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This study aims at understanding the role of the tools chosen throughout the processes of solving a non-routine mathematical problem and communicating its solution. In assuming that problem-solving is a synchronous activity of mathematization and expression of mathematical thinking we take our proposed Mathematical Problem Solving with Technology (MPST) model to analyze the processes of solving-and-expressing-problems. Resorting to qualitative methods for data collection and analysis, we report on the case of an 8th grader working on a covariation problem to examine the role that paper-and-pencil and digital tools play in the development of a conceptual model of the situation. We found that the resources used throughout the solving-and-expressing activity influenced the depth of the conceptual model developed, within a process of progressive mathematization. Whereas paper-and-pencil led to the emergence of a conceptual model based on exploring particular cases, the digital transformation of the solution was triggered by the process of communicating its mathematical justification and expanded the previous model. Moreover, the complexity of this activity is evidenced by its multiple sequences of processes. Finally, the integration process seems crucial as the concomitant use of technological and mathematical resources precedes major advancements in the expansion of the conceptual model.

This study involves two classes from different educational levels, namely 9th grade and university. Students in both contexts were given a modelling task that required the development of a hand biometrics recognition system, during which they performed experimentation and simulation. As aims of the study, we look for distinctions and commonalities between the models developed in the two classes and seek to know how simulation and experimentation influence students’ production of meaning. The theoretical framework comprises the relationship between the modelling process and the prototyping process and adopts Peirce’s pragmatic perspective on meaning. The research is of a qualitative nature, assuming the characteristics of a case study. The results reveal many commonalities between the modelling in the two contexts. Moreover, experimentation and simulation were relevant elements for the production of meaning by the students, which is endorsed by a pragmatic perspective on meaning

Las emociones aún son insuficientemente investigadas cuando se estudia la experiencia de los jóvenes estudiantes, principalmente en el que concierne a las emociones positivas que implican en la actividad de resolución de problemas. Por otro lado, hay muchos estudios que se relacionan con las dificultades, la ansiedad, la resistencia y la pasividad, a menudo asociadas con el fracaso en las matemáticas. La investigación ha mostrado que la actividad matemática no puede verse estrictamente cognoscitiva y libre de emociones; en el contrario, el sistema afectivo juega un rol central en el aprendizaje de las matemáticas. En este artículo, presentamos resultados de un proyecto de investigación llevado a cabo en el contexto empírico de las competiciones matemáticas inclusivas que se realizan a través de Internet: SUB12 y SUB14. Se presentan y analizan datos de un cuestionario a los participantes, entrevistas abiertas y correos electrónicos intercambiados durante las competiciones. Las conclusiones del estudio señalan que los estudiantes experimentan fuertes emociones positivas, a saber, entusiasmo, alegría, disfrute, orgullo y felicidad, asociadas a un desempeño exitoso en la resolución de problemas matemáticos, como era de esperar. Los resultados también muestran que las emociones negativas frente a la dificultad y el fracaso tienden a ser emociones suaves que parecen ser transitorias y se convierten en emociones positivas. Explicamos estos resultados en función de las características específicas del entorno cultural de estos concursos, es decir, fomentando la búsqueda de ayuda, proporcionando comentarios positivos y dando a los participantes la oportunidad de mejorar.

The research on deductive reasoning in mathematics education has been predominantly associated with the study of proof; consequently, there is a lack of studies on logical reasoning per se, especially with young children. Analytical reasoning problems are adequate tasks to engage the solver in deductive reasoning, as they require rule checking and option elimination, for which chains of inferences based on premises and rules are accomplished. Focusing on the solutions of children aged 10–12 to an analytical reasoning problem proposed in two separate settings—a web-based problem-solving competition and mathematics classes—this study aims to find out what forms of deductive reasoning they undertake and how they express that reasoning. This was done through a qualitative content analysis encompassing 384 solutions by children participating in a beyond-school competition and 102 solutions given by students in their mathematics classes. The results showed that four different types of deductive reasoning models were produced in the two venues. Moreover, several representational resources were found in the children’s solutions. Overall, it may be concluded that moderately complex analytical reasoning tasks can be taken into regular mathematics classes to support and nurture young children’s diverse deductive reasoning models.