Academic self-efficacy, academic amotivation, attitude toward the teaching profession, and classroom management anxiety are four of the most significant factors for both teacher training and performance because these psychological and behavioral constructs are first developed during the initial training, and reflect on the actual teaching quality of teachers. Therefore, investigation into their development and relationships, particularly with regard to prospective teachers, is significant both for the theory and practice of teaching. Hence, the current study aims to explore the casual relationships between these variables with a sample of prospective mathematics teachers, using the structural equation modelling (SEM). The participants were selected using simple random sampling method from prospective mathematics teachers studying at educational faculties of seven universities in different regions of Turkey. The data were collected using the academic amotivation scale, academic self-efficacy scale, attitude toward the teaching profession scale, classroom management anxiety scale, and a personal information form developed by the researchers. Data obtained from 581 participants were analyzed using path analysis. The findings showed that prospective mathematics teachers had a positive attitude toward the profession, and were eager to teach. Their academic self-efficacy predicted their attitude toward the teaching profession. Similarly, prospective mathematics teachers’ attitude toward the teaching profession correlated negatively with their academic amotivation. In other words, as prospective mathematics teachers’ attitude scores toward the profession increased, their academic amotivation scores decreased. However, prospective mathematics teachers had a high level of classroom management anxiety. Interestingly, prospective mathematics teachers with a positive attitude toward the profession experienced higher levels of classroom management anxiety. The findings mostly supported previous results in the literature. Implications were suggested both for teacher training and practice of quality teaching. Full article

This study seeks to explore the relationship between recent findings on mathematical connections and the Mathematics Teacher’s Specialised knowledge model. From a qualitative approach, we seek to explore the specialised knowledge mobilised during the establishment of mathematical connections in different contexts. The study takes into consideration the results from previous studies that were conducted with both prospective and in service teachers. The results suggest the need to include the notion of complexity in the mathematical connections defined by the Mathematics Teacher’s Specialised knowledge model. Similarly, they suggest that it is possible to find some ambiguities in the use of the model, so it would be enriching to consider the current classification of mathematical connections in order to improve the model as an analytical tool. Finally, the results suggest the need to include mathematical connections as part of the pedagogical content knowledge domain, since the knowledge of this domain could be mobilised during the establishment of mathematical connections. Full article

Mathematical modelling enjoys affirmed relevance in educational curricula worldwide, and teacher education programs consider that this process should also be experienced during educational internships. The interest of this study focuses on the argumentation of a prospective teacher to justify the incorporation (or not) of mathematical modelling in his lessons. To do this, we analyzed the reflection of a prospective mathematics teacher on the design of a modelling task during his educational internship. Methodologically, it is a case study in which, based on the didactic suitability criteria tool, the study subject structured the reflection on his educational internship in his master’s degree final project (MFP), whose central axis was modelling. We collected data from video recordings of group reflection sessions with the study subject and other prospective teachers of a professionalizing master’s program, and from the analysis of his MFP. The results evidenced the prospective teacher’s arguments to justify the design of a modelling task, his knowledge, and his beliefs about this process, among other aspects. We conclude that the specialized knowledge that is inferred from this argumentation is of different types and is part of a conglomerate formed, in addition, by values, beliefs, and guidelines for action. Full article

This research proposes theoretical-methodological strategies and tools to guide teaching, reflection, and assessment on the practice of the prospective teacher of mathematics when performing teaching and learning processes on the notion of function. It exemplifies our proposal’s use, through the reflection and characterization of the didactic-mathematical knowledge, of a prospective Chilean teacher, underlying his practice of teaching the power function. For the development of our proposal, we used the theoretical-methodological notions of the Didactic-Mathematical Knowledge (DMK) model and micro-teaching contexts, understood as rich and essential spaces for teacher education. As a conclusion, we could observe that the theoretical-methodological proposal here presented serves to systematize the reflection and assessment processes of teaching practice (one’s own or that of others) for the teaching of functions, and, thus, determine (or anticipate) actions that improve the teaching processes on this important mathematical notion. Full article

