https://hdl.handle.net/10481/25936 Sun, 12 Apr 2026 06:27:22 GMT 2026-04-12T06:27:22Z https://hdl.handle.net/10481/110643 ChatGPT as a tool for posing of mathematical problems by prospective teachers Burgos Navarro, María José; Tizón-Escamilla, Nicolás Problem posing is a fundamental competence of the mathematics teacher, which motivates the interest in including this activity in teacher training plans. Incorporating problem posing into teaching practice involves considering the tools available to the teacher for this purpose, in particular generative artificial intelligence programs such as ChatGPT. This article analyzes how prospective teachers use ChatGPT to pose a problem involving mathematical modeling and equations and inequalities. The results highlight the difficulties of prospective teachers in providing effective instructions and identifying errors in ChatGPT responses. The problems that were finally proposed by the prospective teachers were, for the most part, not suitable for fostering algebraic reasoning. The joint analysis of the interaction of prospective teachers with ChatGPT and their final problem proposal made it possible to detect shortcomings in relation to their didactic-mathematical knowledge of algebraic reasoning and, in particular, of modeling. We conclude that using ChatGPT for posing mathematical problems has potential in teacher training, but didactic-mathematical training is needed for efficiently using this tool to elaborate meaningful problems. https://hdl.handle.net/10481/110643 https://hdl.handle.net/10481/91720 Probabilistic literacy and reasoning of prospective secondary school teachers when interpreting media news Álvarez Arroyo, Rocío; Batanero Bernabéu, Carmen; Gea Serrano, María Magdalena Educating students to apply probability literacy and reasoning in out-of-school contexts requires the previous preparation of teachers, which should include the assessment of their mathematical and didactic knowledge. Consequently, we investigated three research questions concerning the probabilistic reasoning and literacy of 66 prospective secondary school teachers when solving probability questions related to a report taken from the media news, their ability to identify the fundamental stochastic ideas needed to solve the task, and their capacity to predict their students’ potential difficulties. The participants needed to compute the probability of a complementary event, several conditional probabilities, and perform critical reading of the information in the report. Despite the participants’ good mathematical knowledge, a high percentage showed reasoning biases, such as the fallacy of the transposed conditional, confusion between conditioning and causation, and few identified the information missing to solve a question. There was a poor capacity to determine the stochastic ideas needed to solve the questions, beyond probability, sample space, conditional probability, and sampling. The participants quoted a few potential errors of their students, mainly conceptual mistakes with scarce recognition of interpretation errors. These results reveal the need to reinforce teachers’ probabilistic literacy, reasoning, and related didactic knowledge. https://hdl.handle.net/10481/91720 https://hdl.handle.net/10481/90170 Onto-semiotic analysis of the emergence and evolution of functional reasoning Díaz Godino, Juan; Burgos Navarro, María José; Rodríguez Wilhelmi, Miguel Developing students’ adequate functional reasoning requires paying attention to the design and planning of teaching from the first educational levels. This implies considering and progressively articulating the diversity of meanings of the function, attending to the generality and formalization levels that emerged in its historical evolution. In this paper, we review historical and epistemological studies on function using theoretical tools of the Onto-semiotic Approach to characterize different levels of functional reasoning. We interpret meaning in terms of systems operative and discursive practices related to solving types of problems. In line with previous research, we identify partial meanings of function (operative-tabular, operative-graphic, algebraic-geometric, analytic, arbitrary correspondence between numerical sets, and mapping between arbitrary sets) that should be part of the overall reference meaning in the planning and management of function teaching and learning processes. This study provides a complementary view of the multiple investigations that describe the phylogenesis of the concept of function in mathematics with a historical and epistemological approach.; Desarrollar un adecuado razonamiento funcional en los estudiantes requiere prestar atención al diseño y planificación de la enseñanza de las funciones desde los primeros niveles educativos. Esto supone considerar la diversidad de significados de la función y articularlos de manera progresiva, atendiendo a los niveles de generalidad y formalización emergentes en las etapas de su evolución histórica. En este trabajo revisamos estudios históricos y epistemológicos sobre la función utilizando herramientas teóricas del Enfoque Ontosemiótico para caracterizar distintos niveles de razonamiento funcional. En particular, aplicamos la interpretación