Abstract:
The sample mean in statistics is a concept of great importance, with its properties being extensively utilized in other areas, such as computer science. This research cen...Show MoreMetadata
Abstract:
The sample mean in statistics is a concept of great importance, with its properties being extensively utilized in other areas, such as computer science. This research centers on the concept of the sample mean and its characteristics in a cohort of computer engineering students undertaking a required course in statistics at a university in the Netherlands. The objective of this study was to analyze students’ comprehension of the fundamental structure, properties, and applications of the sample mean. A digital mini-course on sample mean was developed and employed with 97 students, who had the option to apply the concepts at their own pace. The action-process-object-schema (APOS) theoretical framework was utilized to analyze the interview responses of seven participants. The majority of participants were able to demonstrate an understanding of the Process conception of the sample mean, with only a minority demonstrating an understanding of the Object conception. The lack of comprehension of the sample mean hindered students’ capacity to effectively utilize the associated applications and properties. These findings imply that educators should strive to ensure that students have a sound comprehension of the sample mean so that they are better equipped to work with related applications. Suggestions of this study and further research ideas are indicated.
Published in: IEEE Transactions on Education ( Volume: 67, Issue: 4, August 2024)
Applied Mathematics Department, The University of Twente, Enschede, AE, The Netherlands
Fulya Kula received the bachelor’s degree in mathematics and the master’s and Ph.D. degrees in mathematics education.
She is an Assistant Professor with the Department of Applied Mathematics, University of Twente, Enschede, The Netherlands. Her educational journey has equipped her with an understanding of mathematical principles and pedagogical methodologies. Her research endeavors predominantly revolve around mathematics ...Show More
Fulya Kula received the bachelor’s degree in mathematics and the master’s and Ph.D. degrees in mathematics education.
She is an Assistant Professor with the Department of Applied Mathematics, University of Twente, Enschede, The Netherlands. Her educational journey has equipped her with an understanding of mathematical principles and pedagogical methodologies. Her research endeavors predominantly revolve around mathematics ...View more
Mathematics and Computer Science Department, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands
Nelly Litvak received the Ph.D. degree in applied probability from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2002.
She was with the University of Twente, Enschede, The Netherlands, from 2002 to 2023, teaching many courses with a continuous passion for teaching innovations. She is currently a Professor of Applied Mathematics with the Eindhoven University of Technology. Her research is in the mat...Show More
Nelly Litvak received the Ph.D. degree in applied probability from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2002.
She was with the University of Twente, Enschede, The Netherlands, from 2002 to 2023, teaching many courses with a continuous passion for teaching innovations. She is currently a Professor of Applied Mathematics with the Eindhoven University of Technology. Her research is in the mat...View more
Applied Mathematics Department, The University of Twente, Enschede, AE, The Netherlands
Tracy S. Craig received the Ph.D. degree from the University of Cape Town (UCT), Cape Town, South Africa, in 2007. Her dissertation was titled “Promoting Understanding in Mathematical Problem-Solving Through Writing: A Piagetian Analysis.”
She taught and carried out research with UCT from 1998 to 2017, mainly in the Academic Support Programme for Engineering in Cape Town (ASPECT). She is currently an Associate Professor of...Show More
Tracy S. Craig received the Ph.D. degree from the University of Cape Town (UCT), Cape Town, South Africa, in 2007. Her dissertation was titled “Promoting Understanding in Mathematical Problem-Solving Through Writing: A Piagetian Analysis.”
She taught and carried out research with UCT from 1998 to 2017, mainly in the Academic Support Programme for Engineering in Cape Town (ASPECT). She is currently an Associate Professor of...View more
Contents Applied Mathematics Department, The University of Twente, Enschede, AE, The Netherlands
Fulya Kula received the bachelor’s degree in mathematics and the master’s and Ph.D. degrees in mathematics education.
She is an Assistant Professor with the Department of Applied Mathematics, University of Twente, Enschede, The Netherlands. Her educational journey has equipped her with an understanding of mathematical principles and pedagogical methodologies. Her research endeavors predominantly revolve around mathematics and statistics education, particularly within higher education. With a keen focus on the intricate dynamics of teaching and learning, she delves into the nuances of transitioning to university-level mathematics and the pedagogical intricacies of the statistical concepts within higher education settings. Through her scholarly pursuits, she aims to contribute significantly to advancing educational practices, seeking innovative approaches to enhance student learning experiences and foster academic success in mathematics and statistics.
Fulya Kula received the bachelor’s degree in mathematics and the master’s and Ph.D. degrees in mathematics education.
She is an Assistant Professor with the Department of Applied Mathematics, University of Twente, Enschede, The Netherlands. Her educational journey has equipped her with an understanding of mathematical principles and pedagogical methodologies. Her research endeavors predominantly revolve around mathematics and statistics education, particularly within higher education. With a keen focus on the intricate dynamics of teaching and learning, she delves into the nuances of transitioning to university-level mathematics and the pedagogical intricacies of the statistical concepts within higher education settings. Through her scholarly pursuits, she aims to contribute significantly to advancing educational practices, seeking innovative approaches to enhance student learning experiences and foster academic success in mathematics and statistics.View more
Mathematics and Computer Science Department, Eindhoven University of Technology, Eindhoven, AZ, The Netherlands
Nelly Litvak received the Ph.D. degree in applied probability from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2002.
