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In this paper, we describe an educational experience in the context of the Master's degree that is compulsory in Spain to become a secondary education mathematics teacher. Master's students from two universities in Madrid (Spain) attended lectures that addressed—emphasizing the concourse of a dynamic geometry software package—some historical, didactic and mathematical issues related to linkage mechanisms, such as those arising in the 18th and 19th centuries during the development of the steam engine. Afterwards, participants were asked to provide three different kinds of feedback: (i) working on an assigned group task, (ii) individually answering a questionnaire, and (iii) proposing some classroom activity, imagining it would be addressed to their prospective pupils. All three issues focused on the specific topic of the attended lectures. In the framework of Mason's reflective discourse analysis, the information supplied by the participants has been analyzed. The objective was to explore what they have learned from the experience and what their perception is of the potential interest in linkages as a methodological instrument for their future professional activity as teachers. This analysis is then the basis upon which to reflect on the opportunities (and problems) that this particular bar-joint linkages methodological approach could bring towards providing future mathematics teachers with attractive tools that would contribute to enhancing a STEAM-oriented education. Finally, the students' answers allow us to conclude that the experience was beneficial for these pre-service teachers, both in improving their knowledge on linkages history, mathematics, industrial, technological and artistic applications, and in enhancing the use in the classroom of this very suitable STEAM context. [ABSTRACT FROM AUTHOR]

This paper reports on how 10 middle and high school preservice teachers (PSTs) designed a social justice focused lesson using the culturally responsive mathematics teaching (CRMT) tool. Results from our analysis indicate that most of the PSTs were able to select appropriate social justice topics, though not all the PSTs integrated mathematics and social justice throughout their lessons. The results show that most of the PSTs need more experience with mathematization, handling controversial discussions, and developing transformative student action. Our work also led to a modification of the tool (CRMT-M). We discuss the implications of the study for mathematics teacher preparation. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this paper, we examine the impact of a massive open online course (MOOC) in the context of outdoor mathematics on the participating teachers' professional development. We firstly introduce the theoretical background on outdoor mathematics, focusing on math trails with the digital tool MathCityMap and professional development to be accomplished using MOOCs. By taking into account the MOOC "Task Design for Math Trails", with 93 finalists, we analyze the learning progress of 19 selected case studies from different nations and learning levels by taking into account their answers in a pre- and post-questionnaire and their posts on a specific communication message board, with a special focus on the MOOC's topics' task design for outdoor mathematics and the digital tool MathCityMap. The analysis is performed using different quantitative and qualitative approaches. The results show that the teachers studied have benefited from professional development, which is evident in the expansion/evolution of their knowledge from a content, pedagogical, and technological perspective. Finally, we formulate consequences for professional development in STEM education, and conclude the paper with limitations to be drawn and a perspective for further research. [ABSTRACT FROM AUTHOR]

Assessment for learning (AFL) has been associated with curriculum and teaching reform for the past three decades. However, studies on undergraduate students' perceptions of their mathematics teachers' AFL practices are still very limited in the Chinese higher education context. This quantitative study investigated three independent variables—teacher formal feedback and support, interactive dialog and peer collaboration, and learning-oriented assessment—that influence undergraduate students' ability to take responsibility for their learning through the mediation of the factor of active engagement with subject matter in first-year mathematics courses. One hundred and sixty-eight students from a Chinese "double-first-class" university were recruited to provide valid questionnaire data using the convenience sampling method. Partial least-squares structural equation modeling (PLS-SEM) was used to analyze the data. The results showed that interactive dialog and peer collaboration, as well as learning-oriented assessment, have a direct effect on students' active engagement with the subject matter and an indirect effect on undergraduate students taking responsibility for their learning in first-year mathematics courses. In addition, learning-oriented assessment was the biggest factor influencing undergraduate students' ability to take responsibility for their learning in first-year mathematics courses. This study contributes by developing a conceptual model and providing new insights into Chinese higher education sectors on factors that can improve undergraduate students' ability to take responsibility for their learning. [ABSTRACT FROM AUTHOR]

