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As soon as a new technology emerges, the education community explores its affordances and the possibilities to apply it in education. In this article, we analyze sessions with ChatGPT around topics in basic linear algebra. We reflect on the affordances and changes between two versions of ChatGPT since its worldwide publication in our area of interest, namely, linear algebra. In particular, the question of whether this software can be a teaching assistant or even somehow replace the human teacher is addressed. As of the time this article is written, the answer is generally negative. For the small part where the answer can be positive, some reflections about an original instrumental genesis are given.

The development of technology has changed the way people communicate in academic contexts as well as working places, for example from print messages to screened messages, and from face-to-face classroom and office meetings to virtual classes and offices. This has prompted the shift from traditional teaching practices to student-centered in which students are guided by their teachers to develop skills for 21st Century careers through the Project-Based Learning model. However, in Tanzania colleges, the teaching of a Communication Skills Course perpetuates traditional teaching practices, which could reduce the chance for students to participate in global democratic activities. Consequently, the present study aimed at exploring how to enhance the 4 C's (critical thinking, communication, collaboration, and creativity) among the college students of the Communication Skills Course in Tanzania through the Project-Based Learning model. Qualitative participatory action research with two cycles was adopted. Data from ten students, one teacher, and the curriculum were collected through observation, document analysis, and reflective journals. Data were analyzed thematically. Findings show that current teaching practices for Communication Skills Course in Tanzania colleges hardly enhance the development of the 4 C's among students. It was also observed that the implementation of PBL resulted in enhancing the 4 C's among college students in Tanzania colleges. However, large class sizes, poor technological infrastructure, and lack of facilities are among the challenges experienced during the implementation of PBL in enhancing the 4Cs. The study recommends the reformation of current teaching practices, to focus on developing skills needed to cope with students' real-life contexts, instead of focusing on content knowledge. Also, the study calls for the adoption of PBL in Tanzania colleges in teaching Communication Skills to develop necessary skills for the 21st Century. To cope with any potential challenges, the study suggests that there should be collaborative efforts among education stakeholders.

There is a large amount of research that indicates that the use of 3DMP in STEM education improves students' knowledge, motivation, and participation in the learning process. Nevertheless, despite the existing attempts to market 3DMP in education, its adoption in schools remains low. A number of studies with teachers in secondary schools and colleges indicate that teachers' perceptions of 3DMP are one of the key factors for its successful use. However, to our best knowledge, there is no research that examined STEM upper primary school teachers' perception on 3DMP. Through phenomenographic approach, this study is seeking to address the existing gaps. Four conceptions of 3DMP teaching emerged: (1) 3DMP as tools for classroom modernization; (2) 3DMP technical and software characteristics' impact on implementation; (3) 3DMP as a tool for learning and improvement in teaching; (4) 3DMP and students' professional orientation, teachers' professional development. These four categories are connected by five key aspects of variation: impact on students, impact on teachers, classroom activity management, authenticity, subject-curriculum matters. The results of our study indicate that the mathematics and science teachers have a more sophisticated opinion on 3DMP than teachers of technical education, engineering, and informatics who mostly require additional training when it comes to using 3DMP in STEM education. Comparatively, science and mathematics teachers need support with implementation of software and 3D printers as a technical tool. Considering that this study's teachers were early adopters of 3DMP, any future research should explore conceptions of experienced users.

Geometric loci are an important topic in geometry. We explore constructs of plane curves and of space curves inspired by space trajectories (bicircular and tricircular motions). The exploration relies on joint usage of Dynamic Geometry Software (DGS) and of a Computer Algebra System (CAS), and involves automated methods to determine loci and sometimes dichotomy methods. The computer assisted work reveals some surprises, in particular the respective roles of the two kinds of software may be different from what previous works revealed. If previously the roles were quite distinct, DGS for exploration and numerical approach, and CAS for symbolic proof, here the CAS is needed for numerical methods also. The curves are described by trigonometric parametrization, and implicitization is performed using elimination, for 2D and 3D models. Finally, we discuss approaches to developments using models and elaborate on the importance to develop automatic dialog between kinds of software. [ABSTRACT FROM AUTHOR]

