Advances of Research in Mathematics Education
Avances de Investigación en Educación Matemática (‘Advances in Research in Mathematics Education’), www.aiem.es, is the journal of the Sociedad Española de Investigación en Educación Matemática (‘Spanish Society of Research in Mathematics Education’), www.seiem.es. Since 2012, AIEM aims at advancing knowledge on the processes implied in mathematics education and in mathematics education research. AIEM covers all domains of research in mathematics education and has a strong international vocation. Hence, although Spanish is the preferential language of publication, the journal is also open to submissions in English, Portuguese and French. AIEM welcomes submissions of both theoretical and experimental papers which meet the criteria of scientific quality established. The texts submitted must present research in any domain of mathematics education with novel results contributing to knowledge production within the international scientific community of mathematics education. Papers should be informative and comprehensible to mathematics education researchers and, when possible, to mathematics education professionals. Manuscripts must include sufficient detail regarding theories, constructs and methods used and avoid generalities not directly related to the study. Editor-in-chief: María C. Cañadas, Universidad de Granada
Sociedad Española de Investigación en Educación Matemática
The articles published in this journal are under a license Creative Commons: By 4.0 España from number 21 (2022). Authors who publish with this journal agree to the following terms: Authors retain copyright and keep the acknowledgement of authorship. The texts published in this journal are – unless indicated otherwise – covered by the Creative Commons Attribution 4.0 international licence. You may copy, distribute, transmit and adapt the work, provided you attribute it (authorship, journal name, publisher) in the manner specified by the author(s) or licensor(s). The full text of the licence can be consulted here: http://creativecommons.org/licenses/by-nc/4.0. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
The Importance of Problem Formulation in the Development of Mathematical Knowledge
Problem posing in mathematics has been regarded for several decades as both a research tool and a teaching and learning strategy, not only with students at different educational levels but also with pre-service and in-service teachers. The articles included in this special issue highlight that research on problem posing is gaining increasing importance in Mathematics Education. The diversity of perspectives and theoretical frameworks supporting studies on problem formulation, as well as the variety of objectives addressed, provides a broad view that may be of interest to the international research community, with particular emphasis on studies conducted in Spain.
Copyright (c) 2025 María Burgos , Alicia Bruno https://creativecommons.org/licenses/by/4.0
Mathematical Problem-Posing Research: Revisiting Some Answered and Unanswered Questions
In 2015, Cai et al. reviewed the state of knowledge in problem-posing research. The purpose of the current review is to explore what we have learned as a field over the last 10 years by focusing on three questions from Cai et al.’s (2015) review: Can students and teachers be effectively trained to pose high-quality problems? What do we know about the cognitive processes of problem posing? How are problem-posing activities included in mathematics curricula? Specifically, we review what we know currently with respect to the three questions, including the progress made so far and additional findings on mathematical problem-posing research. We conclude this review by offering additional questions and suggestions for future research.
Copyright (c) 2025 İbrahim Burak Ӧlmez, Jaepil Han, Stephen Hwang, Jinfa Cai https://creativecommons.org/licenses/by/4.0
Bridging Problem-Solving and Problem-Posing: Third Graders Learning to Formulate Mathematical Problems in Geometry and Measurement
This study examines the relationship between problem solving (PS) and problem posing (PP) in mathematics education, focusing on 3rd-graders’ ability to create problems in Geometry and Measurement. A theoretical framework was adopted to assess the evolution of the problems posed, which considers mathematical and linguistic complexity. The study also compared posed and solved problems, for a deeper understanding of the connections between PS and PP skills. Conducted over eight lessons, it combined curriculum-aligned PS and PP tasks. Students’ written work was analyzed qualitatively. Findings show substantial improvements in PP skills, including better mathematical language, grammar and expression, alignment to task prompt, and problem solvability. Initially, students replicated structures from solved problems but gradually showed more creativity and autonomy. The study highlights how task design and the interplay between PS and PP enhance mathematical competencies and offer a viable approach to integrating PP as a learning objective in primary mathematics education.
