In-service Mathematics Teachers Research Articles

STEAM practices connecting mathematics, arts, architecture, culture and history in a non-formal learning environment of a museum

This study adopts STEAM practices integrating architecture, arts, culture, and history into mathematics education in a museum learning environment. A workshop was conducted with five in-service mathematics teachers in an Egyptian museum, utilizing digital technologies such as GeoGebra, Augmented Reality, and 3D Printing to model, visualize and connect the museum collections to their teaching practices. Teachers’ modelled artefacts were qualitatively analysed for their artistic, cultural and historical connections. Findings indicate that participants followed the design expected outcomes of these STEAM practices by implementing a transdisciplinary approach towards mathematically modelling the museum objects while connecting to their mathematical, cultural, historical, and artistic relations. Participants’ reflections showed positive changes in their attitudes towards considering the museum learning environment for mathematics teaching during the implementation of these STEAM practices. Furthermore, such STEAM practices allowed participants to explore and connect disciplines through interacting with museum collections from artistic, cultural, historical, mathematical, and technological perspectives.

Where experience makes a difference: teachers' judgment accuracy and diagnostic reasoning regarding student learning characteristics.

The concept of teacher professional vision suggests that experienced teachers, compared to novice teachers, might be better at making accurate judgments of students' learning characteristics, which can be explained by their advanced reasoning in diagnostic situations. This study examines experienced and novice teachers' diagnoses of different student characteristic profiles: three inconsistent profiles (overestimating, uninterested, and underestimating) and two consistent profiles (strong and struggling). We examined both experienced (n = 19 in-service mathematics teachers) and novice teachers (n = 24 pre-service mathematics teachers) to determine the extent of differences in their judgment accuracy and their diagnostic reasoning about observable cues when diagnosing student profiles while watching a lesson video. ANOVA results indicate that experienced teachers generally achieved a higher judgment accuracy in diagnosing student profiles compared to novice teachers. Moreover, epistemic network analysis of observable cues in experienced and novice teachers' diagnostic reasoning showed that, compared to novice teachers, experienced teachers make more relations between a broader spectrum of both surface cues (e.g., a student's hand-raising behavior) and deep cues (e.g., a student being interested in the subject). Experienced teachers thereby construct more comprehensive and robust reasoning compared to novice teachers. The findings highlight how professional experience shapes teachers' professional skills, such as diagnosing, and suggest strategies for enhancing teacher training.

Evolution of teachers’ and researchers’ praxeologies for designing inquiry mathematics tasks: the role of teachers’ beliefs

AbstractThis paper is focused on the collaborative work of two communities, one of teachers and one of researchers, during a teacher professional development program on the inquiry-based learning approach in mathematics, addressed to lower secondary school in-service mathematics teachers. We conceptualize the design of inquiry mathematics task as the boundary object on which the two communities work collaboratively. We aim to study the evolution of teachers’ and researchers’ meta-didactical praxeologies for designing inquiry mathematics tasks, with the Meta-Didactical Transposition framework, to understand if and how their collaboration favors their convergence toward shared components of final meta-didactical praxeologies. In the results, we show that this convergence is reached thanks to internalization processes of praxeological components for designing inquiry mathematics tasks, as a consequence of the learning mechanisms activated by the common work on the boundary object. In this paper, we address also the issue of understanding the complex relationship between teachers’ beliefs on inquiry mathematics tasks and the meta-didactical praxeologies of teachers and researchers. As a result, we propose a model in which the evolution of teachers’ beliefs is taken into account both as an agent and a consequence of the evolution of the meta-didactical praxeologies of the two communities involved in the teacher professional development program.

Teaching Euclidean geometry with GeoGebra: Perceptions for in-service mathematics teachers

The teaching of Euclidean geometry is characterized by ineffective instructional methods used by in-service teachers as well as the low proficiency levels by learners. The purpose of this study was to survey in-service mathematics teachers’ GeoGebra integrative skills in the teaching of geometry. This study was quantitative and pre- and post-questionnaires were used to collect data. Descriptive and inferential statistics were used to perform statistical analysis of quantitative data. 12 schools were randomly selected, and purposive sampling was employed to select 29 in-service mathematics teachers. The study revealed that the intervention impacted positively on in-service teachers instructional strategies with a high statistical significance and a gain of medium to large effect size on both the pre- and post-intervention. After the training, participants felt that integrating GeoGebra in geometry teaching affords mathematics teachers the opportunity to use learner-centered approaches, teach geometry with confidence and maintain learners’ attention and alertness in class.

