| 11. |
- Mellroth, Elisabet, 1971-, et al.
(author)
-
Differentiated instruction using learning management systems in upper secondary school and university level : A research proposal
- 2019
-
In: Including the highly gifted and creative students: Current ideas and future directions.. - Münster : Verlag für wissenschaftliche Texte und Medien. ; , s. 378-380
-
Conference paper (peer-reviewed)abstract
- There is a need to develop an infrastructure to support and maintain teaching that both challenge all students at their knowledge level and open up the possibility to applying mathematical knowledge in innovative and creative ways. Learning management systems (LMS) are widely used throughout the Swedish school system. However, recent studies shows that few teachers use this resource for teaching development, i.e., using LMS as an instrument to improve forthcoming lessons. In this poster a research proposal is outlined. The aim is to explore how LMS can be used as an instrument for differentiated instruction throughout the intertwined processes of planning, teaching, studying, follow up and assessment.
|
|
| 12. |
- Przybilla, Johannes, et al.
(author)
-
Interactive Mathematical Maps : A contextualized way of meaningful Learning
- 2021
-
In: Bringing Nordic mathematics education into the future. Papers from NORMA 20, Preceedings of Norma 20, The ninth Nordic Conference on Mathematics Education, Oslo, 2021. - 9789198402438 ; , s. 209-216
-
Conference paper (peer-reviewed)abstract
- Student teachers are often not able to link mathematical school and university contents. This problem results in the “double discontinuity” that goes back to Klein (1924)[1], which manifests itself in a lack of understanding and significance of university contents on the part of future teachers. Based on modern learning psychology we assume that this issue can be overcome by defragmentation – a thematically meaningful arrangement – of knowledge. For this purpose, we present a "dynamic interactive mathematical map" which should enable "meaningful learning" in the sense of Ausubel (1963) [2]. By giving the learners the possibility to retrace the formation of mathematical subjects in conjunction with the presentation of similar concepts, understanding is deepened and ultimately transfer of learning is facilitated. We also present one of the tentative studies connected with the map. [1] “The first ‘discontinuity’ concerns the well-known problems of transition which students face as they enter university. The second ‘discontinuity’ concerns those […] which return to school as teachers and the (difficult) transfer of academic knowledge gained at university to relevant knowledge for a teacher.” (Winsløw & Grønbæk, 2013, p. 2)[2] Ausubel (1963) shaped the term “meaningful learning”, which declares that learning is only meaningful (contrasted to rote learning), when connected to past learnings and many different contexts.
|
|
| 13. |
- Przybilla, Johannes, et al.
(author)
-
Rooms of Learning : A conceptual framework for student-centered teaching development in a digital era
- 2021
-
Reports (peer-reviewed)abstract
- In the context of teaching, there is often a clash of different generation cohorts, which have different attitudes to and skills in digital media and corresponding ways of teaching and learning, respectively. The current COVID19 situation works as an intensifying lens and shows the problems occurring in this context even more clearly. Many mathematics teachers feel urged to move away from the instruction- and lecture-centered teaching style and many universities are upgrading digitally, thus creating the conditions for innovative teaching. Considering the change in learning theories and education curricula, we offer a general model called “Rooms of Learning” as a quick-to-see-and-interpret framework for the pre- and post-analysis of course design. It is backed by subject didactical frameworks that focus on interactions between the main actors involved in learning. As starting points, we use the basic needs of today’s learners for autonomy, relatedness, and competence as well as the requirements of the present information society. Focusing on different levels of the learners’ autonomy, as the key factor for building up mathematical competence and life-long learning, we illustrate our practice-oriented model by analyzing different course layouts. Herein the strength of the model is demonstrated, as commonalities of the modern course designs successfully applied today are revealed. It suggests, when designing a course, care should be taken to ensure that the defined Peer teaching room and Self-studies room are given enough space.
|
|
| 14. |
- Szabo, Attila, et al.
(author)
-
Surveying prospective teachers’ conceptions of GeoGebra when constructing mathematical activities for pupils
- 2020
-
In: Proceedings of the 10th ERME Topic Conference (ETC 10) on Mathematics Education in the Digital Age (MEDA), 16-18 September 2020 in Linz, Austria. - Linz : Johannes Kepler University. - 9783950463057
-
Conference paper (peer-reviewed)abstract
- In this poster, we present an ongoing study about prospective mathematics teachers' conceptions about the relationship between mathematics, problem-solving and GeoGebra. The context of our study is a curriculum reform in Sweden that emphasizes the use of digital tools in mathematics education. In that respect, we will investigate prospective upper-secondary teachers´ conceptions when participating in a geometry course at the university level. During the course, participants will construct mathematical activities for pupils by using GeoGebra.
|
|
| 15. |
- Vinerean-Bernhoff, Mirela, 1974-, et al.