Copyright (c) 2025 Hugo Fernandes, Hélia Jacinto, Hélia Oliveira https://creativecommons.org/licenses/by/4.0
Problem Posing Integrated into a Study Process on the Construction of Solids
In this study, developed within the framework of the Anthropological Theory of Didactics, we present and discuss the potential of Study and Research Paths as didactic means of a modality of study that, governed by the paradigm of mathematical modelling, promotes the integration of problem posing in the mathematical activity of students considered globally. Working with students in the third year of compulsory secondary education, we study the spatial problem of packaging design within the field of determination and construction of geometric solids. We analyse the crucial role played by the questions and answers maps elaborated by the students as evidence of the posing of new problems, and we show some institutional constraints that hinder the implementation of this new modality of study.
Copyright (c) 2025 Carlos Rojas Suárez, Tomás Ángel Sierra Delgado, Josep Gascón Pérez https://creativecommons.org/licenses/by/4.0
Prospective Teachers’ Didactic-Mathematical Knowledge when Posing Probability Tasks Based on the News
Using the didactic-mathematical knowledge model of the ontosemiotic approach, we assessed the knowledge of 70 prospective secondary school teachers during their training when creating probabilistic problems from news reports. Participants were asked to choose issue news, create and solve probabilistic questions about the issue, indicate the educational level at which the problem was aimed, and identify possible difficulties. The identified problems were appropriate, addressed topics of interest to students, used news from various sources and covered PISA contexts. Most questions were solved correctly, and, in addition to probabilistic calculations, some included reasoning and decision-making. However, the participants demonstrated lower competence in predicting potential student difficulties. The results provide new information about the knowledge of teachers by creating probabilistic problems in the context and identifying areas for teacher training improvement.
Copyright (c) 2025 Rocío Álvarez-Arroyo, Carmen Batanero, María Magdalena Gea https://creativecommons.org/licenses/by/4.0
Problem Posing and the Use of AI: Motivational Beliefs Among Pre-service Primary School Teachers
Problem posing is central to mathematics education and, like other practices, is challenged by teachers’ motivational beliefs and the use of artificial intelligence (AI). In this study, we applied a proprietary instrument, the ForPro-IA questionnaire, to assess the perceptions as problem formulators and AI users of 175 prospective primary school teachers. As a result, we found that participants found problem formulation more useful and cost-effective compared to the use of AI. The design, validation and application of the instrument are also presented as an original contribution to the field.
Copyright (c) 2025 Sara Embid, Josefa Perdomo-Díaz, Valentina Giaconi https://creativecommons.org/licenses/by/4.0
Problem Posing in Pre-service Secondary Mathematics Teacher Education: Insights of using GeoGebra
This research analyzes how the use of GeoGebra strengthens future teachers’ ability to reformulate problems. A qualitative analysis is applied, based on four phases of the problem formulation process (orientation, connection, generation and reflection), along with the categories established by Baumanns: reformulating to solve the problem and to inquire or investigate; formulating to generate new problems or to design them for didactic purposes. The results show that GeoGebra enabled participants to evaluate prior ideas and assess the feasibility of the problems they proposed. Additionally, visualization and dynamic approaches influenced both the reformulation and the formulation of new problems.
Copyright (c) 2025 Alexánder Hernández Hernández, Aitana Martín Ferraz, Matías Camacho Machín https://creativecommons.org/licenses/by/4.0
Inventing Numerical Sentences and Stories to Evidence the Development of Algebraic Thinking
In this article, we aim to address the following research questions: What algebraic understandings are evidenced when a group of 9–10-year-old students invent numerical sentences and mathematical stories? And what contributions do these tasks make to the development of algebraic thinking from both structural and analytical perspectives? We analyse students’ responses by focusing on the operations and properties involved, the meanings attributed to the equal sign, and the ways in which students refer to and reason about unknown quantities. The results show that students invent sentences involving numbers and unknown quantities, drawing on different properties of operations and demonstrating relational understandings of the equal sign. When inventing stories, they relate unknown quantities to everyday situations and construct narratives that are coherent with the given equation. We discuss the role of problem invention in the construction of algebraic thinking in the early years of primary education.
