Rolf Biehler
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View article: Statistics and data science education as a vehicle for empowering citizens – short summary of a survey
Statistics and data science education as a vehicle for empowering citizens – short summary of a survey Open
This article is a short summary of the report of survey team 3, presented to the 15th International Congress on Mathematical Education (ICME-15) in Sydney in July 2024.
View article: Exploring students’ constructions of data-based decision trees after an introductory teaching unit on machine learning
Exploring students’ constructions of data-based decision trees after an introductory teaching unit on machine learning Open
This study explores how high school students construct decision trees using data cards and the software CODAP (codap.concord.org) in interviews after attending a teaching unit. We conceptualized data-based decision tree construction using …
View article: Young students’ engagement with data to create decision trees
Young students’ engagement with data to create decision trees Open
Statistics and machine learning are critical because they play an essential role in our everyday lives and the careers we may pursue in the future. It may be beneficial to introduce machine learning, such as decision trees (DTs), at an ear…
View article: Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures
Using academic mathematical knowledge when working on interface tasks–analyses of pre-service teachers’ arguments about rotationally symmetric figures Open
Special tasks for pre-service teachers (PSTs) in university mathematics courses (“interface tasks”) are a common innovation in recent years to overcome the second discontinuity. By this, we mean tasks that are situated by typical everyday …
View article: TEACHING AND LEARNING TO CONSTRUCT DATA-BASED DECISION TREES USING DATA CARDS AS THE FIRST INTRODUCTION TO MACHINE LEARNING IN MIDDLE SCHOOL
TEACHING AND LEARNING TO CONSTRUCT DATA-BASED DECISION TREES USING DATA CARDS AS THE FIRST INTRODUCTION TO MACHINE LEARNING IN MIDDLE SCHOOL Open
This study investigates how 11- to 12-year-old students construct data-based decision trees using data cards for classification purposes. We examine the students' heuristics and reasoning during this process. The research is based on an ei…
View article: Designing a Concept Inventory for Real Analysis
Designing a Concept Inventory for Real Analysis Open
International audience
View article: The meaning landscape of the concept of the total derivative in multivariable real analysis textbooks: an analysis based on a new model of meaning
The meaning landscape of the concept of the total derivative in multivariable real analysis textbooks: an analysis based on a new model of meaning Open
In this paper, we propose a novel conceptual framework tailored for modeling the meaning of mathematical concepts in university-level mathematics, addressing their rigorous nature and their relationships with related concepts as well as in…
View article: Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course
Implementing profession orientation as a design principle for overcoming Klein’s second discontinuity – preservice teacher’s perspectives on interface activities in the context of a geometry course Open
Intending to counteract Klein’s second discontinuity in teacher education, we explored and applied the innovation of “ interface ePortfolio ” in the context of a geometry course for preservice teachers (PSTs). The tool offers the possibili…
View article: Jupyter Notebooks for Teaching, Learning, and Doing Data Science
Jupyter Notebooks for Teaching, Learning, and Doing Data Science Open
We report on our work with students in our data science courses, focusing on the analysis of students’ results. This study represents an in-depth analysis of students’ creation and documentation of machine learning models. The students wer…
View article: Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability
Facilitators’ Orientations Towards Learning Goals, Perceived Challenges, and Teaching Resources for a PD Course on Conditional Probability Open
The data age has led to curriculum developments promoting the relevance of stochastics in mathematics education. This has resulted in an increased demand for teacher professional development (PD) courses, and thus in a rising number of fac…
View article: Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications
Revisiting Fundamental Ideas for Statistics Education From the Perspective of Machine Learning and Its Applications Open
Fundamental ideas (Burrill & Biehler, 2011) have been specified to structure the curriculum across different age levels and to focus on and revisit the most important ideas. Such ideas must be based on an epistemological analysis of the sc…
View article: Insights into a reference model for school-based approaches to vectors
Insights into a reference model for school-based approaches to vectors Open
International audience
View article: TEACHING AND LEARNING DATA-DRIVEN MACHINE LEARNING WITH EDUCATIONALLY DESIGNED JUPYTER NOTEBOOKS
TEACHING AND LEARNING DATA-DRIVEN MACHINE LEARNING WITH EDUCATIONALLY DESIGNED JUPYTER NOTEBOOKS Open
This study examines modelling with machine learning. In the context of a yearlong data science course, the study explores how upper secondary students apply machine learning with Jupyter Notebooks and document the modelling process as a co…
View article: EDITORIAL: RESEARCH ON DATA SCIENCE EDUCATION
EDITORIAL: RESEARCH ON DATA SCIENCE EDUCATION Open
A very warm welcome to this Special Issue of the Statistics Education Research Journal (SERJ) on data science education. Our hope is to give an overview of selected theoretical thoughts and empirical studies on data science education from …
View article: ConcepTests in Undergraduate Real Analysis: Comparing Peer Discussion and Instructional Explanation Settings
ConcepTests in Undergraduate Real Analysis: Comparing Peer Discussion and Instructional Explanation Settings Open
Peer Instruction, first introduced by Eric Mazur in the late '90 s, is a method aiming at active student participation in lectures. It includes conceptual questions (so-called ConcepTests) presented to the students, who vote on answer alte…
View article: Enriching videos with interactive questions to enhance students' cognitive activity: concept and implementation
Enriching videos with interactive questions to enhance students' cognitive activity: concept and implementation Open
International audience
View article: Facilitators' views on content goals, learning obstacles, and teaching resources in reference to conditional probability
Facilitators' views on content goals, learning obstacles, and teaching resources in reference to conditional probability Open
International audience
View article: Consultation Phases in Mathematics Learning and Support Centres
Consultation Phases in Mathematics Learning and Support Centres Open
Mathematics Learning Support Centres are becoming more and more common in higher education both internationally and in Germany. Whereas it is clear that their quality largely depends on a functioning interaction in consultations, little is…
View article: Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks
Introducing students to machine learning with decision trees using CODAP and Jupyter Notebooks Open
This paper reports on progress in the development of a teaching module on machine learning with decision trees for secondary‐school students, in which students use survey data about media use to predict who plays online games frequently. T…
View article: A first introduction to data science education in secondary schools: Teaching and learning about data exploration with <scp>CODAP</scp> using survey data
A first introduction to data science education in secondary schools: Teaching and learning about data exploration with <span>CODAP</span> using survey data Open
In this paper, we will describe an introduction to Data Science for secondary school students. We will report on the design and implementation of an introductory unit on “Data and data detectives with CODAP” in which secondary school stude…
View article: Data science education in secondary school: how to develop statistical reasoning when exploring data using CODAP
Data science education in secondary school: how to develop statistical reasoning when exploring data using CODAP Open
Data Science has become an emerging field at the intersection of statistics, computer science and application fields and this discipline requires “new skills” to be enabled to explore for example large and messy datasets, so-called Big Dat…
View article: Data science education in secondary schools: teaching and learning decision trees with CODAP and jupyter notebooks as an example of integrating machine learning into statistics education
Data science education in secondary schools: teaching and learning decision trees with CODAP and jupyter notebooks as an example of integrating machine learning into statistics education Open
In the setting of design-based research, the second version of an experimental course on data science is implemented accompanied by research. The three modules of the course focus on “data and data detectives”, “machine learning” and a com…