# Using interactive JSXGraphs in STACK tasks on probability theory and statistics

*Dr. Michael Kallweit and Jonas Lache*

Ruhr-Universität Bochum, Fakultät für Mathematik, Postfach 70, 44780 Bochum, Germany

### Abstract

In the project “OER.Stochastik.NRW”, digital tasks, interactive applications, and learning videos from the field of probability theory and statistics are being jointly developed as Open Educational Resources at three German universities.

The software combination of STACK and JSXGraph proves to be fruitful for the creation of modern and interactive digital mathematics tasks. Especially in probability theory and statistics, the application of mathematics can be brought to life.

In our talk, we are going to show several sample tasks that are representative of different approaches on how to use JSXGraph within STACK questions. First, we show you a task where students are supposed to draw an empirical distribution function by placing points into a coordinate system. This is representative of tasks where students construct a solution actively instead of just changing sliders or moving objects. Then, we present our approach on using JSXGraph in the feedback of STACK tasks. Here we show two STACK questions representing two different concepts of implementation. The first is to allow students to change their initial answer by performing changes in a graphic that appears in the specific feedback. For this concept, we show a sample task on regression lines where the parameters of the line can be changed by using sliders. The second approach is to allow students to conduct a random experiment based on a probability mass function that they constructed previously. The advantage is that it enables the students to see the mistakes they made when they see that their solution can be empirically disproved. They disprove the correctness of their answer by themselves instead of getting the correct solution from the computer. Our sample task is about the random experiment where an unfair dice is thrown.

The developed tasks will be used on a large scale for the first time in the winter semester of 2021/2022 and subsequently evaluated.