Tareas matemáticas escolares diseñadas por docentes de educación secundaria: un análisis desde la visión funcional de las matemáticas

Background: After mathematics curricular reform in 2012 in Costa Rica, which accentuate the functional vision of mathematics, it is worth inquiring if teachers designed tasks respond to established curricular guidelines and what mathematical and didactic characteristics that these tasks exhibit. Objectives: The aim of the study was to describe and analyze the mathematical and didactic elements, linked to the curricular proposal for Secondary Education in Costa Rica, used by in-service mathematics teachers for designing or selecting school tasks oriented to the development of mathematics skills on the subject of functions. Design: It corresponds to a descriptive-qualitative research, based on an intrinsic study of cases. Setting and Participants: Participants were five mathematics teachers from different educational institutions in Costa Rica during the year 2022 were studied, all teachers participated in a training program to promote teacher reflection competence regarding the design and analysis of school mathematics. Data collection and analysis: Data was collected from school mathematical tasks designed by the participants. The analysis of the information was carried out by defining categories and units of analysis based on the curricular provisions established for the teaching and learning of mathematics in Costa Rica, and the components of didactic analysis, as a methodology for the design of school mathematics tasks. Results: The analyzed tasks exhibit strengths in the curricular component, as well as in the didactic component. However, they lack elements that allow understanding how and when to put the designed tasks into practice, among other aspects. Conclusions: The training of in-service teachers takes a significant enhancement to strengthen knowledge and capacities oriented to the design, selection, and analysis of school mathematics tasks, associated with the functional vision of mathematics that articulates the curricular plan regarding student learning in Secondary Education in Costa Rica.

Mediating Role of Mathematics Teaching Efficacy on the Relationship Between Pedagogical Content Knowledge and Mathematics Teaching Anxiety

Effective education requires teaching efficacy, teaching anxiety, and teaching knowledge, all of which are essential elements. In-service mathematics teachers in the province of Quezon participated in this study to examine the role of mathematics teaching efficacy (MTE) as a mediator in the link between pedagogical content knowledge (PCK) and mathematics teaching anxiety (MTA). 200 in-service mathematics teachers from the Division of Quezon participated in the study by completing a set of questionnaires that included the MTE Scale, MTA Scale, and PCK Scale. The study utilized a quantitative descriptive research design and a mediation analysis. As the main objectives of the study were identified through the problem statement, the researcher decided to adopt the research design as a tool that carried out the study and served as the blueprint to guide the study accordingly. The PROCESS macro was used to conduct mediation analysis to test the theoretical hypothesis. It was found that MTE performs a competitive complete moderating function in the association between PCK and MTA for in-service teachers. The statistics show that high PCK improves in-service teachers’ MTE while decreasing their MTA. Even though PCK predicts MTE, which predicts MTA in turn, further longitudinal and experimental investigations are required to fully comprehend this progression. MTE thus acts as a mediator in the connection between the PCK and MTA. Keywords: mathematics teaching anxiety, mathematics teaching efficacy, pedagogical content knowledge, mediation analysis via the process macro

Onto-semiotic analysis of one teacher’s and university students’ mathematical connections when problem-solving about launching a projectile

An onto-semiotic analysis of the mathematical connections established by one in-service mathematics teachers and university students when solving a problem about launching a projectile using the derivative was carried out. Theoretically, this research was based on the articulation between the Extended Theory of Mathematical Connections and the Onto-semiotic Approach. The methodology was qualitative-descriptive where data was collected through interviews based on a task. Subsequently, following the joint analysis method of both theories, the mathematical activity of the participants when they solved the task was analyzed. The results show that, teacher and students established a system of connections of feature type, different representations, meanings, part-whole, procedural and implications in terms of practices, processes, objects, and semiotic functions that relate them. However, some students presented difficulties caused by some incorrect mathematical connection such as stating that the maximum height of the projectile is the time obtained with the critical number, errors in performing arithmetic calculations when evaluating the function, graphically representing the quadratic function as a straight line and use the general formula in an inappropriate way that prevents the procedural connection from being made.

