One of the aims of compulsory education is for students to adequately handle basic maths, owing to its importance in their future professional and personal lives. However, mechanical knowledge of an algorithm may not be sufficient to train future citizens with critical and creative thinking if it is not accompanied by a comprehensive understanding of the concept. In this regard, existing research shows that a high percentage of students in primary education commit errors when they attempt subtraction. However, little is known about whether adults perform the same calculations correctly. In this context, 535 university students completed a questionnaire composed of 20 subtractions. The results showed that only one quarter of respondents performed the subtractions correctly. Analysis of error type showed that the most frequent mistakes corresponded to the systematic errors made by primary-level students. This may indicate that the types of errors committed during early learning persist over time, implying that subtraction may not have been adequately taught. New educational approaches and initiatives are required to encourage the teaching and learning of subtraction in a more reasoned and critical manner during early learning.

Primary school textbooks can enhance the acquisition of arithmetic word problem solving skills by offering diverse problems based on their semantic-mathematical structure with targeted reasoning aids, including schematics highlighting their mathematical structure. While certain countries, such as the USA and Singapore, have made progress in improving the problems and aids found in their textbooks through the use of specific theoretical-methodological approaches, textbooks from other countries, such as Spain, have included a very limited variety of problems, with hardly any aids to reasoning. Recently, however, two of the most widely used Spanish publishers have released textbooks that adhere to these theoretical-methodological approaches. To assess whether these textbooks progressed past their predecessors in relevant aspects related to the resolution of arithmetic word problems, we conducted an analysis of the quantity of problems and their variety in terms of semantic-mathematical structure and level of difficulty, as well as the inclusion of schematic representations of their mathematical structure. The study demonstrated improvements among textbooks when publishers adopted a theoretical framework, suggesting that a reference framework could enhance textbook design. This is particularly relevant in countries such as Spain, where there are no applicable standards or official curricula for designing textbooks related to solving arithmetic word problems.

[Objective] The aim of this paper is to analyze the self-efficacy of prospective Secondary School Mathematics Teachers at the end of their initial teacher training. [Methodology] The sample was 98 prospective Secondary School Mathematics Teachers who were studying in a University Master’s program for Secondary Education Teachers. The data were their written reflections, which were organized into information units and classified according to the five sources of self-efficacy collected from specialized literature: professional knowledge; classroom practice; physiological, affective and motivational states; cooperation with colleagues and parents; and experience. Subsequently, a content analysis made it possible to identify common topics among them. [Results] The results showed that a teacher's self-efficacy was still in the process of development, far from what might be expected in teachers completing their initial training period. The need to increase the confidence of prospective teachers in their skills to translate knowledge of content into student learning, to implement different teaching strategies and, especially, to increase their confidence in their emotional skills is highlighted. [Conclusions] The results provide valuable information for teacher education programs by indicating the state of teacher self-efficacy at the end of the initial training period. In addition, a tool is provided to analyze the teaching self-efficacy of prospective Secondary Mathematics teachers. All this opens up future lines of research in various areas.

This study examines how 98 prospective secondary mathematics teachers (PTs) from five Spanish universities conceptualize professional orientation (PO) and task orientation (TO), and the extent to which both domains are integrated in their reflections after completing a one-year teacher education program. Using a qualitative approach, the study analyzed PTs’ written reflections on mathematical and pedagogical knowledge and how it is applied in classroom practice for effective mathematics teaching. Results show a predominance of PO over TO. Key categories such as curriculum interpretation, specialized mathematical knowledge, collaborative participation, and challenging tasks appeared less frequently. Although some PTs integrated PO and TO categories, they emphasized what mathematics teachers should know more than how this knowledge is translated into classroom practice. The findings highlight the need to strengthen opportunities within initial teacher education to connect mathematical and pedagogical knowledge with classroom practice, particularly through practice-based experiences.

La necesidad de una sólida formación del profesorado de matemáticas que trascienda el dominio algorítmico e incorpore una comprensión conceptual del cálculo integral ha motivado la revisión de episodios históricos. A partir del cálculo de Leibniz, se diseñó e implementó una ingeniería didáctica que sitúa la suma y la resta como ejes de la definición de la integral. Desde esta perspectiva, la integral se concibe como suma infinita de diferencias infinitesimales, permitiendo interpretar la relación entre integrar y derivar como procesos inversos análogos a sumar y restar, lo que conduce al teorema fundamental del cálculo. La experimentación con futuros profesores, basada en trabajo grupal y análisis de interacciones, muestra una comprensión sólida del concepto, vinculada a la suma continua, y puede constituir una propuesta para la formación inicial del profesorado de matemáticas.