Didactics

Fulya Kula

Fulya Kula

Born in Turkey • Studied Mathematics at Middle East Technical University in Ankara, TurkeyHighest degree PhD in Mathematics Didactics • Lives in Enschede, The NetherlandsOccupation Lecturer at the University of Twente

I actually did not really like mathematics in primary school. I found it difficult to memorize all multiplication tables for example, as I did not really understand the concept behind them. However, during high school, I had a great teacher, who could explain really well. She introduced us to theorems and proofs, and I found this challenging and rewarding.

What prior knowledge is necessary to fully understand the concept of the derivative? And what happens when some of that knowledge is missing?

After that, I did my BSc in mathematics, but I was also very intrigued by the way my professors were teaching, maybe because of my experience in primary school. All were very talented mathematicians, but some of them were not explaining very well, while others were. This motivated me to do my undergraduate and PhD level in the didactics of mathematics. In my PhD for example, I focused on the concept of the derivative. What prior knowledge is necessary to fully understand the concept of the derivative? And what happens when some of that knowledge is missing?

I am now still working in the field of mathematics and statistics didactics. I investigate how we can improve the teaching and learning of mathematical and statistical concepts. This combines my pedagogical skills and scholarly knowledge. I try to gain a better understanding into how people learn, and how this knowledge can improve teaching.

I find this project particularly exciting because it can make a real difference in students’ academic lives, as I often see them struggling in the first year during my teaching.

I am currently working to make the transition from high school math to college-level math easier for students. This means that students should have a better understanding of several mathematical concepts and skills when they are at university. To achieve this, I investigate best practices in curriculum development. I will also create videos and practice material on topics that many students are struggling with. I find this project particularly exciting because it can make a real difference in students’ academic lives, as I often see them struggling in the first year during my teaching.

During my research, I focus on how we can teach mathematics in such a way that students can understand it more easily. I had very interesting results on teaching statistical inference for example. In statistics, you often make probabilistic statements about an entire population while you only investigate at a small sample of it. This concept is often very difficult to grasp for students. Usually, during a course students are first told about the sample (for example the sample mean), and are then told what this sample statistic tells about the entire population. My research shows that it is actually better to start discussing the population first, and how you create a sample from this entire population. After that, you can teach what this then tells you about the entire population that we started with.

I would really like to investigate the most common statistics textbooks to compare their way of explaining to my proposed model. Doing so will help me to slowly but surely change the way statistics is taught.

My research endorsed that this second way of teaching makes students grasp statistical inference more easily. I would really like to investigate the most common statistics textbooks to compare their way of explaining to my proposed model. Doing so will help me to slowly but surely change the way statistics is taught.

My goal is to make sure that research in the didactics of mathematics is actually applied in mathematical teaching. Despite the fact that there is plenty of research that could be useful, the connection between research and practical teaching is weak. I would love to create a course on didactics for mathematics teachers at universities as well. I feel that most people at the university really like their teaching, and are also interested in my didactical research, but it is difficult and time-consuming for them to get a good overview of the existing knowledge. In such a course, we could go over this together, and discuss how we can implement it in practice. In this way, mathematics education research can really make an impact on the way mathematics is taught.

I really enjoy teaching and find it very motivating. My favorite moments are when a student has an “A-Ha” moment and gains a better understanding of a concept. This is also very rewarding for myself, as I managed to make an impact on the student by teaching them a topic that they did not fully understand. It also shows you the beauty of mathematics: if a student understands all single, small concepts, they can understand a much bigger problem.

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Bernadette Spieler

Bernadette Spieler

Born in Deutschlandsberg, Austria • Birth year 1988 • Studied Information Management and eHealth at Graz University of Applied Science in Graz, Austria • Highest Degree PhD in Engineering Sciences from Graz University of Technology in Graz, Austria • Lives in Zurich, Switzerland • Occupation Professor in Computing Skills in Education, Zurich University of Teacher Education, Switzerland