The effect of conceptual understanding principles-based training program on enhancement of pedagogical knowledge of mathematics teachers

The study aimed to investigate the effect of a training program based on the principles of conceptual understanding in enhancing the pedagogical knowledge of mathematics teachers. The study sample consisted of 34 male and female in-service mathematics teachers, who teach the middle grades (5-8). To achieve the objectives of the study, a quasi-experimental approach was used, with a pre-post design for two groups. In order to collect data, a pedagogical knowledge test was used for the content of numbers and algebra contained in the middle grades curriculum. The results showed a significant effect of the training program in enhancing the pedagogical knowledge of mathematics teachers, with two dimensions (knowledge of teaching mathematics: approaches and strategies, knowledge of students’ thinking). The results also showed an improvement in performance levels on the test in general among the teachers of the experimental group, as the percentage of teachers in the level of skilled performance increased from 0% on the pre-test to 53% on the post-test. In light of the results, the study recommended to conduct more research through employing more principles of conceptual understanding to enhance pedagogical knowledge among broader samples of mathematics teachers and different mathematics content.

How does teachers' noticing of students' fixed mindsets relate to teachers’ knowledge, beliefs, and experience? An exploratory study

Students' belief that abilities are unchangeable (fixed mindset) can hamper learning. Teachers should thus be able to recognize such problematic beliefs. We explored whether teachers' skills to notice students' fixed mindset were related to teachers' knowledge about learners' beliefs, teachers' mindset, and their experience. Our sample included pre-service and in-service mathematics teachers (N = 112). Noticing (i.e., attending and interpreting) was measured with text scenarios. Results indicate that knowledge supported noticing, especially interpreting, whereas teachers’ growth mindset was unrelated to noticing. Experience was associated with less declarative knowledge and, in turn, with less noticing.

Exploring mathematical connections in the context of proof and mathematical argumentation: A new proposal of networking of theories

Extended theory of mathematical connections (ETC) and theory of mathematical argumentation (TMA) based on Toulmin’s (1984) model were articulated for the study of mathematical connections activated in the argumentation process. For this purpose, a “networking of theories” was made to obtain the complementarities between both theories. Then, a class episode was selected that dealt with the demonstration of the continuity theorem of functions of real variable “<i>if a function is derivable at a point then it is continuous at that point</i>”, made by an in-service mathematics teacher of differential calculus, who participated in a non-participant observation, where his classes were videotaped. The arguments of this episode were analyzed through with Toulmin’s (1984) model, after with thematic analysis method to identify mathematical connections, and, finally, the connections in the proof and mathematical argumentation were analyzed. The main result of the research reveals that the mathematical connections play a fundamental role in the argumentation process of the episode, given that, connection is important for the establishment and identification the argument and the warrant that supports it. In addition, complementarities were found between both theories, which makes this networking a useful tool for a better analysis of mathematical argumentation processes.

In-service teachers mathematics conceptions through the lens of ethnomathematics

The ethnomathematical perspective brings to light epistemological issues about teachers' conceptions of Mathematics. This study explores teachers' Mathematics conceptions and the evidence in their instruction framed using an ethnomathematical lens that highlights three dimensions: a practical approach that attends to the development of relations of Mathematics to reality, a social approach that proposes a view of Mathematics as a system of meanings of quantity, relationship, and space by a certain group of people, and a cultural approach that focuses on reflections from cultural groups that represent many different perspecAtives on Mathematics. Many researchers and educators recognize the significant influence of these approaches in interpreting and implementing Mathematics curricula. It influences how teachers' conceptions of mathematics affect their approach to teaching and learning mathematics. The survey adapted from Albanese and Perales and Andrews and Hatch reveals that the three approaches were given importance by the in-service Mathematics teachers of a teacher education institution in determining and developing their conceptions of Mathematics. The findings showed that the in-service teachers' conceptions of mathematics were visible from an ethnomathematical perspective. The practical approach in their instruction was highly evident but was the least important for the in-service teachers. Future research on how these conceptions play a part in the teaching-learning process is recommended. Conducting workshops and training for teachers on including an ethnomathematics approach in their instruction will help them more effectively design a lesson and reflect on the learning environment they would create in their classrooms.

