Search Results (43)

The present study investigated the effect of improving prospective teachers’ self-regulation to teach mathematics at primary education through the mathematical courses they attended at a pedagogical department. Forty-eight students of a pedagogical department participated in the conducted quantitative study. The implemented intervention program, which consisted of two math content courses and a teaching methodology course on mathematics, emphasized the acquaintance of unsolved mathematical problems, the historical development of mathematical concepts, the obstacles faced during the development of concepts through the centuries, and the process of mathematical continuity and development. The use of the history of mathematics aimed to enhance participants’ self-regulatory abilities about the learning and teaching of mathematics. We had used data from tools administered four times over a period of the four years of their studies: at the beginning of their studies, after two math content courses, after a course about the teaching of mathematics, and after the field work at a school. The analysis of those data showed that there was an improvement in their mathematical performance and their self-regulation ability to solve problems, but there was a decrease in their self-efficacy beliefs to teach mathematics and to self-regulate their respective teaching behavior. We discuss the effectiveness of the program on the specific dimension and the implications of the design of teacher education programs grounded in the history of mathematics, with the aim to enhance prospective teachers’ self-regulation on handling difficult situation during the teaching of mathematics. Full article

This study explored 10 prospective teachers’ (PTs’) understanding of the area of a rectangular region using square and non-square rectangular area-units. In an hour-long interview, each PT was first asked to explain how they would find the area of a given rectangular region in terms of a non-square notecard. For several PTs, this task prompted discussion of a square unit defined by the edge of the notecard. In a second task, PTs were presented with a rectangular array of squares and were asked to explain to a fictional child why multiplying length times width does not count the top left corner square twice. An analysis of transcripts of the interview suggested three conceptual components to understanding the area of a rectangular region—area-units, multiplication, and their connection to the length times width formula. Based on the PTs’ responses, we propose multi-tiered levels of reasoning. Each new level of understanding was built on the prior level in a hierarchical fashion. Juxtaposing tasks involving different area-units revealed PTs’ thinking about non-square and square area-units and how these related to the formula “L × W”. Full article

In an evolving perspective, lecturers consider that inquiry is one of the best forms of learning to drill critical thinking. This study assesses the practice of inquiry to develop the critical thinking skills of prospective science, technology, engineering, and mathematics (STEM) teachers in Indonesia, which is a suitable way to address the problems in the country. Through the experimental design, three groups were formed, which were intervened with inquiry learning, inquiry-creative, and traditional teaching. The learning intervention was carried out within one month using a pre-validated instrument. The critical thinking data were analyzed descriptively based on the pre-test and post-test mean parameters and n-gain on critical thinking indicators, as well as individual critical thinking performance. Statistical analyses (paired-t test, ANOVA, and least significant difference test) were employed to provide confidence in the differences in critical thinking skills across the three learning treatments (p < 0.05). The prospective STEM teachers’ critical thinking skills showed varied performances among the three groups. The inquiry-creative group had the strongest impact, followed by inquiry and traditional teaching, all differing significantly. In summary, the findings suggest that current teaching practices in STEM education need to be reconsidered, showing the advantage of the inquiry-creative model in developing the critical thinking skills essential for future teachers and creators in the STEM fields. Full article

To promote optimal learning in their students, mathematics teachers must be proficient in problem posing, making this skill a cornerstone in teacher training programs. This study presents a formative action in which pre-service teachers are required to create and analyze a problem involving proportional reasoning within a probabilistic context. For this problem, they must identify the objects and processes involved in its resolution, recognize the degree of algebraic reasoning implied and identify potential difficulties for students. Subsequently, they need to formulate and analyze a new problem with variation, which mobilizes higher-level algebraic activity. Results indicate that prospective teachers struggle to pose problems that engage proportional reasoning, as well as to identify in their analysis which elements of proportional and algebraic reasoning are present in their solutions. Despite this fact, a significant percentage of participants adequately modify the original problem to address higher levels of algebraic reasoning, identifying in these cases the new algebraic objects and potential difficulties that might arise as the degree of generalization required in the solution increases. The study concludes by underscoring the importance of training in problem posing to enhance the knowledge and competences of prospective teachers concerning proportional and algebraic reasoning. Full article

After providing a brief summary of what has already been said about pedagogical imagination, data are presented showing how prospective mathematics teachers can become engaged in such imaginations. With reference to this data, the notion of pedagogical imagination is explored further by relating it to dialogue, social justice, mathematics, hope, and sociological imagination. To illustrate these relationships, different episodes from the data are highlighted. Finally, the central role that pedagogical imagination can play in mathematics teacher education is discussed. Full article

This paper extends earlier research on prospective and practicing teachers’ (PPTs’) developing understandings of culturally responsive pedagogy (CRP) while enrolled in a teacher education course for CRP and mathematics. Here, we take as our starting point a framework we refer to as COFRI, which describes five integral components of PPTs’ perspectives on CRP: Challenges, Opportunities, Fears, Resistance, and Insights. Viewing PPTs’ reflective journal entries through the lens of this framework, we noticed interesting relationships between the five components that had not been evident in our initial analysis. Specifically, we observed that, as we coded participants’ reflections according to C, O, F, R, and I, each I (insight) appeared to be related to one (or more) of the other components in quite different ways. Additionally, careful study of the insights expressed by PPTs lead to our categorization of insights according to one of three types: mathematical, pedagogical, or ideological. As a result, this paper offers a new way to interpret the five components, specifically their relationships to new insights into CRP and the corresponding types of insights that PPTs produce over the course of one semester. In closing, this paper discusses implications for mathematics teacher educators in understanding and processing PPTs’ evolving understandings of CRP. Full article

