Search Results (16)

This paper presents a study whose aim was to formulate a conceptual framework that allows us to understand the degree of complexity of the connections between the knowledge that a mathematics teacher can possess, based on the model of the mathematics teacher’s specialized knowledge model and the Piaget’s schemas. To this end, a literature review was carried out to analyze how these connections are made in the minds of mathematics teachers and how complex they are, identifying a deficit. Therefore, the schema structure proposed by Piaget, with its three stages of intra-, inter-, and trans-development, was considered. Based on an instrumental case study with two prospective teachers, an analysis was performed on semi-structured interviews conducted while the teachers separately discussed a lesson plan based on the understanding of multiplication and division of natural numbers, aimed at third-grade students. The results show that three types of knowledge schemas emerged among the participating teachers, with the respective types of connections between the knowledge. This shows that the connections between the knowledge of the model in teachers’ minds can vary in complexity. Full article

This study examines the quality of university teaching in Mathematics, focusing on the evolution of teaching performance from students’ perspectives. It highlights the importance of adhering to quality standards to enhance teaching, research, and administrative processes, guided by the Andalusian Knowledge Agency. Key factors analyzed include effectiveness, planning, classroom performance, tutorials, and the use of bibliographic materials, using exploratory and confirmatory factor analyses (EFA and CFA) with structural equations. The research involved 229 students from various programs, such as Physical Activity and Sport Sciences, Primary Education, Early Childhood Education, and a Master’s Degree in Secondary Education with a Mathematics specialization, within an Andalusian university center. The results confirmed the reliability and validity of the questionnaire and demonstrated the effectiveness of structural equation methodologies. The findings underscore the importance of integrating effective knowledge transmission, teacher-led motivation, careful planning, individual attention, and complementary materials to improve Mathematics teaching. It concludes that quality teaching depends on a holistic approach that balances pedagogical strategies with student-centered practices. Full article

Many Saudi students lack the motivation to pursue STEM careers due to their teachers’ limited experience and low efficacy in teaching science, technology, engineering, and mathematics (STEM). Teachers’ perceptions are central to efficient STEM education; however, little is known about the perceptions of teachers toward STEM education in Saudi Arabia. Therefore, this study attempted to identify the perceptions of secondary stage science teachers toward STEM education and their knowledge about the requirements for its implementation. The study also investigated whether there were statistically significant differences that could be attributed to teachers’ qualifications, years of experience, and specialization variables. A questionnaire was applied to 175 in-service science teachers. The results showed that the secondary stage science teachers had a medium level of positive perceptions toward STEM education and a high level of knowledge about the requirements for its implementation. It was also revealed that there were statistically significant differences in teachers’ perceptions due to their qualifications and years of experience, in favor of teachers with graduate degrees and with more years of experience, while there were no statistically significant differences due to teachers’ specialization. Based on the findings of this study, a number of recommendations on improving science teachers’ knowledge of STEM education and the requirements for its implementation are provided. Full article

In this study, we examined aspects relating to the impact of integrating question-asking activities and providing answers to these questions while reading historical mathematical texts on prospective mathematics teachers’ self-reported cognitive load. The research design of the study was quasi-experimental. The study participants included two groups of 20 students each (experimental and control). The experimental group was instructed to ask questions while coping with the texts, whereas the control group received no special instructions. The experimental group participants were asked to think aloud while coping with the texts and audio record themselves. These records were transcribed into written protocols. Both groups had to respond to a self-esteem index questionnaire in which they had to report the level of difficulty they experienced during their attempts to cope with the texts, as an indicator of their sense of cognitive load. This process was repeated at three time points, relating to three different texts. The data were analyzed using quantitative and qualitative methods. Two main observations were obtained: (1) A significant difference was found between the control and the experimental groups regarding the decrease in cognitive load along the time points. Because the only difference between the control and experimental groups was the activity of question-asking, it might be concluded that question-asking affects the reduction in cognitive load. (2) Question-asking supports the assimilation of new information up to a specific limit, depending on the gap between existing knowledge and new information. Full article

The current paper explores the relationship between technological knowledge, beliefs about technology use in education, beliefs about the limits of technology use with respect to children with disabilities, self-efficacy beliefs, and their effects on technology use or teacher practices in the special education setting regarding mathematics education. Research was conducted via an online questionnaire. A total of 83 teachers working in the field of special education answered the questionnaire. The answers were analyzed via quantitative and qualitative analyses. In addition, correlational analyses were conducted. A prediction model that included all the aforementioned variables was tested. Our regression analysis evidenced the strong predictive value of technology-related knowledge with respect to technology integration practices but not toward the other models that included beliefs. Through mediation analysis, we found that technology-related knowledge mediates the relationship between self-efficacy and technology integration practices. The qualitative findings provided information on the interplay between knowledge, practice, and beliefs that are contextualized; on the specificity of technology-related knowledge. Implications are discussed with reference to factors important for the professional development of teachers with regard to technology integration. Full article