The paper is a reflection on the author's work with students enrolled in undergraduate and graduate elementary mathematics content and methods courses. Two specific pedagogical issues make up the focus of the paper. The first issue deals with demonstrating to future teachers the diversity of mathematical ideas behind a contextual question asked by a second-grade pupil allowing for multiple solution strategies to be used in addressing the question. The second issue deals with the use of Wolfram Alpha in aiding different mathematical features of this demonstration. The paper is congruous with mathematics teaching standards used across six continents and illustrated by reflective comments of the author's students regarding their mathematics teacher education experiences. Teaching ideas shared in the paper may be of interest to instructors who want to explore elementary mathematics in depth with teacher candidates. [ABSTRACT FROM AUTHOR]

Number theory is an area of mathematics not unknown to students majoring in mathematics teaching. As early as in junior high, they may encounter basic number theory concepts such as prime numbers, multiples, divisors, or even the fundamental theorem of arithmetic—the proof of which, however, will only be included in the university curriculum of mathematics teacher students. When teaching number theory, in addition to inspiring and motivating students, it is important to have them ask the right questions. Proofs are important, but so is the proper formulation of mathematical conjectures, not to mention intuitions regarding mathematical properties and relationships. These processes are facilitated by the software used, developed to visualize functions related to number theory. Our study aims to assess the relevance of visualization in the teaching and understanding of certain arithmetic functions among mathematics teacher students. Furthermore, we aim to investigate the practical usability of our visualization software, relying on student feedback. According to our results, students found the software useful, as it helped them to discover previously unknown relationships in the examined arithmetic functions. We may conclude our software fills a niche, with student feedback indicating its usefulness. [ABSTRACT FROM AUTHOR]

With an empirical study, we explore the process of designing modeling tasks for teaching mathematics in a Dynamic Geometry environment. We address the research questions: What are the characteristics of the tasks that pre-service teachers design to teach mathematics in digital and modeling environments? What are the activities like that these tasks encourage in students? By means of a qualitative methodology, we characterize the tasks designed by secondary pre-service mathematics teachers and identify the activities that these tasks encourage in students. By analyzing the process of designing and planning a class, we can determine how the characteristics of the modeling tasks are modified based on the software used. In this context, the software also acts as a medium that reflects aspects of the models involved, the objectives of the tasks, and the activities intended for the students. The results contribute to the discussion regarding task design, where technology is a means of supporting the exploration, understanding, and study of different phenomena. [ABSTRACT FROM AUTHOR]

'Mastery' is central to current policy in mathematics education in England, influenced by East Asian success in transnational assessments. We scrutinise the prospects for mastery pedagogies to improve pupil attainment in English primary schools. The Mathematics Teacher Exchange (MTE)—an element of the mastery innovation—involves teachers visiting Shanghai and then hosting Shanghai teachers in their schools. Informed by programme evaluation, core component practices are analysed, which were implemented by schools belonging to the first cohort of MTE schools. These consist of: varied and interactive teaching; meaningful and coherent mathematical activity; and full curriculum access for all. These elements are supported, optimally, by collaborative, embedded, and mathematically focused professional development. Details of the implemented pedagogy and forms of professional development are reported. Differences from prevailing practice in primary mathematics in England are highlighted. Evidence is reviewed from quasi-experimental trials, reviews and meta-analyses, and rigorous observational studies of the efficacy of practices similar to the MTE mastery pedagogy components in order to assess the prospects for increases in pupil attainment. The analysis suggests that many of the specific practices, if considered individually, have the potential to improve attainment, though overall policy ambitions may not be realised. Based on the review, component practices are identified for which existing evidence justifies immediate implementation by schools and teachers. In addition, practices that would benefit from further testing and evaluation are highlighted. [ABSTRACT FROM AUTHOR]

Our research was born with the objective of evaluating the level of gamification of high schools in Italy, specifically for mathematics, and the use of the serious game of chess as a resource for learning this discipline. The methodology is a mixed design, based on the combination of quantitative and qualitative techniques. Regarding the quantitative design, the instrument used was a questionnaire filled out by 4845 adolescents living in Italy. The qualitative methodology has focused on the analysis of the discourse of 12 in-depth interviews with mathematics teachers from high schools. Among the main results, we found that teachers, although unconsciously, apply gamification in classrooms (without having had any training about it) and, despite recognizing the mathematical benefits of chess, they do not use this game as a serious game. Our study confirms that gamification deserves more because of the benefits it brings, especially for a subject that scares students and demands greater motivation. [ABSTRACT FROM AUTHOR]