Copyright (c) 2025 Eder Pinto, Cristina Ayala-Altamirano, Marta Molina, María C. Cañadas https://creativecommons.org/licenses/by/4.0
Slow Reveal Graphs and Graph Reading Levels in the Formulation of Statistical Problems
Problem posing promotes problem comprehension and solving, but its application in statistics is limited in the literature. This study analysed how 164 Pre-service Teachers (PSTs) posed statistical problems based on graph reading levels, following the Slow Reveal Graphs approach. The results showed that the PSTs were able to contextualise their proposals, align them with the curriculum, and use appropriate language, but they made errors in identifying the graph reading levels. The study represents a novel line of inquiry in statistical education, highlighting ways to strengthen the didactic-mathematical knowledge of PSTs in problem posing and graph reading levels.
Copyright (c) 2025 Pablo Giadas, Laura Muñiz Rodríguez, Luis J. Rodríguez Muñiz https://creativecommons.org/licenses/by/4.0
Problem Posing as a Framework to Invent Games that Stimulate Mathematical Thinking
Researchers in psychology emphasize the importance of games during children’s learning and development processes; on the other hand, researchers in mathematics education emphasize the importance of problem posing in mathematics learning. This leads us to integrate both points of view and explore game invention as a means to stimulate probabilistic thinking in children, using the framework of problem posing. In this sense, we qualitatively analyze the reactions of children in primary education when playing games invented by them, by modifying the rules of a game in one case and based on the material presented to them in another. Through the implemented processes, we found that inventing games using the problem posing framework helps stimulate probabilistic thinking in children.
Copyright (c) 2025 Martín Malaspina, Uldarico Malaspina, Grecia Barraga https://creativecommons.org/licenses/by/4.0
Evolution of Non-Institutional Representations in a Modeling Process of Teaching (ACODESA)
The purpose of the study is to analyze the process of mathematical knowledge co-construction from a sociocultural perspective. Using a qualitative methodology, we present the results of implementing five research situations and how these results relate to the covariation between variables, this as a prelude to the concept of function. Using a multiple case study design, we present the results for four high school students aged 14 to 15. The results focus on the production process of functional-spontaneous representations and their evolution towards Socially constructed representations. This evolution process is determined by the discussion of ideas across the five stages of the ACODESA method. We also discuss the concept of habitus in the mathematics classroom. The study concludes that Socially constructed representations in mathematics classrooms are both constructed and transformed through a process of communication and objectification of signs or concepts.
Copyright (c) 2026 Fernando Hitt Espinoza, Samantha Quiroz Rivera https://creativecommons.org/licenses/by/4.0
Didactic-Mathematical Knowledge of Prospective Early Childhood Education Teachers: The Case of Probability
This study analyses the didactic-mathematical knowledge for probability of 32 Chilean prospective early childhood education teachers. An exploratory-descriptive study was carried out with mixed methodological approach, which analyses the mathematical practices from the answers to the CDM-Childhood Probability questionnaire. This analysis allowed us to study the different facets involved in this type of knowledge. The results show insufficient didactic-mathematical knowledge, although more complete in the case of common content knowledge. The conclusion is the need to strengthen the opportunities for acquiring and deepening the didactic-mathematical knowledge associated with probability in the training programs for early childhood education teachers.