Locus computation is an essential issue in mathematics education, and a traditional feature of Dynamic Geometry software (DGS). Nowadays, the rising of new DGS programs, such as GeoGebra, merging DGS and Computer Algebra software (CAS) has fostered a combined approach to locus computation, quite performing in standard examples, but demanding an extended theoretical, and the related algorithmic counterpart, able to deal with less conventional situations. Here we formulate--and reflect about, yielding some proposals--on a few pending issues related to the protocols for the computation of parametric families of loci. Then we focus on a different source of difficulties, through the example of the very elementary and classical theorem of Thales. Thus, in the framework of the current development of automated deduction in geometry (ADG) tools, we will show how the automatic discovery of Thales's converse statement might require a locus computation that gives rise to an unexpected family of octic curves. Finally, we will exhibit how the handling (finding the equation, plotting, geometric characterization, etc.) of such curves requires the concourse of DGS and CAS programs, a mixed graphic-symbolic-numeric approach, and human-machine interaction, a cooperation that could be the basis towards achieving the required improvements concerning locus computation software. [ABSTRACT FROM AUTHOR]

We present an initial description of an ongoing research project. Students are attracted to learn mathematics, not only for its application but also for their cultural interest. The students’ cultural backgrounds are used, and situations are analyzed and modeled using technology. This first step has been instrumental in making the transition to distance learning necessary due to the Covid-19 crisis. We focus on a specific population of students who had to overcome, within a short time, two important transitions in the learning processes.

We study a 1-parameter family of trigonometric definite integrals, showing how the joint usage of Information and Communication Technologies and paper-and-pencil work lead to different outputs, revealing different mathematical meanings and different concrete meanings. This family of integrals is useful for describing a phenomenon in soil mechanics, whence the importance of such integrals in STEM education.

Canal surfaces are a special occurrence of envelopes of parameterized families of surfaces in 3D space, namely envelopes of families of spheres centered on a given space curve. When the radius of the sphere is constant, they are called tubular surfaces, or simply tubes. In every country, numerous examples can be found all around (water pipes, canals for traffic of merchandises, etc. All these can incite to study such objects or models in mathematics. Dynamic Geometry Systems are an efficient tool to model such concrete objects, as they enable both a geometric construction and an exploration of the corresponding algebraic data (equations, parametric presentation). In order to have a more powerful tool for the algebraic computations, a Computer Algebra System can be used, whence a new need to communicate between DGS and CAS. In the past, a concrete construction of such canal surfaces was viewed as an artistic creation, whose abstract basis was quite complicated to grasp. For the beginner, understanding the switch from a concrete occurrence towards abstraction (equations, etc.) was a non-trivial issue. Neither was the reverse direction. We start from a geometric description of a spinal curve and of spheres centered on it, from there we derive equations whose solutions describe the desired surface. Nowadays, these paths can be completed by a new step, from an abstract presentation with equations towards a concrete realization using 3D printing. This approach, from real world to mathematical presentation, and then back to concretization, is typical of STEAM education. [ABSTRACT FROM AUTHOR]

We provide constructions of 3 classical curves, using novel approaches, based on tools for automated exploration and reasoning, especially for the determination of geometric loci. Dragging and animations are the core features in use. The different ways yield an output based either on numerical computations or on symbolic computations (these use Gröbner bases packages). These curves, which are generally presented as separate cases, appear here in a unifying frame. This work is a contribution to the study of plane curves and to a working frame aimed at developing the dialog between different kinds of mathematical software. [ABSTRACT FROM AUTHOR]

We explore the construction of curves of degree 8 (octics) appearing as geometric loci of points defined by moving points on an ellipse and its director circle. To achieve this goal we develop different computer algebra methods, dealing with trigonometric or with rational parametric representations, as well as through implicit polynomial equations, of the given curves. Finally, we highlight the involved mathematical or computational issues arising when reflecting on the outputs obtained in each case. [ABSTRACT FROM AUTHOR]

We compute closed forms for some parametric integrals. The tools used are MacLaurin developments and other infinite series. Finally, Stirling numbers appear. (Contains 1 figure.)

We present a sequence of improper integrals, for which a closed formula can be computed using Wallis formula and a non-straightforward recurrence formula. This yields a new integral presentation for Catalan numbers.

Looking for closed forms for an integral depending on one parameter, we obtain integral identities and new integral presentations of Catalan numbers. Wallis formula appears as an important tool.