The aim of this study was to explore the specialized knowledge of five mathematics teachers who participated in a continuing training project. Teachers were asked to formulate conjectures about the type of mathematical work that students enrolled in a calculus course would develop when approaching the graphical representation of functions as an introductory activity to the calculation of the volume of solids of revolution. The data collected was analyzed using the categories of the MTSK (Mathematics Teacher’s Specialized Knowledge) model. The results report how knowledge of topics and the knowledge of features of learning mathematics, particularly in relation to the knowledge of strengths and difficulties, served as fundamental pillars for the formulation of the conjectures about students’ mathematical behavior. Full article

(1) Background: This research shows how the identification of conceptual advances (CA) that determine the transition between the stages of a progression model in a learning trajectory will help prospective primary teachers (PPT) to develop the teaching competence “professional noticing of students’ mathematical thinking”. Conceptual advances are key moments in the construction of mathematical structures and involve a change in the way students understand mathematical relationships. (2) Methods: A teaching module has been designed in which students of the Teaching Degree will analyze the responses of primary education students to tasks of pattern generalization from the identification and use of conceptual advances. (3) Results: The results of the teaching module show that professional noticing can be developed in suitable teaching environments. (4) Conclusions: The recognition of conceptual advances helps to interpret students’ thinking and learning trajectories which are effective tools to structure and develop professional noticing. Full article

This study relies on a theoretical perspective to provide a model that can be used to observe the educational practice of mathematics teachers. To this end, various existing observation instruments are studied, which, in the case of mathematics, aim to observe the teaching practice employed in the classroom, without considering the before and after of the implementation, which is what characterizes the professional task of teaching. Indicators that emerge from the teaching practice are proposed, together with the teacher’s knowledge and reflection constructs, based on three phases: for, in, and on the educational practice. As a result, understanding the educational practice of mathematics teachers would allow various educational stakeholders (teachers, administrators, instructors of teachers, and others) to focus their attention on what elements develop so as to improve how students are taught, and consequently learn, mathematics. Full article

During the last decades, research in teacher noticing has increased since its development is considered important in teacher training programs. An issue that needs more research is the relationship between teachers’ mathematical knowledge for teaching in a specific mathematical domain and their ability to notice. This study focuses on how pre-service primary school teachers (PPTs) solve a measurement division problem with fractions and interpret (score and justify) students’ answers to this problem. The participants were 84 PPTs who answered two tasks. Task 1 consisted of solving a measurement division problem with fractions. Task 2 involved interpreting (scoring and justifying) the answers of four primary school students to the problem. Responses to Task 1 were classified based on their accuracy and the procedure used. For Task 2, the scores given along with their justifications were analyzed. The results show that PPTs’ knowledge of division with fractions is limited and that they had difficulties in identifying conceptual errors in students’ answers. This study provides information on the relationships between PPTs’ knowledge of these types of problems and how PPTs interpret students’ answers. This information could aid in adjusting mathematical teaching knowledge in training programs. Full article

Mathematics teachers’ knowledge is considered one of the most critical factors in instruction and student achievement. As such, various studies have focused on mathematics teachers’ knowledge. Despite the expansion of the field, however, a systematic review was rarely implemented. Therefore, this study aimed to identify major research topics and trends on mathematics teachers’ knowledge by analyzing abstracts of 3485 scholarly articles published from 1987 to 2021. Using a text-mining technique, 11 underlying topics were found in the articles. The topics were classified based on their relationships and the following four groups were identified: “assessment”, “teachers’ knowledge for teaching”, “students’ knowledge and understanding”, and “teachers’ professional learning”. Over time, the analysis of research trends showed that professional development is the most popular topic, followed by pedagogical content knowledge and students’ mathematical understanding. Moreover, the popularity of these topics has not changed considerably over time. This study provides implications based on these results. Full article

