Instrumentation Schemes for Solving Systems of Linear Equations with Dynamic Geometry Software
By Melih Turgut and Paul Drijvers
In this paper we focus on the link between the use of dynamic geometry software and student understanding for the solution of systems of linear equations from an instrumental genesis perspective. Three task-based interviews were conducted with an undergraduate linear algebra student majoring in mathematics education and proficient in using dynamic geometry software. Data included video recordings, student written work and screen recordings. The data analysis was guided by the theoretical lens of instrumental genesis, to elaborate on how student thinking was shaped by the use of the digital artefacts. The digital technology supported the participant’s solution steps and over time the student developed four interrelated instrumentation schemes, which are parameter scheme, combined algebra and geometry scheme, the intersection of figures scheme and echelon form scheme.
Helpful and Hindering Features of GeoGebra: Understanding What Affords Conceptual Understandings of Definite Integrals Among Pre-Service Middle Grades Mathematics Teachers
By Emma P. Bullock, Joseph S. Webster, Dustin L. Jones
This paper introduces the Affording Understanding Conceptual Framework as a way for mathematics teacher educators to analyze student’s perceptions of a digital math tool’s helpfulness (e.g., GeoGebra) versus the instructor’s perceptions when seeking insights into how a lesson design could be improved. An example of this action research process is provided using GeoGebra to help pre-service middle grades mathematics teachers (MGMTs) develop their conceptual understandings of definite integrals. Findings showed that the pre-service MGMTs noticed four categories of what they considered to be primarily helpful features: “Ease of Use,” “Pictorial Representation,” “Colored,” and “Slider/Dynamic Movement” types. While the pre-service MGMTs all described these as helpful, the content of their comments showed that there was a material difference in how they viewed the “Ease of Use” type from the other three suggesting ways in which the lesson could be revised to be more effective.
Guidelines for Creating Video Podcasts in Mathematics Higher Education
Sidonie Costa, Elaiana Costa e Silva and Aldina Correia
b-Mat@plicada is a b-learning Mathematics course for Higher Education students, mainly composed of educational videos available in the institutional Moodle platform. These contents were created by following a set of guidelines, where three components are considered: the quality of students’ learning, the teacher’s time and computer skills, as well as the equipment made available by the institution. With the aim of evaluating the procedure used to make these videos, an experiment was carried out in classroom context, using a video on matrix multiplication which is included in the course syllabus. After its visualization, the 49 students who participated in the experiment completed a questionnaire assessing viewing behaviour, perception, attitudes, satisfaction, and learning performance. The findings demonstrate the importance of using video podcasts in Higher Education as complementary tools and the adequacy of the selected b-Mat@plicada video. Also, the results indicate that, from the students’ perspective, the speech, sound, and image are the most important features in a video podcast.
Teaching and Learning with SAS® University Edition: A Foundation Course in a Statistics and Data Science Programme
Man Fung Lo and Peggy M. L. Ng
With reference to the framework in The International Data Science in Schools Project, this paper aims to discuss the course design, teaching and learning, and assessment of a foundation course offered in an undergraduate statistics and data science programme. SAS® University Edition (a free software package) is adopted in this foundation course. With this integrated development environment, this paper shares three teaching and learning examples using a point-and-click approach and a programming approach. In addition, the design of a project-based assessment is discussed. Lastly, practical recommendations in two areas are provided to educators in this field.