Mathematics student personas for the design of technology-enhanced learning environments

To benefit from the quickly expanding range of new possibilities of technology-enhanced education, school systems, schools, and teachers need to adapt quickly. Conversely, the needs of students and teachers in a technology-enhanced classroom require technology developers to provide and improve suitable technologies. In this paper, we aim to show how to make the professional knowledge of mathematics teachers accessible to developers of technologies and also to teacher trainers and trainees by the use of student personas, i.e., portraits of archetypical students with particular characteristics and needs. We have collected qualitative data from pre-service and in-service mathematics teachers in Austrian academic upper secondary schools about the characteristics and needs of their students. We have analysed these data using a grounded theory approach to derive demands of students on technology-enhanced learning environments (TELEs). We have identified and presented five personas, each with specific demands on TELEs, to represent this target group. By introducing this approach that combines techniques from mathematics education research and from user experience research, we are able to represent user groups of a mathematics technology-enhanced learning environment in a more relatable way than was previously possible. These relatable representations of students in Austrian academic upper secondary schools could be of particular importance for developers of technology-enhanced learning environments for teaching and learning mathematics. The methodology presented in this paper is adaptable to other contexts.

Developing in-service mathematics teachers’ pedagogical content knowledge and skills to teach trigonometry: Using cooperative teaching and learning approach

The study is aimed at enhancing pedagogical content knowledge (PCK) and skills of in-service mathematics teachers (IMTs) using cooperative teaching and learning approach (CTLA). A sequential multiple case study was employed to develop eight IMTs knowledge and skills to design, develop, and enact lessons in trigonometry. The lessons were anchored on CTLA in two phases of a professional development arrangement (PDA) initiated in the study. The analysis of classroom observation, interview, CTLA lessons and the independent sample t-test is suggestive of significant improvement in the IMTs PCK. Further, although, the IMTs were rooted in teacher-centered pedagogies and encountered challenges, they effectively incorporated CTLA as a pedagogical tool in the teaching and learning of trigonometry. As a result of which, IMTs exhibited an enhanced content knowledge. Implications and recommendations for effective PDA in incorporating CTLA as an innovative pedagogical strategy for the teaching of mathematics at high school are discussed.

The specialized knowledge of middle school teachers concerning the concept of function

This study presents research focusing on in-service mathematics teachers and their approach to tasks aimed at developing of functional thinking. The analysis is based on the model of The Mathematics Teachers' Specialised Knowledge -- model MTSK by Carrillo et al. (2018). The research question is the following: What ``specialised knowledge'', in the sense of the MTSK framework, is revealed when a~middle school teachers solve and discuss the selected tasks? The research was conducted with 9 teachers, who voluntarily participated in the professional development. The teachers solved a~set of 30 tasks that were selected with a~focus on 4 aspects of the concept of function, different representations and transitions between them and different actions that learners engage in the task solving. In this study, we analysed the teachers' written solutions and the discussion with the teachers about a~particular task. Reflecting on their work as learners was very important in moving from dealing with the mathematics itself to shifting to developing their knowledge of mathematics teaching (KMT) and knowledge of features of learning mathematics (KFLM) in terms of the MTSK framework. The results helped us to identify gaps in teachers' specialised knowledge and consequently will help us to improve professional development courses for both in-service and pre-service teachers.

Didactic-Mathematical Knowledge and Teacher Education: An Investigation with Pre-Service and In-Service Mathematics Teachers

Background: The mathematical and didactic knowledge in mathematics teachers’ domain should constitute a permanent focus of investigations and reflections. Objective: To investigate the development of knowledge and procedures concerning geometry teaching among pre-service and in-service mathematics teachers engaged in the final years of elementary school. Design: The investigation is inserted in a qualitative perspective and follows the assumptions of action research. Setting and Participants: Fifty-four pre-service and in-service mathematics teachers from the Brazilian city of Paulo Afonso, Bahia, participated in a teacher education process. Data Collection and Analysis: Participant observation, data collection and analysis following an analysis protocol guided by the constructs of the onto-semiotic approach; analysis of productions. Results: Development and application of 24 sequences of activities focusing on the study of geometry. High epistemic adequacy was observed based on the application of the analysis protocol concerning structuring sequences of activities. Regarding the other dimensions, concerning the analysis of the application of the activities (cognitive-affective, interactional-mediational, ecological), high adequacy was observed. Conclusions: It is relevant to invest in teacher education courses proposing the expansion of didactic-mathematical knowledge to enhance the use of different ways to teach and learn mathematics.

