1,721,108 research outputs found
Tools to "get mathematics in your fingers"
No full textOver het gebruik van ICT-gereedschap in de wiskundeles zijn de meningen verdeeld. In dit themanummer over wiskunde en nieuwe media schetst Paul Drijvers twee theoretische invalshoeken om tegen deze inzet aan te kijken. Instrumentatietheorie beschrijft hoe ICT een instrument wordt voor wiskunde, en de theorie van belichaamde cognitie benadrukt de rol van het lichaam in het leren, ook van wiskunde. Na enkele voorbeelden pleit Paul voor een integratie van de twee, onder de noemer van belichaamde instrumentatie, om te bevorderen dat leerlingen wiskunde door de inzet van ICT in de vingers krijgen
Scientific and Mathematical Literacy in Life and Society: Research program Freudenthal Institute 2021-2026
Full text linkLearning algebra in a computer algebra environment : design research on the understanding of the concept of parameter
Full text linkIt is well known that algebra is a difficult topic in the school mathematics curriculum, and is often experienced as a stumbling-block. One of the directions in which solutions to the problems with the learning of algebra can be sought is the integration of information technology (IT) into mathematics education. Although originally not developed for educational purposes, a computer algebra system is an IT tool that seems promising because of its algebraic power. The basic aim of this study, therefore, is to investigate whether computer algebra use can contribute to the understanding of algebra. This leads to the following main research question:
How can the use of computer algebra promote the understanding of algebraic concepts and operations?
Chapter 1 contains the research questions and explains the aims and backgrounds of the study. In Chapter 2 the research design and methodology are described. Key words are design research and hypothetical learning trajectory. Chapters 1 and 2 together indicate what the research is about and how it is conducted.
Chapters 3, 4 and 5 form the theoretical part of the thesis. They treat the main themes of the study: algebra in general, the concept of parameter in particular and the possible roles of computer algebra. Chapter 3 concerns algebra in general. It sketches different views on algebra and describes the standpoint of this study. The theoretical issues of symbol sense, symbolizing, the process-object duality and Realistic Mathematics Education are addressed.
In Chapter 4, we zoom in on the concept of parameter. After a brief historical perspective, a conceptual analysis of the parameter is given. Then we describe what we consider a higher level understanding of the concept of parameter. This is connected to the theoretical notions from Chapter 3.
Chapter 5 deals with the tool that students use in this research project: computer algebra. Besides an overview of previous research in this domain, it contains a description of the theory of instrumentation that will be used in Chapter 10 in particular.
Chapters 6 - 10 form the empirical part of the dissertation. Chapters 6, 7 and 8 describe the development of the hypothetical learning trajectory and the classroom experiences during the three subsequent research cycles.
Chapter 9 concerns the contribution of computer algebra use to the understanding of the concept of parameter. In Chapter 10, the results concerning the instrumentation of computer algebra are presented.
Chapter 11, finally, answers the main research question. After that, we look back on the study and discuss the results and the methodology. Also, the relevance of the theoretical framework and the generalizability of the findings are evaluated. The chapter ends with recommendations for teaching, for software design and for further researc
Developing Techno-mathematical Literacies in higher technical professional education
No full textDue to an increased use of technology, engineers’ workplace practices have changed. So-called Techno-mathematical Literacies (TmL) are necessary skills for current and future engineers. This dissertation describes four studies that investigate how to develop these skills in first-year higher technical professional education (HBO). Firstly, seven TmL frequently used by engineers, have been identified in an interview study with fourteen engineers of different technical domains. These TmL include Data literacy, Technical software skills, Technical communication skills, Sense of error, Senso of number, Technical creativity, and Technical drawing skills. Second, with these TmL as central learning goals, an innovative course in applied mathematics was designed and implemented using the approach of Design-based Implementation Research. This course consists of two complementary learning tracks in parallel. The basic abstract mathematical skills are practiced in an electronical learning environment and in the second track students work collaboratively on context-based cases. In class, the lecturers use the pedagogical approach of Inquiry-based learning (IBL). In a pilot study, the lecturer used the following types of teaching strategies to stimulate TmL learning: pedagogical, process, general IBL, and TmL specific IBL. Thereafter, the course became part of the curriculum of the School of Life Sciences and Environmental Technology at Avans University of Applied Sciences in the Netherlands. In a period of three academic years, eleven lecturers taught the new course to over 1400 students. The course was monitored, evaluated and adjusted each year. Thirdly, lecturers reported challenges in teaching the new course, in particular related to their changing role. Therefore, an interview study with all participating lecturers was conducted to understand their experiences, opinions, dilemmas, feelings, and beliefs. The fourth study evaluated the effectiveness of the course on students’ development of TmL through a pre- and posttest design. In this study, an instrument was designed to measure TmL. The results showed a positive effect on students’ development of some of the TmL, for example, sense of error and technical software skills. More complex TmL, such as data literacy and technical creativity proved to be more difficult to measure, and perhaps learned. Altogether, the PhD study yielded theoretical knowledge about the nature of TmL, practical knowledge on the implementation of TmL in education, and the design of a course in applied mathematics that is adjustable for all technical domains
The Unseen Potential of Film for Learning: Film's Interest Raising Mechanisms Explained in Science and Mathematics Education
No full textEducational video is more than audio-visual technology for knowledge
dissemination. From the perspective of film studies, video is a powerful
tool to evoke interest – a key engine for learning. Interested pupils
learn more, process knowledge more deeply, and experience more
enjoyment while learning. In the Netherlands and abroad, interesting
pupils in science and mathematics is a difficult task and we believe that
video could make a difference.
