Discrete mathematics as a resource for developing scientific activity in the classroom

Abstract

In this paper we present a theoretical discussion on how problems issued from discrete mathematics can develop the attitudes, skills, and knowledge required for scientific mathematical activity in the classroom. We do so via the research situation for the classroom model by performing mathematical and didactical analyses of a problem issued from discrete geometry, and we present the results of a preliminary experiment conducted with Chilean students between the ages of 11 and 13. Our chosen problem asked students to tile a fixed square with a finite number of smaller squares. From the theoretical analysis and the preliminary experimentation, we conclude that this problem, and problems issued from discrete mathematics in general, can induce genuine mathematical activity in lower-secondary school students. In particular, we conclude that this problem is effective in developing the knowledge, skills and attitudes advocated in the Chilean mathematics curriculum.

Farewell to Virtual Environments and Welcome to Post-pandemic Mathematical Problem Posing and Solving

“…There are problems derived from mathematics that help to develop students' skills, attitudes and knowledge through geometric research [16], the effect of didactic strategies of e-learning environment during Covid-19 is learning whose development of problem solving skills in primary level students were positive [17], these effects also impacted with interactive mathematical games in an online way demonstrating characteristics and numerical influences on students [18]. The data process that reflects the development of problem solving provides greater understanding in the classification of perspectives to understand mathematical competencies [19] and its implementation of the curriculum is necessary and of utmost importance to generate adjustments and changes in the methodology, thanks to the pandemic the use of the blackboard has been left to use technological tools and devices that were very helpful for teachers and students [20], [21].…”

Teaching and learning discrete mathematics

“…In England, students focusing on mathematics can take a special track in which they have extensive exposure to discrete mathematics. In many countries, it appears that the opportunities for dealing with discrete mathematics in schools, especially when it goes beyond combinatorics, are often only seen on the level of optional recreational mathematics (Colipan & Liendo, 2022;Gravier & Ouvrier-Buffet, 2022;Greefrath et al, 2022).…”

“…For example, graphs can be considered as modeling tools (Greubel et al, 2020;Thomas et al, 2015). Colipan andLiendo (2022), andGravier andOuvrier-Buffet (2022) deal with students developing problem solving and reasoning skills through discrete puzzles. As a consequence, we can say there is an indication that topics in discrete mathematics can develop some critical reasoning and ways of thinking.…”

“…Further, integers form the core for young children to begin mathematical modeling because they can both visualize numbers of objects through pictures and can manipulate them with the use of blocks or tiles. For example, Colipan and Liendo (2022) consider the problem of how many squares can one square be partitioned into. Students can draw squares within squares to investigate this problem.…”

“…These games can also appeal to a variety of learning styles and develop several of the desired competencies mentioned earlier. We already mentioned such a discrete puzzle (Colipan & Liendo, 2022) in which students try to see how many different numbers of squares a given square can be partitioned into. This problem supports problem solving and communication while supporting the understanding of some simple geometry related to squares and rectangles.…”