Copyright (c) 2026 Claudia Vásquez, Carmen Batanero https://creativecommons.org/licenses/by/4.0
Generalization of the Function f(n)=n-1 in Children from a Functional Approach to Algebra
This work is part of a research project on algebraic thinking in early childhood and primary education students. The research objective of this document is to analyze the relationships between variables, representations, and strategies that preschool students demonstrate when working with a generalization task. We implemented a teaching experiment of 4 to 5 sessions for preschool students. We analyzed the work in one of the sessions, where the number of children invited to a birthday party was related to the number of juices needed, considering that one child does not drink ( ). The session took place in three moments: (a) introduction, (b) individual work, and (c) assembly. In the students’ written productions, pictorial representation predominated, and we identified physical and cognitive strategies. There were children who generalized, noting that “we will not give this child juice because he does not like it” to reflect the “-1” implied in the function.
Copyright (c) 2026 Sandra Fuentes, María C. Cañadas https://creativecommons.org/licenses/by/4.0
Learning the Logarithm Concept as Repeated Division
Traditionally, logarithms are introduced in classrooms as the inverse of the exponential function. Weber (2016) argues that this definition leads to errors and hinders understanding, suggesting teaching based on alternative basic models. We present a lesson designed to guide students toward constructing the concept of logarithm as repeated division and to provide empirical evidence of its explanatory potential. Students’ discussions were analyzed using the Abstraction in Context theoretical-methodological framework to identify the epistemic actions that occurred during the activities. The results indicate that this model supports concept construction: students recognize its necessity and reach the construct before receiving a formal definition. They were also able to understand and reason about some of its basic properties.
Copyright (c) 2026 Antonio Martín Barcala, María Teresa González Astudillo, Marta Molina https://creativecommons.org/licenses/by/4.0
Assessment of a Mathematics Textbook by a Colombian Rural School Teacher
This article presents the assessment of a mathematics textbook by a Colombian rural school teacher. This assessment is analyzed based on the didactic suitability facets of the ontosemiotic approach to didactic-mathematical knowledge, such as epistemic, cognitive, interactional, mediational, affective, and ecological suitability. The study involved a content analysis using Atlas.ti software. The research participant provides information on using a textbook to prepare and implement mathematics lessons. She uses the textbook as a guide for lesson planning but supplements it with additional resources. In addition, this participant makes some criticisms of this resource. Overall, the study highlights the importance of considering didactic appropriateness in analyzing textbooks for teaching mathematics in rural elementary schools.
Copyright (c) 2026 Juan Sebastián Cuartas-Carmona, Walter F. Castro Gordillo https://creativecommons.org/licenses/by/4.0
Teacher Competence in Managing Semiotic Conflicts in Mathematical Problem Solving
The objective of this article is to assess the didactic-mathematical competence of a teacher in identifying and resolving semiotic conflicts that arise in chemical engineering students when faced with a problem involving the differential of a function of one variable. The experience described in this study was carried out in an Analysis I class with 70 first-year engineering students. The analysis of task resolutions and the teacher’s interventions is based on the Onto-semiotic Approach. The results show the emergence of four cognitive conflicts, which were addressed with the class group under the teacher’s coordination. In conclusion, the importance of preliminary task analysis is highlighted as a fundamental tool for making appropriate teaching interventions and competently managing them.
Copyright (c) 2026 Manuel Alejandro Verón, Belén Giacomone, Silvia Etchegaray https://creativecommons.org/licenses/by/4.0
Using Algebraic Language with Understanding: The Role of Conjectures, Generalizations, and Justifications
This article aims to address the following research question: what relationships exist between the formulation of conjectures, generalizations, and justifications and students’ use of algebraic language with understanding? Drawing on a teaching experiment and adopting a qualitative and interpretative perspective, data are collected through students’ written and oral answers during classroom work and in interviews. The results show that conjectures, generalizations, and justifications play a fundamental role in reflecting on the meanings of algebraic symbols and on how these can express mathematical relations. Promoting these reasoning processes supports students in assigning meaning to algebraic symbols from multiple perspectives, thereby contributing to the use of algebraic language with understanding.