del significado en términos de sistemas de prácticas operativas y discursivas relativas a la resolución de tipos de problemas. De acuerdo con investigaciones previas, identificamos significados parciales de la función (operatorio-tabular, operatorio-gráfico, algebraico-geométrico, analítico, correspondencia arbitraria entre conjuntos numéricos y conjuntista) que pueden ser considerados como parte del significado de referencia global en la planificación y gestión de los procesos de enseñanza y aprendizaje de las funciones. Este estudio aporta una visión complementaria de las múltiples investigaciones que describen la filogénesis del concepto de función en matemáticas con un enfoque histórico y epistemológico.; O desenvolvimento de um raciocínio funcional adequado nos alunos requer atenção à conceção e planificação do ensino das funções desde os primeiros níveis de ensino. Isto implica considerar a diversidade de significados de função e articulá-los de forma progressiva, atendendo aos níveis de generalidade e formalização emergentes nas etapas da sua evolução histórica. Neste artigo, fazemos uma revisão dos estudos históricos e epistemológicos sobre função, utilizando ferramentas teóricas da Abordagem Ontossemiótica para caraterizar diferentes níveis de raciocínio funcional. Em particular, aplicamos a interpretação do significado em termos de sistemas de práticas operacionais e discursivas relacionadas com a resolução de tipos de problemas. Na linha de investigações anteriores, identificamos significados parciais de função (operatório-tabular, operatório-gráfico, algébrico- geométrico, analítico, correspondência arbitrária entre conjuntos numéricos e conjuntista) que podem ser considerados como parte do significado global de referência na planificação e gestão dos processos de ensino e aprendizagem de funções. Este estudo fornece uma visão complementar das múltiplas investigações que descrevem a filogénese do conceito de função em matemática com uma abordagem histórica e epistemológica. https://hdl.handle.net/10481/90170 https://hdl.handle.net/10481/84252 Teaching and learning of probability Batanero Bernabéu, Carmen; Álvarez Arroyo, Rocío In this paper, we develop a personal synthesis of the most outstanding research on the teaching and learning of probability in the past years. We conducted a systematic search to examine publications on this topic in mathematics education, statistics education, education, and psychology journals. This exploration was complemented by additional studies published in conference proceedings or books. We classified these papers to highlight the main recent research tendencies in the field, according to the theme studied and considering the research objectives. Epistemological analyses suggest that informal inference based on simulation diminishes the topic abstraction but reduces probability to its frequentist view. Topics receiving particular attention include children’s probabilistic knowledge, the effect of visualizations on solving conditional probability problems, teachers’ education and probability modelling. In the final section, we recommend relevant points in which more investigation is needed to complete our knowledge about teaching and learning. In particular, we miss research on teachers’ mathematical knowledge of many probability concepts and on their didactic knowledge. https://hdl.handle.net/10481/84252 https://hdl.handle.net/10481/71627 Resolución de Tareas Probabilísticas en Contexto Geométrico por Estudiantes de Educación Primaria Hernández Solís, Luis Armando; Batanero Bernabéu, Carmen; Gea Serrano, María Magdalena; Álvarez Arroyo, Rocío Se presenta un estudio exploratorio de resolución de tareas probabilísticas de comparación de probabilidades y construcción del espacio muestral por parte de una muestra de 55 niños costarricenses de 6º curso de primaria, analizando sus estrategias y errores. Comparando con investigaciones previas, se observa un mejor desempeño en el ítem en que se puede comparar casos favorables y posibles y en el que es necesaria la comparación de áreas, pero no hay diferencias en aquel en que se introduce como distractor el orden de colocación de los casos favorables. Se observa que, en general, se construye correctamente el espacio muestral en los casos de suceso posible y equiprobable, no así en los de sucesos imposible o seguro.; We present an exploratory study of solving probabilistic tasks proposed to a sample of 55 primary school 6th grade Costa Rican children on comparison of probabilities and the construction of the sample space, analysing their strategies and errors. Comparing the results with previous investigations, an improvement is observed in the item in which the comparison of favorable and possible cases can be applied, and where the comparison of areas is necessary; however, there were no differences in the item in which the order in which the favorable cases are located is introduced as a distractor. The sample space is generally correctly built in the cases of possible and equiprobable event, but not in those of impossible or certain events. Agradecimientos – Proyecto PID2019-105601GB-I00 / AEI / 10.13039/501100011033 y Grupo de Investigación FQM-126 (Junta de Andalucía). https://hdl.handle.net/10481/71627