Deepening the specialised knowledge of mathematics teachers is necessary for teaching, and it is one of our concerns as researchers; accordingly, in this study we analyze the knowledge that a teacher mobilizes when giving a first lesson on geometry to a class of fifth year of primary education at a Spanish school. We provide this analysis with a complementary perspective that leads us to broaden our focus of attention to other aspects of classroom management, thus identifying the specialised knowledge evoked in the researcher by the opportunities observed in the classroom. We take opportunities to mean classroom situations that occur as a result of the teacher’s management for which the researcher considers that an alternative management of such situations would be supported by relevant specialised knowledge for the teaching of the given content. Considering the possible alternative management of specific classroom situations makes this specialised knowledge emerge, which, together with that mobilized by the teacher, generates specialised knowledge useful for guiding the content of the training of primary education teachers. Full article

The mathematical knowledge for teaching (MKT) model emerged from the advances proposed by Shulman in 1986 and 1987 as part of the teacher’s professional knowledge model, and refers to the mathematical knowledge that the teacher employs to carry out the instruction process in the classroom. MKT has become an international benchmark for research into mathematics education and boasts a great scope and impact to date. The objective of this study is to conduct a systematic review of the way in which the MKT of early algebra teachers has been conceptualized and empirically studied in the scientific literature from 2010 to 2021. A systematic search in the Web of Science and Scopus databases led to a review of 17 papers. The results show great advances in the conceptualization of mathematical knowledge for teaching early algebra, focusing mainly on primary education teachers and on specialized knowledge of the content. In turn, there is a predominance of studies that address functional thinking as a content area. We conclude that more empirical studies are needed that address the mathematical knowledge that childhood and primary education teachers have of early algebra. Full article

The aim of this study is to deepen our understanding of the practice of a lecturer in linear algebra by exploring the connections he makes between his content knowledge and his pedagogical content knowledge while working on the topic of matrices. Data were collected through video recordings of his classes and semi-structured interviews, and were analysed with the Mathematics Teacher’s Specialised Knowledge model. Instances of classroom performance, supported by the teacher’s own affirmations, provided evidence relating to the categories comprising the model, and enabled us to establish connections between the lecturer’s knowledge, his understanding of his students’ learning capabilities, and his knowledge of teaching mathematics, which together account for his classroom practice: the use of varied examples to introduce new content, the highlighting of the most salient aspects of the topic, and alerts about potential errors and difficulties. The contribution that these results could make to the training of university teachers, which would be done with the knowledge of the areas of difficulty shown by the teacher in mind, could be used to deepen other elements of their pedagogical content knowledge. The interconnections between areas of knowledge identified by the study also serve to validate the usefulness of a theoretical model for studying teachers’ knowledge. Full article

Research on mathematics teachers’ knowledge has generally focused more on mathematics concepts than mathematical processes. This paper addresses the latter with a focus on mathematical problem solving (PS). It reports on a study that investigated the pedagogical knowledge for PS of prospective elementary school teachers of mathematics (PTs). Participants were 149 PTs at a university in Spain. They were at the end of their teacher education program. Data sources consisted of a questionnaire on knowledge of learning PS and a questionnaire on knowledge of teaching PS. Findings indicated that the PTs held combination of different levels of knowledge of PS learning and teaching. Many of them demonstrated appropriate knowledge of many characteristics for (1) PS learning consisting of student as a problem-solver, PS as a worthwhile task, non-cognitive factor related to PS, and (2) PS teaching consisting of PS teaching approaches, discourse in PS, intervention during stuck state in PS, PS assessment, and PS resources. However, there were also contradictions and limitations to their knowledge with implications for teacher education. These combination of appropriate and inappropriate knowledge resulted in some conflicts that are related to teaching actions and would limit student’ learning of PS. Full article