There is a growing emphasis on the role of language in teaching and learning mathematics, most significantly in classrooms with increased language diversity. Consequently, teachers face considerable challenges in accommodating diverse needs and must employ strategies to support all students. It is, therefore, crucial to provide prospective teachers with opportunities to enhance their pedagogical approaches while raising their awareness of the relationship between language and mathematics. In this respect, Live Brief assessments in Higher Education, which involve students working on authentic projects/tasks from a school, may be a promising avenue. This research draws on the 19 Live Brief group presentations prepared by a total of 118 Year 1 prospective primary school teachers, specifically focusing on the language-related challenges faced by a local school in early years mathematics. The data encompassed prospective teachers’ proposed practices, including one-to-one, small group and whole class activities, that aimed to address language diversity. Data analysis was informed by Moschkovich’s three perspectives on the relation between language and teaching and learning mathematics, namely lexicon, register and situated-sociocultural perspectives. While a lexicon perspective was commonly evident in the activities, the manifestation of a situated socio-cultural perspective mainly in the one–to-one activities is noteworthy, given its social and discursive nature. Three themes encapsulated a range of practices suggested in the findings: explicit vocabulary teaching, different strategies of scaffolding and utilising multi-sensory approaches. While the lexicon and register perspectives were commonly evident, the situated socio-cultural perspective was much less commonly manifested in the practices. We offer implications to initial teacher education curriculum, future research and policies about teaching and learning mathematics. Full article

Teachers’ perceived efficacy of their ability to teach using a gender approach is key for future generations to become more gender-sensitive and respectful towards gender inequities. However, little is known about graduate training for gender-responsive STEM (science, technology, engineering, and mathematics) teaching. In this study, after exploring the measurement invariance across countries (Greece and Spain) and sexes (male and female) of the TEGEP (Teacher Self-Efficacy for Gender Equality Practice) scale, a total of 222 prospective secondary school STEM teachers (136 Greek, 86 Spanish) from seven public universities were surveyed. Results showed that (1) the TEGEP has acceptable measurement invariance across countries and among sexes allowing comparison between groups and (2) that Greek and Spanish STEM students finish their master studies without sufficient confidence in gender knowledge, skills, and attitudes to practice a gender-sensitive teaching. The ability to teach gender knowledge was significantly higher in Greek than in Spanish students (4.52 vs. 4.03), while the latter felt more competent than the Greek students in conveying values/attitudes in regard to gender (4.54 vs. 4.83). The study calls for reflection, and considering that gender mainstreaming in STEM is anecdotal and not aligned with existing curricula, seeks to raise awareness and institutional compromise in implementing a gender-responsive approach in STEM. The TEGEP could be utilized to assess and monitor the gender competencies required of graduates in order to provide a more equitable and gender-sensitive STEM education in Greece and Spain. 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

This study endeavors to illustrate how research on the professional development of mathematics teachers can help to enhance and nurture the professional knowledge of mathematics teacher educators (MTEs), thus becoming a potential source of professional growth for MTEs. To achieve this, a professional task was administered to 38 prospective secondary teachers from two Spanish public universities to explore their level of development in professional noticing. Specifically, the study focused on their skill of attending to children’s strategies in relation to transformations between semiotic representations as well as their awareness of the role of the semiotic register in task design. Drawing from the responses provided for the task, we offer a range of insights regarding expected or desirable Pedagogical Content Knowledge (MTEPCK) aimed at fostering the development of professional noticing, such as several challenges to be overcome by pre-service teachers or the identification of three potential levels of progression in their skill to attend to children’s strategies. Full article

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. Full article

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

Educational data classification has become an effective tool for exploring the hidden pattern or relationship in educational data and predicting students’ performance or teachers’ competency. This study proposes a new method based on machine learning algorithms to predict the technology-integrated competency of pre-service mathematics teachers. In this paper, we modified the inertial subgradient extragradient algorithm for pseudomonotone equilibrium and proved the weak convergence theorem under some suitable conditions in Hilbert spaces. We then applied to solve data classification by extreme learning machine using the dataset comprised of the technology-integrated competency of 954 pre-service mathematics teachers in a university in northern Thailand, longitudinally collected for five years. The flexibility of our algorithm was shown by comparisons of the choice of different parameters. The performance was calculated and compared with the existing algorithms to be implemented for prediction. The results show that the proposed method achieved a classification accuracy of 81.06%. The predictions were implemented using ten attributes, including demographic information, skills, and knowledge relating to technology developed throughout the teacher education program. Such data driven studies are significant for establishing a prospective teacher competency analysis framework in teacher education and contributing to decision-making for policy design. 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

In this study, prospective teachers engaged in professional noticing of their students’ mathematical thinking captured in pieces of written work. Researchers then worked to characterize the prospective teachers’ professional noticing using a lens of responsive teaching. Results indicate that prospective teacher decisions about how to respond to their students’ mathematical thinking fall on a responsiveness continuum, often shifting in responsiveness across pieces of student written work. The findings of this study provide guidance for teacher educators who work to develop K–12 educators’ responsive teaching practices. Full article