This dissertation introduces the film studies perspective to the discourse
on video in education to initiate an interdisciplinary approach. It
shifts the dominant focus of research and educational practice from
video for knowledge dissemination to raising pupils’ interest. In four
subsequent studies, we first explored the practice of educational video
use focussing on teacher aims and video characteristics. Second, we
integrated theories from multiple disciplines to model the mechanisms
underlying interest in film and video. Third, we empirically tested and
validated the model. Finally, we conducted a qualitative study to better
understand and to explain the model’s underlying mechanisms.
In conclusion, the experience of a balance between posed challenges
and coping potential proved to be crucial for interest development.
Video naturally activates viewers to seek this balance, if well structured.
This dissertation presents a method for assessing the structure of
educational videos, based on a validated interdisciplinary model of
Film’s Interest Raising Mechanisms (FIRM model). Furthermore, it offers
guidance for professionals to optimize the educational use of video for
its unseen potential to raise interest
Introducing Statistical Inference: Design and Evaluation of a Learning Trajectory
No full textThe increasing amount of data in media over the last year—think of COVID—illustrates the necessity for students to become statistically literate—including interpreting inferences. Drawing inferences involves making data-based claims under uncertainty when only partial data are available. However, inferences are challenging for students in Grade 10 and higher. This thesis focused on the question: How can a theoretically and empirically based learning trajectory introduce 9th-grade students to statistical inference? To answer this question, we used a design-based research approach, complemented with a case study into learning statistics from and with technology. The design of the trajectory was informed by theories on repeated sampling and statistical modeling using a black box paradigmatic context. The learning trajectory was implemented in teaching practice during three interventions. A pre- and posttest were designed to evaluate the trajectory’s effects in the large-scale final cycle. A national and international comparison of student results showed that students who took part in the learning trajectory (N = 267) scored significantly higher on statistical literacy than the comparison group that followed the regular curriculum (N = 217), in particular, on the domain of statistical inference. We also observed positive effects on other domains of statistical literacy. These findings suggest that current statistics curricula for grades 6–9 can be enriched with an inferential focus. The benefit of this early introduction is that students learn more about inference and not less about the other domains of statistical literacy, to anticipate for subsequent steps in students’ statistics education
Automated intelligent feedback in university statistics education
No full textIntroductory statistics courses are both essential and challenging for many university students. Students struggle to understand the abstract concepts involved, such as significance level and p-value, and the role of uncertainty in statistical procedures. Appropriate feedback could support students in gaining understanding, but is difficult to provide for teachers, since the number of students enrolled in such courses is often large. In this thesis, a solution is sought in automated feedback in an Intelligent Tutoring System, guided by the question: How can automated feedback support students in higher education in gaining understanding of statistics? In two first-year introductory statistics courses for social-sciences students, two feedback types were implemented: inner loop feedback on steps in hypothesis-testing tasks by a domain reasoner and outer loop feedback over series of tasks in the form of inspectable student models.
Separate studies focused on the design, implementation, and student’s use of the two feedback types. Design was based on promising paradigms, such as model-tracing and constraint-based modeling for the domain reasoner. Students’ use of the feedback was evaluated by investigating their feedback-seeking and decision-making behavior. Finally, the influence of both feedback types on student’s course performance was assessed. Lower-achieving students were found to benefit from student models, and students who had had enough time to familiarize themselves with the feedback were found to benefit from the domain reasoner. Hence, the combination of feedback types has the potential to provide many students with useful guidance in the process of learning statistics
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