In this article, grounded in the concept of interpretative knowledge (IK), which is well known in the literature, we introduce and discuss the construct of semiotic interpretative knowledge (SIK). This theoretical tool unfolds the interpretation of conceptual knowledge into a broader construct that intertwines the use of semiotic representations with the manifold aspects of mathematical learning. In the first part of the article, we first introduce Duval’s semio-cognitive approach, in which semiotics is the element characterizing the specific cognitive functioning of mathematics. On the basis of some classic examples from the relevant literature, we then show the necessity of introducing the semiotic component into IK to expand the interpretive power of the teacher. In the second part of the article, through the analysis of six episodes involving students with a specific learning disorder (SLD) engaged in mathematical activities, we show how the development of the teacher’s SIK emerges as a necessary condition for the implementation of inclusive teaching practices. This permits us to face the research question focused on how SIK allows us to understand the student’s behavior in a special needs educational context and provide effective feedback. In this sense, SIK is shown to be an intrinsic prerequisite of inclusive teaching, thus extending the concept of IK to the components of pedagogical content knowledge (PCK). 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

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

The competencies that today’s citizen must possess have led to a transformation of the teaching of probability, which has been repositioned on the school curriculum from an algorithmic view to a practical one based on the understanding of the concepts and their application in daily life. In this task, the understanding of the binomial distribution is essential as it allows the analysis of discrete data, the modeling of random situations, and the learning of other notions. However, weaknesses are identified in teachers and students with respect to the binomial distribution attributed to the lack of knowledge of its origin and meaning throughout history. For this reason, our work consists of the identification of its partial meanings and essential components as well as its relationships from a historical epistemological study and its analysis, based on the notions of the Ontosemiotic Approach (OSA) to Mathematical Knowledge and Instruction and the specialized literature on statistics and probability. As a result of our work, we present a reconstruction of the holistic meaning of the binomial distribution from the elements that compose it, which are essential for didactic purposes such as the identification and resolution of learning conflicts, the design or evaluation criteria, and teacher education. Full article

In recent years, daily practice at universities all over the world has involved online teaching due to the COVID-19 pandemic. Teaching online requires knowledge of new ways to engage with the students, but limited research concerning pedagogical aspects of online formats has been conducted to examine this further. Research shows that the teacher–student relationship is a critical factor in a student’s development and learning in both traditional and online teaching. Limited research has examined teacher–student relationships in online teaching at universities further. In the present pilot study, a university mathematics teacher’s digital relational competence is examined and visualized by using Halliday’s Systematic Function Linguistics to explore what is said, the verbal language, and Burgoon and Hobbler’s framework to visualize how it is said, i.e., the nonverbal language. Data were collected in autumn 2020 and involved a seminar with ten pre-service special educators in mathematics in Sweden; approximately 3 h of video-recorded material was collected. The result shows that the teacher’s verbal language, such as the choice of questions, personal pronouns, and being personal, but also her nonverbal language, involving gestures, facial expressions, and paralanguage, are essential when building supportive teacher–student relationships in mathematics. Full article

The preservice primary school mathematics teacher needs training that focuses on school mathematics and its didactics. Research has shown the importance of developing mathematical content knowledge as well as adequate didactic knowledge. Teacher education programs must address both to provide an effective teaching-learning process. The present research aims to assess the mathematical content knowledge of 194 prospective teachers about fraction word problems faced by students at the Primary Education stage, based on the Mathematics Teachers′ Specialized Knowledge (MTSK) model. By means of the preservice teachers’ written answers, we explored their knowledge and identified the associated error to fraction word problems (one-step and multistep) in which the fraction has a meaning as an operator. Preservice teachers showed some difficulties when working with this content, difficulties that were intensified when they solved multistep problems. The most common error founded in both types of problems is related to the meaning of fraction as operator. The results show a weak prior mathematical content knowledge and as a consequence, it is necessary to establish preventive actions in the training degrees since an insufficient mathematical content knowledge prevents them having a proper didactic knowledge. Full article

Since the development of the technological pedagogical content knowledge (TPACK) framework, researchers have been developing a variety of instruments to measure the TPACK of pre-service and in-service teachers. The task of developing an efficient, reliable, and valid instrument is difficult. Even validated instruments require guidance for consistent use that preserves the instrument fidelity. The purpose of this study is to provide guidance for using the TPACK Levels Rubric, a validated instrument that was developed on the basis of the model for the progressive levels of TPACK. The authors systematically examined the criteria of the rubric in order to understand the differences in the levels of TPACK for each rubric component, and developed lesson exemplars to create guidelines for educators using this tool in assessing the TPACK levels of teachers. The iterative instrument analysis also led to the revision of the original rubric to establish the horizontal and vertical alignments and the consistency of the rubric, for each level across four components, and for each component across five levels. The construct validity of the revised rubric was confirmed on the basis of a exploratory factor analysis of 175 mathematics lesson plans and videos of taught lessons developed by graduate special education pre-service and in-service elementary school teachers. Full article

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. 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

In the paper, we present a study devoted to the utilization of multiple-solution tasks (MSTs) in combinatorics as a part of a pre-service teachers course on didactics of mathematics from the view of the mathematics teachers’ specialized knowledge (MTSK) theoretical framework. The study was carried out over the standard course of a summer semester in 2021. The course was attended by 13 pre-service teachers (PSTs). It was carried out online, due to COVID-19 restrictions. Ten combinatorial multiple-solution tasks were assigned to the PSTs. Analyzing pre-service teachers solutions to these tasks, we sought the description and better understanding of the combinatorial knowledge of the topic from the perspective of MSTK. The results revealed some critical aspects of mathematical knowledge in combinatorics that pre-service teachers education should focus on. Full article