She was with the University of Twente, Enschede, The Netherlands, from 2002 to 2023, teaching many courses with a continuous passion for teaching innovations. She is currently a Professor of Applied Mathematics with the Eindhoven University of Technology. Her research is in the mathematical study of complex networks, such as social networks and the World Wide Web. By co-authoring this article, she aimed to reflect on her extensive experience teaching statistics to nonmathematics students. She labels herself as a practitioner of education. Her motto is that university teachers must rely on evidence-based scientific research in designing education. Her experience in innovation in her own courses resulted in several practice-oriented publications, e.g., in the International Journal of Mathematical Education in Science and Technology (2022) and a series of articles titled “Better Than Blackboard” in Nieuw Archief voor Wiskunde, the journal of the Royal Dutch Mathematical Society (2023, 2024). In preparation, an openaccess dataset with the entire material of her blended course, Linear Algebra, will be published for mathematics students. She makes it her mission to spread the knowledge and experience of novel evidence-based education. Her scientific presentations are often interactive, and she initiates many educational discussions during scientific events. She gave many presentations about novel education to colleague scientists and the general audience.
Prof. Litvak has received several teaching awards, including the Teacher of the Year Award from the University of Twente in 2022.
Nelly Litvak received the Ph.D. degree in applied probability from the Eindhoven University of Technology, Eindhoven, The Netherlands, in 2002.
She was with the University of Twente, Enschede, The Netherlands, from 2002 to 2023, teaching many courses with a continuous passion for teaching innovations. She is currently a Professor of Applied Mathematics with the Eindhoven University of Technology. Her research is in the mathematical study of complex networks, such as social networks and the World Wide Web. By co-authoring this article, she aimed to reflect on her extensive experience teaching statistics to nonmathematics students. She labels herself as a practitioner of education. Her motto is that university teachers must rely on evidence-based scientific research in designing education. Her experience in innovation in her own courses resulted in several practice-oriented publications, e.g., in the International Journal of Mathematical Education in Science and Technology (2022) and a series of articles titled “Better Than Blackboard” in Nieuw Archief voor Wiskunde, the journal of the Royal Dutch Mathematical Society (2023, 2024). In preparation, an openaccess dataset with the entire material of her blended course, Linear Algebra, will be published for mathematics students. She makes it her mission to spread the knowledge and experience of novel evidence-based education. Her scientific presentations are often interactive, and she initiates many educational discussions during scientific events. She gave many presentations about novel education to colleague scientists and the general audience.
Prof. Litvak has received several teaching awards, including the Teacher of the Year Award from the University of Twente in 2022.View more
Applied Mathematics Department, The University of Twente, Enschede, AE, The Netherlands
Tracy S. Craig received the Ph.D. degree from the University of Cape Town (UCT), Cape Town, South Africa, in 2007. Her dissertation was titled “Promoting Understanding in Mathematical Problem-Solving Through Writing: A Piagetian Analysis.”
She taught and carried out research with UCT from 1998 to 2017, mainly in the Academic Support Programme for Engineering in Cape Town (ASPECT). She is currently an Associate Professor of Mathematics Education with the Department of Applied Mathematics and the Chair of Mathematics of Imaging and AI (MIA), University of Twente, Enschede, The Netherlands. She teaches undergraduate calculus and linear algebra to students in technical programs and carries out practice-led research on the teaching and learning of mathematics. She is the Leader of the research group Fundamental Education Research in Mathematics at Twente (FERMAT). Her core research interest is the teaching and learning of multivariable and vector calculus, and her interests extend to early undergraduate statistics, linear algebra, and alternative assessment.
Prof. Craig has won awards for teaching and educational innovation.
Tracy S. Craig received the Ph.D. degree from the University of Cape Town (UCT), Cape Town, South Africa, in 2007. Her dissertation was titled “Promoting Understanding in Mathematical Problem-Solving Through Writing: A Piagetian Analysis.”
She taught and carried out research with UCT from 1998 to 2017, mainly in the Academic Support Programme for Engineering in Cape Town (ASPECT). She is currently an Associate Professor of Mathematics Education with the Department of Applied Mathematics and the Chair of Mathematics of Imaging and AI (MIA), University of Twente, Enschede, The Netherlands. She teaches undergraduate calculus and linear algebra to students in technical programs and carries out practice-led research on the teaching and learning of mathematics. She is the Leader of the research group Fundamental Education Research in Mathematics at Twente (FERMAT). Her core research interest is the teaching and learning of multivariable and vector calculus, and her interests extend to early undergraduate statistics, linear algebra, and alternative assessment.
Prof. Craig has won awards for teaching and educational innovation.View more
