In this paper, the author presents a new tool, called The Convergence Plane, that allows to study the real dynamics of iterative methods whose iterations depends on one parameter in an easy and compact way. This tool can be used, inter alia, to find the elements of a family that have good convergence properties and discard the bad ones or to see how the basins of attraction changes along the elements of the family. To show the applicability of the tool an example of the dynamics of the Damped Newton's method applied to a cubic polynomial is presented.
One of the main objectives in mathematics education is to motivate students due to the fact that their interest in this area is often very low. The use of different technologies, as well as gamification in the classroom, can help us to meet this goal. In this case, it is presented the use of two techniques, which are a digital escape room, using Genial.ly and a breakout, for learning algebra in the third course of secondary education. To carry out the experience, a comparison of the course 2018/2019 and the course 2019/2020 is made. Students of both courses completed an exam of algebraic fractions and then an equations exam; the exams were done in the course 2019/2020 taken after having used the techniques. The results show that there are low significant differences between both courses in the algebraic fractions exam qualifications, but those of the equations exam were significant, with a difference of almost two points, which led us to conclude that the use of this techniques improved the qualifications of students. Finally, the perception that students had of the experience was very positive, as shown by the data obtained and allowed them to improve their knowledge as well as their motivation and teamwork.
Educational robotics (ER) is increasingly present in secondary education classrooms and has acquired greater projection, especially with the appearance of championships, such as FIRST® LEGO® League. These competitions are based on a globalizing focus of the different areas of the curriculum, therefore, we consider that it directly links with the achievement of STEAM (science, technology, engineering, arts, and mathematics) skills. We present a research study that provides objective data based on the opinions of teachers and students that participated in this championship during the course 2017/2018 about its impact in the learning process. To this end, Spanish students and teachers answered questionnaires to collect their perceptions and assessments just after their participation. The results obtained allow us to conclude that both teachers and students believe this project promotes interest and scientific curiosity, as well as social skills through teamwork.
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