Since February 2021, I have been at the Zurich University of Teacher Education (PHZH, Switzerland) as a professor for “Computing Skills in Education”. This professorship is located at two centres: the Centre for “Media Education and Informatics” and the Centre for “Education and Digital Transformation.” Previously, I was the Head of the Department of Informatics Didactics and a visiting professor (W2) at the Institute for Mathematics and Applied Informatics at the University of Hildesheim (Germany). I received my PhD in 2018 from the Institute of Software Technology at Graz University of Technology (TU Graz, Austria). At TU Graz, I worked first as a project assistant in the H2020 project “No One Left Behind“, and later as a postdoctoral researcher. I completed my dissertation on the topic “Development and Evaluation of Concepts and Tools to Reinforce Gender Equality by Engaging Female Teenagers in Coding”. For my thesis, I focused on the conception of a framework for a more gender equal classroom setting for inclusive computer science activities. This so-called “Playing, Engagement, Creativity, Creating” (PECC) framework suggests inclusive activities during different stages, considers the gender dimension in different intrinsic and extrinsic motivators, and shows how all students can benefit equally from them. It puts an emphasis on how to foster intrinsic motivators like pupils’ sense of belonging to computing fields, to generate interest for this area, to improve pupils’ self-efficiency towards computing, and finally, to bring fun elements to the classroom. Second, I developed different apps to engage girls in game design, e.g., “Luna&Cat” and Embroidery Designer.

(…) The focus in education is changing; it is less about imparting knowledge and more about enabling competence acquisition that is independent, reflective, and cooperative.

With its multitude of facets, computer science (CS) offers many exciting topics for children and young people. Girls in particular often do not have the opportunity to take an interest in such topics, or are quickly depreciated as a target group. For future generations, it is crucial not merely to use these technologies, but to understand and apply them. At the same time, the focus in education is changing; it is less about imparting knowledge and more about enabling competence acquisition that is independent, reflective, and cooperative. Education in a culture of digitality ensures the participation of all learners with their different prerequisites and equal opportunities. This requires the promotion of digital competences in a level-appropriate delivery (from school to teacher education to vocational training).

At the PHZH, I have the opportunity to reach teachers as multipliers in training and education. Various concepts such as game design, Maker-Education, or playful CS with quizzes and analogue activities enhance both inspiration and motivation. Furthermore, it is essential to dispel misconceptions that computer science is “not creative” or “too difficult”. Playing and creating games on smartphones are both popular activities for the new generation of digital natives, and therefore are a perfect match for the development of creativity, problem solving, logical thinking, system design, and collaboration skills. Particularly in my current project “Making at School“, we show exciting possibilities for interdisciplinary project work in various Maker activities. Making as a method for free experimentation, exploration, or (digital) tinkering enables new learning formats for education. Thus, Making facilitates open learning spaces with problem-solving tasks, interdisciplinary connections, and transversal competencies. For instance, technical understanding, creativity, craft skills, or concepts of sustainability and entrepreneurship are promoted.

In order to significantly influence future developments in CS didactics, I am involved in various expert groups. For example, as a product owner in the Catrobat Association, I am responsible for the development of apps to support children and young people in learning programming, as a member of the Swiss steering committee of the Informatics Beaver team, we create informatics riddles for the annual Bebras competition, as a member of the steering committee of digital switzerland (education and skilled workforce), we support the next generation of STEM students, and finally, I am a member of the working group for the curriculum development for informatics at the high school/secondary level.

The number of women in [computer science] is still very low, but there are promising ways to encourage and support more women to be deeply interested in [computer science] (…).

In my research, I address the aforementioned issues of equal opportunities in education, and highlight the importance of CS didactics within the context of education. Thereby my aim in this is to ensure greater diversity in technology. In my research, it is particularly important to empirically verify a positive effect on pupils. The extracurricular level should not be underestimated either. Since I have been offering courses specifically for girls in game design and programming for years, it was always a great wish to establish our own programming club in Zurich. With the help of the Manava-Foundation, we were able to realise our idea in March 2022 and proceeded to found the CoetryLab. From Summer 2022, we offer informatics and media courses for children and young people aged 10-20. This is intended to effectively support children in these subjects precisely where their needs are greatest.

By researching new concepts and standards in the field of gender-sensitive CS education and training, I hope to seek out and implement improvements in CS curricula, different CS-topics and to support girls and female adolescents in particular to gain CS skills. The number of women in CS is still very low, but there are promising ways to encourage and support more women to be deeply interested in CS and I am confident that gender-conscious pedagogy, especially in areas of CS education, is particularly useful and necessary!

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