Copyright (c) 2026 Kelly Aguiar, João Pedro Mendes da Ponte, Marisa Alexandra Ferreira Quaresma https://creativecommons.org/licenses/by/4.0
Specialized Knowledge of Prospective Secondary Mathematics Teachers in Developing Proof-Based Tasks
Proof is a fundamental activity in mathematics, and its integration across different educational levels, with appropriate approaches, is relevant. Engaging in proof-related activities enhances students’ mathematical understanding, making it crucial for prospective teachers to develop a deep knowledge of this practice. In this study, using a qualitative approach, we aim to understand the knowledge of three prospective secondary mathematics teachers as they engage in proof-related tasks. We identify their knowledge about specific proofs, proof as a mathematical practice, and the didactic aspects of proof. We highlight the recognition of proof as a practice that fosters mathematical learning by these future teachers and, in this regard, emphasize the importance of including proof in initial teacher education.
Copyright (c) 2026 Elizabeth Advíncula Clemente, Isabel Torres Cespedes, Rosa Delgado Rebolledo, Flor Hau Yon https://creativecommons.org/licenses/by/4.0
A Variational Approach for the Significance of Derivative Criteria in Motion-Modeling Situations
In this paper, we present the results of research that aims to signify the criteria of the first and second derivatives through a variational analysis of a motion modeling situation that incorporates technological elements. To construct the evidence, a movement-modeling situation was applied to a group of undergraduate students. The results show that the discussion on the criteria is based on how the motion (position, velocity, and acceleration) of a mobile must reproduce a certain proposed position graph and to reach a dialogue on how to generate the different behaviors (constant, increasing, and decreasing) observed in it and, therefore, of the variational characteristics (represented in the monotony and concavity of the curve). The importance of the variational strategies of comparison and seriation on the significance of the criteria is evident.
Copyright (c) 2025 José David Zaldívar-Rojas, Luis Cabrera, Amaranta Jiménez https://creativecommons.org/licenses/by/4.0
Analysis of Spatial Sense in Secondary School Students in PISA Activities
This article analyzes the components of spatial sense in solving activities proposed by PISA. For that purpose, categories are established that allow identifying the manifestations of the spatial sense of 122 15-year-old students who are in the first year of Uruguayan high school when solving the PISA activities and are related to the performance achieved in the classroom tests proposed by their teachers. From the correlation analysis, relationships are obtained between performance and visualization skills and the management of geometric concepts in some activities. It is evident that those who present a better performance in the evaluation implemented by the teachers tend to have a greater manifestation of the spatial sense in the PISA activities. The spatial sense required in the PISA activity that best predicts the performance achieved by students in the evaluation implemented by the teachers is also described. 2.11.0.0
Copyright (c) 2025 María Isabel Elvas Fernández, Rafael Ramírez Uclés https://creativecommons.org/licenses/by/4.0
Interdisciplinarity Between Mathematics and Physics: Solving Strategies for Simple Proportionality Problems
This article analyses the strategies used by 3rd year ESO and 1st year Bachelor students to solve simple proportionality problems in mathematics and physics classes, with the aim of understanding how the teaching traditions of each discipline influence students’ responses. The results show that students in the 3rd year of ESO use a greater variety of strategies, while those in the 1st year of Bachelor have a higher success rate. It is also observed that the strategies used in Physics are different from those used in Mathematics, regardless of the year. These findings highlight the importance of interdisciplinary teaching that promotes a deeper understanding of simple proportionality, adapting teaching strategies to the characteristics and needs of students at each educational level.
Copyright (c) 2025 Juan Carlos Tinoco, Lluís Albarracín, Jordi Deulofeu https://creativecommons.org/licenses/by/4.0
Design and Validation of an Instrument to Analyse Spatial Thinking in Early Childhood Education
From an early age, children begin to develop their spatial thinking by exploring their environment, acquiring informal knowledge about space. This study aims to design and validate a tool to assess spatial thinking in childhood. The methodology followed consists of three phases: instrument design, content validation by a panel of experts, and application to a pilot sample. The results showed agreement among the expert committee on all items, except for three of them where changes were suggested towards manipulative situations and adjustments in some aids. It is concluded that the application to the pilot sample confirmed the relevance of the changes proposed by the experts and allowed refining the way of communicating the instructions for each item.
