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This experience has taken place at the School of Education of the Universidad Complutense de Madrid. The goals of the subjects considered are to show how the computer can help in the teaching-learning process in Primary and/or Secondary Education and to clarify and strengthen the mathematical concepts of our students. Mastering a specific computational language or package is not a goal. We'll focus here on a very specific problem, discussed and precised together with the second author: implementing arithmetic operators as nontrivial examples of iterative sentences (not exactly using Peano's arithmetic, but a similar constructive approach). We'll analyse along the article why we believe the best ordering for developing the corresponding algorithm and implementing the code for the operators: power (with positive integer exponent), multiplication (by a positive integer) and addition (of a positive integer), is the reverse ordering in which they are introduced in elementary mathematics or introduced in an axiomatic.

Many mathematics educators are not aware of a strong connection that exists between the education of computer programming and mathematics. The reason may be that they have not been exposed to computer programming. This connection is worth exploring, given the current trends of automation and Industry 4.0. Therefore, in this paper we take a closer look at the Common Core's eight Mathematical Practice Standards. We show how each one of them can be reinforced through computer programming. The following discussion is virtually independent of the choice of a concrete programming language. Therefore, in the interest of simplicity, we will use a well-known educational programming language named Karel the Robot based on (Pattis, 1995) which is freely available online in NCLab (NCLab, 2019). The visual character of this language will allow us to provide more illustrative examples than would be possible with a standard programming language such as Java, C++ or Python.

The educational laws establish an organization and a grouping of the contents of the educational system they rule. As far as we know, the set of experts who design it neither follow precise objective criteria nor use computer tools. That is why they are not usually rotund. We consider that defining precise objective criteria is the key to develop alternative ways of organizing and grouping contents in a technically sound way. To achieve this, we propose to base the research in the meaningful learning theory. We have therefore designed and implemented a proposal that has been applied to the mathematical contents of the compulsory Secondary Education of the Spanish educational system. A modelling using graphs and a cluster analysis using software specialized in network analysis have determined an alternative grouping to the one proposed by the Spanish educational law.

Usually, all the applications of dynamic geometry systems (DGS) presented to our students are strictly mathematical, meanwhile their interests are normally far away from mathematics. We would like to introduce here a motivating example outside the "standard applications" of DGS, presenting a completely different application of this kind of software. It is well-known that a tennis player should not always recover to the centre of the court. Several authors and coaches maintain that the best place where a tennis player should recover (usually known as "recovery position") is a point that lies on the angle bisector of the angle formed by the union of all the possible trajectories of a shot of the opponent. The purpose of this paper is to show how a DGS can justify why the recovery position is nearby, but is not exactly on the angle bisector of the aforementioned angle.

Sequencing contents is of great importance for instructional design within the teaching planning processes. We believe that it is key for a meaningful learning. Therefore, we propose to formally establish a partial order relation among the contents. We have chosen the binary relation "to be a prerequisite" for that purpose. We have applied this approach to the mathematical contents of the compulsory Secondary Education of the Spanish educational system and the information obtained has been modeled as a graph. The amount of contents considered (814) and the number of ordered pairs in the order relation considered (17,782) has produced a big graph. In order to work effectively with that amount of data, we have used software specialized in network analysis. More precisely, we have used the software packages Pajek and Gephi. This software, together with the use of techniques borrowed from graph theory, has allowed providing a tool for debugging curriculum developments (similar to rule based expert systems verification).

Decision-making in a railway station regarding the compatibility of the positions of the switches of the turnouts and the indications (proceed/stop) of the railway colour light signals is a safety-critical issue that is considered very labor-intensive. Different authors have proposed alternative solutions to automate its supervision, which is performed by the so-called railway interlocking systems. The classic railway interlocking systems are route-based and their compatibility is predetermined (usually by human experts): only some chosen routes are simultaneously allowed. Some modern railway interlocking systems are geographical and make decisions on the fly, but are unsuitable if the station is very large and the number of trains is high. In this paper, we present a completely new algebraic model for decision-making in railway interlocking systems, based on other computer algebra techniques, that bypasses the disadvantages of the approaches mentioned above (its performance does not depend on the number of trains in the railway station and can be used in large railway stations). The main goal of this work is to provide a mathematical solution to the interlocking problems. We prove that our approach solves it in linear time. Although our approach is interesting from a theoretical perspective, it has a significant limitation: it can hardly be adopted in an actual interlocking implementation, mainly due to the heavy certification requirements for this kind of safety-critical application. Nevertheless, the results may be useful for simulations that do not require certification credit. [ABSTRACT FROM AUTHOR]

The authors were surprised by the number of bibliographic citations to the computer algebra system DERIVE long after it was discontinued and developed a small bibliographic study about its evolution. They later carried out a similar one about the successful dynamic geometry system GeoGebra. Finally, they presented at Maple Conference 2022 a comparative small bibliographic study about Maple and other computer algebra systems, which can be found here. [ABSTRACT FROM AUTHOR]

Technology and, in particular, computer algebra systems, allows us to change both the way we teach mathematics and the mathematical curriculum. Curiously enough, unlike what happens with linear system solving, algebraic system solving is not widely known. The aim of this paper is to show that, although the theory lying behind the "exact solve" commands (Grobner bases) is far more complex than the Gauss method, understanding and interpreting the output of the corresponding commands is not much more difficult than in the linear case, and can be introduced to non-specialists even at high-school level, if the computer is used as a black-box. Let us underline the case of statistical packages, which allow non-specialists to perform complex statistical studies. Similarly, computer algebra systems open a whole new world of exciting possibilities, covering a variety of fields. (Contains 4 figures.)