(author)
-
“Literally I Grew Up” Secondary–Tertiary Transition in Mathematics for Engineering Students beyond the Purely Cognitive Aspects
- 2023
-
In: Open Education Studies. - : De Gruyter Open. - 2544-7831. ; 5:1
-
Journal article (peer-reviewed)abstract
- High dropout rates in the first year of undergraduate studies are an expression of the secondary–tertiary transition problem and they seem to be particularly high in those degree programs where specialized mathematics courses are taught in the first year of study. Research shows that students’ difficulties during the transition period cannot be reduced to purely cognitive factors. In this article, we address the secondary–tertiary transition problem in mathematics for engineering students. Based on a questionnaire with focus beyond the purely cognitive aspects, a comparison of the transition problem at three European mid-sized universities is carried out, to identify common challenges and difficulties, as well as differences. The questionnaire concentrates on the four dimensions (personal, organizational, content related, and social) and corresponding critical requirements for a successful transition described in Trautwein, C., & Bosse, E. (2017). The first year in higher education – critical requirements from the student perspective. Higher Education, 73, 371–387. A group of 308 first-year engineering students partook in the study. In the presentation, we highlight students’ perceptions regarding the transition, changes, and challenges they experienced under the above-mentioned four dimensions and discuss similarities and differences between countries.
|
|
| 16. |
- Vinerean-Bernhoff, Mirela, 1974-, et al.
(author)
-
Prospective teachers constructing dynamic geometry activities for gifted pupils : Connections between the frameworks of Krutetskii and van Hiele
- 2022
-
In: Gifted Education International. - : Sage Publications. - 0261-4294 .- 2047-9077. ; 38:2, s. 273-294
-
Journal article (peer-reviewed)abstract
- The Swedish educational system has, so far, accorded little attention to the development of gifted pupils. Moreover, up to date, no Swedish studies have investigated teacher education from the perspective of mathematically gifted pupils. Our study is based on an instructional intervention, aimed to introduce the notion of giftedness in mathematics and to prepare prospective teachers (PTs) for the needs of the gifted. The data consists of 10 dynamic geometry software activities, constructed by 24 PTs. We investigated the constructed activities for their qualitative aspects, according to two frameworks: Krutetskii’s framework for mathematical giftedness and van Hiele’s model of geometrical thinking. The results indicate that nine of the 10 activities have the potential to address pivotal abilities of mathematically gifted pupils. In another aspect, the analysis suggests that Krutetskii’s holistic description of mathematical giftedness does not strictly correspond with the discrete levels of geometrical thinking proposed by van Hiele.
|
|
| 17. |
- Vinerean, Mirela Cristina, 1974-
(author)
-
Discrete Kinetic Models and Conservation Laws
- 2005
-
Doctoral thesis (other academic/artistic)abstract
- Classical kinetic theory of gases is based on the Boltzmann equation (BE) which describes the evolution of a system of particles undergoing collisions preserving mass, momentum and energy. Discretization methods have been developed on the idea of replacing the original BE by a finite set of nonlinear hyperbolic PDEs corresponding to the densities linked to a suitable finite set of velocities. One open problem related to the discrete BE is the construction of normal (fulfilling only physical conservation laws) discrete velocity models (DVMs). In many papers on DVMs, authors postulate from the beginning that a finite velocity space with such "good" properties is given, and after this step, they study the discrete BE. Our aim is not to study the equations for DVMs, but to discuss all possible choices of finite phase spaces (sets) satisfying this type of "good" restrictions.We start by introducing the most general class of discrete kinetic models (DKMs) and then, develop a general method for the construction and classification of normal DKMs. We apply this method in the particular cases of DVMs of the inelastic BE (where we show that all normal models can be explicitly described) and elastic BE (where we give a complete classification of normal models up to 9 velocities). Using our general approach to DKMs and our results on normal DVMs for a single gas, we develop a method for the construction of the most natural (from physical point of view) subclass of normal DVMs for binary gas mixtures. We call such models supernormal models (SNMs). We apply this method and obtain SNMs with up to 20 velocities and their spectrum of mass ratio. Finally, we develop a new method that can lead, by symmetric transformations, from a given normal DVM to extended normal DVMs. Many new normal models can be constructed in this way, and we give some examples to illustrate this.
|
|
| 18. |
|
|