Copyright (c) 2025 Lígia Gonçalves Nogueira, Teresa Fernández Blanco, Cláudia Maia-Lima https://creativecommons.org/licenses/by/4.0
The Nature and Role of Mathematical Connections in the Teaching and Learning of Mathematics
Research on learning and teaching mathematics has highlighted the importance of connections in this process. A global look at the articles in this monograph shows that research on mathematical connections is an increasingly relevant topic for Mathematics Education and, also, that its theoretical references are becoming more developed.
Copyright (c) 2024 Vicenç Font Moll, Camilo Andrés Rodríguez-Nieto https://creativecommons.org/licenses/by/4.0
Mathematical Connections Associated with the Vector Concept in a High School Textbook of the New Mexican School
Mathematics is a universe of connections between concepts, theorems, and procedures, they are even conceived as a feature of the discipline, not just internal connections but with some other. These connections play a fundamental role in concepts understanding; therefore, it is necessary to promote them in curricular materials. The goal of this paper is to analyze mathematical connections risen about the vector concept in the textbook “Saberes y Pensamiento Científico” of the high school education of the New Mexican School, based on three categories: unifying topics, mathematical procedures, and mathematical connectors. Mathematical connections are considered as relations between mathematical ideas, and they are one of the main features of mathematics. Methodologically, we use qualitative text analysis. Our results show that unifying topics, procedures, and mathematical connectors are understanding promoters, and they develop connections between conceptual and procedural knowledge of the vector concept.
Copyright (c) 2024 Flor Monserrat Rodríguez Vásquez, Viana Nallely García-Salmerón, Jesus Romero Valencia https://creativecommons.org/licenses/by/4.0
Ethnomathematical Connections in the Classroom with the Spinning Top Made of Bottle Caps
The spinning top made of bottle caps (TT, by its acronym in Spanish) is a toy made by children living in some villages of the Colombian Caribbean. The objective of this research is to explore the ethnomathematical connections constructed by sixth grade students in a public educational institution in Barranquilla when they interact with the TT in the classroom. The methodology of this research is qualitative and exploratory, and was developed in three stages: 1) Ethnographic study of the development and the game of TT, 2) Design of a lesson plan to incorporate TT in the classroom under a framework of dialogue and respect, and 3) Exploration of ethnomathematical connections constructed by students when implementing various activities in the classroom. Among the results and conclusions, it is highlighted that, applying the activities, students build ethnomathematical connections between their knowledge of cultural practice and school mathematics.
Copyright (c) 2024 Kamilo Andrés Manchego Palacio, Yeidrys Yojana Utria Hernández, Armando Alex Aroca Araujo https://creativecommons.org/licenses/by/4.0
Understanding the Solution Set of Linear Inequalities in Two Variables to Propose a Genetic Decomposition
The objective of this research is to analyze the understanding of a group of students in order to propose a Genetic Decomposition (GD) on the solution set of a linear inequality in two variables (SSLITV). We employ the APOE Theory (Action, Process, Object, and Scheme) as a theoretical and methodological framework. Three undergraduate mathematics students participated, selected based on their good academic performance. For data collection, we conducted three virtual sessions that were recorded using Google Meet; during these sessions, participants solved and discussed nine tasks. The findings revealed that students graphically represent the SSLITV by constructing three types of processes: utilizing points, rays, or generalizing properties from to . Furthermore, we found that they conceptualize the SSLITV as an area or region where some points satisfy the inequality. Lastly, we recommend further research to expand upon the proposed GD.