Space and shape is one of the geometry topics that should be mastered by students and require proper teachers' Mathematics Content Knowledge (MCK) for teaching to avoid misconception. This study aimed at developing a constructive conceptual framework as an instrument to examine mathematics pre-service teachers' MCK on space and shape contents and describing their profile on this topic. The present study used mixed methods, in which the obtained data were analyzed both quantitatively using Exploratory Factor Analysis (EFA) and qualitatively described in nature. The developed MCK instrument was administered to 21 senior Indonesian mathematics pre-service teachers who were in their third year of study which and by a purposive sampling technique. The results showed that the instrument had very good 10 final items with a consistent reliability coefficient of 0.67 and resulted in four factor components, namely, figural representation, area and circumference of object, relationship between properties of objects, and figural reasoning. Of the four factors, figural representation and reasoning factors had mostly been the challenges for Indonesian mathematics pre-service teachers. On the contrary, they performed better in the area and circumference of objects and the relationships between properties of objects. The findings lead to redesigning the curriculum for mathematics pre-service teachers' learning to accommodate all their challenges. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this research, we explored the potential of using a research-based teaching and learning sequence to promote pupils' engagement in practices that are coherent with those of real world mathematical and scientific activity. This STEM (Science, Technology, Engineering and Mathematis) sequence was designed and implemented by pre-service teachers and science and mathematics education researchers with the aim of modeling the growth of a real population of rabbits. Results show explicit evidence of pupils' engagement in relevant mathematical and scientific practices, as well as detailed descriptions of mathematical connections that emerged from those practices. We discuss how these practices and connections allowed the progressive construction of models, and the implications that this proposal may have for STEM task design and for the analysis of extra-mathematical connections. [ABSTRACT FROM AUTHOR]

The article provides an overview of research focusing on pre- and in-service teacher education, conducted in the Czech Republic by teams of researchers of which the authors were members. It employs the methodology of a qualitative meta-analysis of studies aimed at distinguishing key areas of research and their main results. Twenty-one studies were analyzed, 11 of which targeted pre-service teachers and 10 in-service teachers. The article briefly describes the historical and cultural context that informs mathematics education in the Czech Republic. It also elaborates on key theoretical concepts shared by the studies analyzed, including teachers' pedagogical content knowledge, competence and pedagogical reflection. The meta-analysis uncovered a common core of the studies in their focus on the process of professionalization for mathematics teachers in its three dimensions: professional vision, professional knowledge, and professional action. Six core research strands are identified within the group of studies: lesson study as a means of developing teachers' pedagogical content knowledge; joint reflection; professional vision and its development; culture of problem solving and teacher development; problem posing to support subject-didactic competence and teachers' competencies for content and language integrated learning and culturally responsive teaching. The article outlines the methodology and main results of the studies in each research strand and discusses their implications. Finally based on the meta-analysis, a discussion of the core concepts of teacher reflection, problem solving and problem posing is developed. [ABSTRACT FROM AUTHOR]

Young American children in today's public schools live in a world in which tensions around about identity (i.e., ethnicity and race, gender continuums, language backgrounds and proficiencies, cultural values and beliefs, economic resources, schooled experiences, literacy, and im/migration history) are part of everyday conversation. However, many early childhood science and mathematics educators are reticent to engage deeply in dialogue around these identities, not only due to a common narrative where science and mathematics are interpreted as culturally-neutral, but also because few models within early childhood science and mathematics education exist on how to engage in these conversations. Given this, we ask, how can we prepare and support teachers in developing a positive awareness of culture, identity, diversity, and other critical tensions faced by our youngest learners? How can we prepare and support teachers in engaging in these critical conversations as connected to science and mathematics with young children? [ABSTRACT FROM AUTHOR]