Mathematical Maturity of In-Service Junior High School Mathematics Teachers in Imus City, Cavite, Philippines

This study determined the in-service junior high school mathematics teachers’ level of mathematical maturity in terms of expertise in knowledge of the subject matter. Validated questionnaires, interviews, and statistical tools were used to address the objectives. The results revealed that the respondents were found to have outstanding performance in Trigonometry, very satisfactory performance in Basic Math and Algebra, satisfactory performance in Geometry, and did not meet the expectation in Statistics. In addition, the teacher respondents have high confidence level in the use of general computer processes and telecommunications and average level of confidence in the use of other technologies in teaching and learning. In addition, a high confidence level in the use of general computer processes and telecommunications and an average level of confidence in the use of other technologies in teaching and learning were shown by the respondents. Given these findings, it is recommended that in-service mathematics teachers should have intensive trainings and seminars on Mathematics to improve their knowledge in the subject, and a special training on the use of Information and Communication Technology (ICT) to maximize its use in teaching and learning.

Instruments and schemes of in-service mathematics teachers during the design of teaching based on questioning

Instruments and schemes of in-service mathematics teachers during the design of teaching based on questioning

Formative Assessment and Mathematics Education: the Perspective of In-Service Mathematics Teachers

Background: Although there is consensus on the favourable impact of formative assessment (FA) on learning, it is unclear to what extent general FA strategies are directly applicable to the specific field of mathematics education. Objective: Study the relevance of a questionnaire which describes 26 FA practices supported by Wiliam’s model in the particular context of mathematics education. Design: Mixed, the frequency and feasibility are consulted through a questionnaire and in-depth interviews. Participants : Thirty in-service mathematics teachers answered the survey and of ten invited, three agreed to be interviewed. Data analysis : We carried out a descriptive analysis for quantitative data and qualitative thematic analysis. Results : The strategies of collecting evidence, feedback, collaboration, and self-regulated involvement in learning are viable and frequent in mathematics education, however, the strategy of clarifying and sharing goals requires adaptation to the context. In addition, nine novel FA practices are described. The implementation of formative assessment creates tensions with the summative function, it is laborious to implement and consequently takes time outside the classroom. Conclusion : We identified that FA practices are frequent and feasible to implement. Clarifying and sharing goals requires the adequacy of the mathematical context.

Examining the pedagogical content knowledge of in-service mathematics teachers on the permutations and combinations in the context of student mistakes

Permutations and combinations are generally taught by requiring students to memorize formulas and solve problems using the appropriate formula. Students who learn these topics may succeed in gaining high scores on end-of-chapter exams in textbooks, while lacking the conceptual understanding required to deal with problems in the real world. Therefore, this study aimed to examine in-service mathematics teachers' pedagogical content knowledge (PCK) to determine students’ mistakes in solving permutations and combinations problem and their teaching strategies to eliminate these errors. Data were collected by distributing vignettes, CoRe, and PaP-eRs to thirteen mathematics teachers from ten provinces in Indonesia after they finished an online professional teacher education program to determine their PCK in teaching permutations and combinations. The data collected were analyzed qualitatively using a content analysis approach to obtain categories inductively. The result showed that PCK of in-service mathematics in teaching permutations and combinations was observed by identifying student mistakes conceptually and procedurally, even though some could not determine their mistakes in permutations. On the other hand, the knowledge of instructional strategies can engage all students in active learning, but most of them only give general answers. Furthermore, an in-depth understanding of permutations and combinations topic is needed to support the development of teachers’ pedagogic competencies sustainably. The contribution of this research will be of interest to curriculum development and mathematics educators.

Preservice mathematics teachers' perceptions of mathematical problem solving and its teaching: A case from China.

Preservice mathematics teachers' accurate understanding of mathematical problem solving and its teaching is key to the performance of their professional quality. This study aims to investigate preservice mathematics teachers' understanding of problem solving and its teaching and compares it with the understanding of in-service mathematics teachers. After surveying 326 in-service mathematics teachers, this study constructs a reliable and valid tool for the cognition of mathematical problem solving and its teaching and conducts a questionnaire survey on 26 preservice mathematics teachers. Survey results reveal that preservice mathematics teachers have a good understanding of mathematical problem solving and its teaching and are more confident in the transfer value of problem solving ability. By contrast, in-service teachers are more optimistic that problem solving requires exploration, continuous thinking, and the participation of metacognition. This article concludes that preservice mathematics teachers should focus more on the initiative and creativity of students and put students at the center of education. In addition, teacher educators should provide more teaching practice opportunities for preservice teachers. The findings also show that in-service teachers' understanding of problem solving and its teaching is inferior to that of preservice teachers on some indicators, implying the importance of post-service training for in-service teachers.