incorporate physical actions, also known as sensorimotor experiences, which enhance the learning process. For example, students are required to drag specific measurements to the correct position on the horizontal axis. This "dragging" activity helps develop the understanding that measured values are represented on a histogram along the horizontal axis. The material has undergone testing in a laboratory with a small group of secondary school students. Teachers interested in accessing these materials can contact Boels.

## Personalized education with AI

In addition to the conventional teaching materials she has developed, Boels envisions opportunities for creating artificial intelligence systems that offer students exercises tailored to their individual learning strategies. She has trained software to recognise a student's strategy and then provide exercises that align with it. Such a system necessitates the use of webcams to record eye movements, and research must determine the extent to which this is feasible. However, according to Boels, this software would be especially valuable. "When you have thirty students in your class, providing personalized education in any other way is simply impossible," Boels remarked.