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Accuracy analysis of continual geodetic diagnostics of a railway line
Published in Soňa Molčíková, Viera Hurčíková, Vladislava Zelizňaková, Peter Blišťan, Advances and Trends in Geodesy, Cartography and Geoinformatics, 2018
Analytic geometry models geometric objects as points, straight lines, circles, planes, surfaces, etc. and defines the relations between them by using linear and nonlinear formulations. The principles of methods of analytic geometry are based on manipulation with the geometric object by means of kartesian coordinates of the particular points defined in two or three dimensions (Villim et al. 2013). For defining the transversal and height track changes, we used linear formulations of points, lines and planes and their perpendicular distances. However, the two and three-dimensional techniques of analytic geometry were applied to compare the final track shifts and their accuracy.
How do students assess the impact of integrating digital technologies on the mathematics classroom?
Published in International Journal of Mathematical Education in Science and Technology, 2023
Irina Gurevich, Mercedes Barchilon Ben-Av
The research was carried out through the academic year 2017–2018. Forty-seven students from the Mathematics Teaching Department at a College of Education took part in the study. We focused on the following courses taught by the same lecturer, namely: Calculus, Analytic Geometry, and Function Theory. We distinguished between the courses taught with and without the use of computers as follows: Control Group (18 participants in the Calculus course) – no digital tools were used.Digital Tools Group (29 participants in Analytic Geometry and Function Theory courses) – two digital tools were used, namely, GeoGebra (a specialized software for teaching and learning mathematics) and the Socrative smartphone app. (an Internet-based Student Response System). Short quizzes consisting of three to five review questions referring to the material taught were composed with Socrative. The students were requested to answer the quiz at the beginning of each lesson. GeoGebra was used in most of the lessons when new topics were being presented both analytically and via GeoGebra. All participants in this project, including those in the control group, had experience of studying in a technology-rich environment. During their education, they used numerous digital tools, such as GeoGebra, the Wolfram platform, applets, Excel, and PowerPoint.
Why do prospective teachers have difficulties in mathematical modelling? Insights from their perspectives
Published in International Journal of Mathematical Education in Science and Technology, 2023
Aysel Sen Zeytun, Bulent Cetinkaya, Ayhan Kursat Erbas
The first group consisted of three 3rd-year prospective middle school mathematics teachers (PTA1, Male; PTA2, Female; PTA3, Female). The second group consisted of two master’s students who had just graduated from the same middle school mathematics education programme and did not start a formal teaching job (PTB2, Female; PTB3, Female) and one 4th-year prospective computer education and instructional technology teacher (PTB1, Male). Before enrolling in the modelling course, the prospective middle school mathematics teachers and the master’s students had taken math courses such as calculus with analytic geometry, calculus for functions of several variables, discrete mathematics, basic algebraic structures, basic physics, and introduction to probability and statistics. The prospective computer education and instructional technology teacher had taken math courses covering mathematical concepts such as sets, functions, matrices, probability, limit, continuity, differentiation, and integration. All of the graduate and undergraduate participants reported that they had not taken any course on or about mathematical modelling prior to the current study.
Enhancing pre-service mathematics teachers’ understanding of function ideas
Published in International Journal of Mathematical Education in Science and Technology, 2022
Hande Gülbağci Dede, Zuhal Yilmaz, Hatice Akkoç, David Tall
Participants were a convenience sample of PMTs studying in a teacher preparation programme at a state university in Istanbul, Turkey. The first cycle of the module was completed with 17 PMTs who enrolled in the Mathematics Teaching I and II courses. The PMTs’ learning experiences concerning the concept of function in high school were as follows: (a) PMTs were introduced to functions as a special kind of a relation at 9th grade, (b) the national mathematics curriculum and mathematics textbooks at that time privileged ideas of mapping, input-output, algebra, and rule, (c) there was no learning objective in this curriculum that focused on relations between variables or covariation. Before the module, the PMTs took sixteen mathematics courses such as calculus, linear algebra, and analytic geometry. Also, all participants took mathematics education courses including geometry teaching, algebra teaching, and mathematics curriculum.