Copyright (c) 2025 Adrian Muñoz Orozco, Gustavo Martinez-Sierra, Marcela Ferrari-Escolá https://creativecommons.org/licenses/by/4.0
The Role of Intra-mathematical Connections in Learning Decimal Numbers
Several characterizations proposed for number sense coincide in the need to promote the establishment of connections for the strategic use of rational numbers by students. This study follows a case study design for the analysis of eight class sessions of a group of 12–13-year-old students who study decimal numbers. Results show a relationship between the emergence of specific types of mathematical connections and the possible development of specific components of number sense in students. A special relevance of “justification” type connections is pointed out in the construction of fundamental aspects of number sense. Opportunities to refine reference models of mathematical connections are also discussed.
Copyright (c) 2024 Genaro De Gamboa, Sofía Caviedes, Edelmira Badillo Jiménez https://creativecommons.org/licenses/by/4.0
Extra-mathematical Connections Made by Prospective Elementary School Teachers when Designing Geometric Homework Assignments
We describe the extra-mathematical connections that emerge when a group of 250 prospective elementary school teachers are confronted with two professional tasks that deal with different geometric notions. The analysis considers the theory of extra-mathematical connections and the tool of the Ontosemiotic Approach (epistemic configurations) to evidence the emergence of generic metaphorical and interdisciplinary connections; the former referred to the constitution of a metaphor as a tool to access from an extra-mathematical idea to an intra-mathematical object; while the latter refers to the use of elements belonging to a particular discipline and therefore extra-mathematical, to understand an intra-mathematical object. The results and conclusions revolve around the evidence presented on the emergence of such connections. It contributes to the reflection on the theory of extra-mathematical connections, and it shows the potential of the design of school tasks in the training processes of Primary Education teachers.
Copyright (c) 2024 Juan Pablo Vargas Herrera, Yuly Vanegas, Joaquin Giménez https://creativecommons.org/licenses/by/4.0
Mathematical Understanding Evidenced by Secondary School Students on Exponential and Logarithmic Functions
A framework of reference on levels of comprehension was refined based on the establishment of mathematical connections. To this end, the networking between the Ontosemiotic Approach to Knowledge and Mathematical Instruction and the Extended Theory of Mathematical Connections is used as a theoretical reference. This qualitative research is a case study in which the productions and responses to a questionnaire of three high school students were analyzed. The data were analyzed using ontosemiotic analysis. The results showed that the refined frame of reference allowed to assess the level of understanding of the students, who, through the establishment of connections, evidenced a different level of understanding concerning the exponential and logarithmic functions. The case studies did not show a high level of understanding; some reasons were due to the lack of time to socialize and deepen some characteristics of the functions during the sessions.
Copyright (c) 2025 Karen Gisel Campo-Meneses, Javier García-García https://creativecommons.org/licenses/by/4.0
Mathematical Connections in Preservice Secondary Mathematics Teachers’ Solution Strategies to Algebra Problems
This study investigated the mathematical connections found in the solutions provided by 22 preservice secondary mathematics teachers to a set of algebra problems. Interest in, and research on, mathematical connections has gained prominence of the past decade. Here, we use the Extended Theory of Mathematical Connections or ETMC to explore the types of connections that this framework does and does not capture in the preservice teachers’ solutions. The ETMC surfaced four types of mathematical connections across four problems: ‘different representations’, ‘procedural’, ‘part-whole’ and ‘meaning’. The other types of connections defined in ETMC such as ‘reversibility’ or ‘feature’ were not found in our data, perhaps because of the specific problems that were used. Some mathematical connections were not highlighted when examining the solutions through the lens of ETMC (‘meaning’, ‘implication or if/then’ and modelling) addressing areas in which ETMC might be limited in its capacity to support researchers in identifying mathematical connections in different contexts.
Copyright (c) 2024 Vesife Hatisaru, Kaye Stacey, Jon Star https://creativecommons.org/licenses/by/4.0