In-service Mathematics Teachers Research Articles

Design, Implementation and Assessment of a Web-Based Ethnomathematics Instructional Content Repository for Mathematics Teachers in Benue State, Nigeria

This study developed and assessed a web-based ethnomathematics instructional content repository for pre-service and in-service mathematics teachers in Benue State, Nigeria. The study adopted a developmental research design to systematically build and evaluate the educational intervention as a solution to complex problems in mathematics education practice. The development was achieved using WordPress Version 5.4, hosted online at https://villagemath.net on Linux OS server running with cPanel v80.p (Build 20), Apache Version 2.4.39, PHP Version 5.6.40 and MySQL Version 5.7.26. The study was guided by seven research questions posed around common web metrics, key performance indices, and quality assessment in terms of content, navigation, structure, appearance and uniqueness of the designed web tool. Five hypotheses were formulated and tested at 0.05 level of significance using t-test. The sample for the study comprises 341 pre-service and in-service mathematics teachers drawn from a population of 2981 using purposive sampling. The main instrument of the study is the researcher-developed Web-based Ethnomathematics Instructional Content Repository Assessment Questionnaire – WEICRAQ (Cronbach Alpha Coefficient = 0.98, indicating a high level of internal consistency of the instrument). Additional data collection was handled using WP Statistics, Pingdom Tools, Google PageSpeed Insights, GTmetrix and WebPage Test. The research questions were answered using charts, graphs, mean and standard deviation. Analysis of the results of the study yielded a positive pattern of common web metrics for the designed web tool, indicating that the platform appeals to a wide range of users, with key performance indicators such as speed index, page size, and last painted hero affirming that the platform is robust, elegantly designed and fast. The results also showed that pre-service and in-service mathematics teachers in Benue State, Nigeria unanimously rated the Web-based Ethnomathematics Instructional Content Repository high in terms of content, navigation, structure, appearance and uniqueness. The outcomes of this study has demonstrated that culture can indeed become an integral part of every aspect of instructional design, making it important to consider social and cultural peculiarities in planning and delivering mathematics instruction. The Web-based Ethnomathematics Instructional Content Repository has humanized Mathematics for users and provided a reservoir of resources for training students in conceptual understanding, procedural fluency, strategic competence, adaptive reasoning and productive disposition. Based on the findings of the study, it was recommended that Mathematics teachers should continue to use the Web-based Ethnomathematics Instructional Content Repository as a worthy companion tailored to their specific professional needs, and that students across all levels of education should seek deeper and more enriched learning experience by continuously leveraging on instructional resources available on the web tool to enhance their individualized learning, enrich their cultural rediscovery, and add aesthetic value to their learning of Mathematics as a school subject. It was also recommended that Mathematics educators in colleges of education and universities should deploy the instructional environment as a veritable tool for re-directing narratives across the field of Mathematics Education, and that Non-governmental organizations (NGOs) and government agencies in the educational and cultural sectors should make use of the ethnomathematics platform to drive their initiatives in grassroots development.

Zimbabwean in-service teachers' views of geometry: an ethnomathematics perspective

This study reports on in-service mathematics teachers’ views of geometry in the context of ethnomathematics. A convergent parallel mixed method design which includes both quantitative and qualitative methods was used to provide a deeper understanding of how the participants view geometry from an ethnomathematics perspective. Questionnaires and focus group discussions were used to gather data from 40 in-service mathematics teachers. The teachers’ views of geometry were classified under the cultural, social and practical dimensions of ethnomathematics. The views held by the teachers influence the way they teach geometry. The study suggested that knowledge construction and conceptual understanding in geometry are essential for its application in everyday life.

Specialised Knowledge Network Activated in Teacher Education to Answer to a Mathematical Why on Fraction Division

Background: One way to deal with the complexity inherent in teaching is to advance in understanding the relationships between the different types of knowledge used in teaching practice. Objective: To characterise specialised teaching knowledge and its connections established in a formative context of elaborating an answer to students on why to invert-and-multiply to divide fractions. Design: Qualitative analytical-descriptive study, associating the mathematics teachers’ specialised knowledge (MTSK) and a teacher education course anchored in a teaching practice situation. Setting and participants: A teacher education workshop for in-service and preservice mathematics teachers, from which we carried out an in-depth analysis of the data collected from two participants (a preservice teacher and a teacher). Data collection and analysis: We obtained data during the workshop and an interview with the subjects and used content analysis, the MTSK analysis instrument, the MTSK cluster and the MTSK network diagram enabled to describe the connections between types of knowledge. Results: The activated network contains knowledge from all MTSK subdomains, exercising different levels of importance and roles (from the action itself to its support). The route of construction of the answer started from a mathematical layer towards didactic elements, reflecting the level of development (including gaps) of the subjects on justifications of algorithms and didactic aspects. Conclusion: A seemingly simple teaching action (answering a student question) mobilised all the MTSK subdomains and activated an intricate procurement network, requiring specialised, reasoned, and intentional teaching preparation.

Mathematics Teachers’ Inclusion of Modelling and Problem Posing in Their Mathematics Lessons: An Exploratory Questionnaire

In this paper the results of a questionnaire about mathematics teachers’ inclusion in their teaching of mathematical modelling and problem posing are presented. To make teachers able to choose a coherent teaching method for a mathematical topic, teachers’ knowledge of valuable methods for the teaching of mathematics should be fostered. In this sense, studying teachers’ practice of modelling and problem posing is crucial in order to know if and which kind of support and professional development they need on such educational strategies. The questionnaire was administrated to Italian in-service mathematics teachers of primary and secondary school. Findings indicate that despite teachers implement regularly some aspects of mathematical modelling in their lessons, they ask more materials to support their preparation and practice. Problem posing, instead, might be more integrated in the classroom work, and consequently in teachers’ professional development courses.

An Investigation of Indonesian In-Service Mathematics Teachers’ Perception and Attitude Toward STEAM Education

To face the global challenge, people need to master mathematics comprehensively which one of the ways is to integrate it with other fields such as science, technology, engineering and arts. Therefore, the implementation of STEAM Education approach is considered to be essential for in-service mathematics teachers especially in Indonesia. This study aimed to investigate the perceptions and attitudes of Indonesian in-service mathematics teachers towards the application of STEAM-based education in the teaching mathematics. Cross-sectional survey was used in this study engaging 110 respondents along the survey. The result was that STEAM Education is nor well-known by the majority of the respondents. For the perception, those who knew STEAM Education mostly believed that each topic of this approach was connected to each other, otherwise for those who did not know STEAM Education mostly said that each topic was stand alone. As for the attitude of respondents also divided into two, the first group of respondents stated that STEAM Education will be increasingly popular in the future and they will feel happy if teaching mathematics with STEAM Education. Whereas the second group of respondents looked more pessimistically related to projections of future application of STEAM Education that would be less popular, not to mention that they would feel unexcited to teach mathematics with the STEAM Education approach.

Repeating Decimals and Irrational Numbers on the Number Line: Through the Lens of Pre-Service and In-Service Mathematics Teachers

Abstract: The purpose of the study is to examine how pre-service and in-service mathematics teachers locate repeating decimals and irrational numbers on the number line. The participants of the study included 274 pre-service and 106 in-service mathematics teachers. Data were collected through a written questionnaire including four open-ended questions. In the questionnaire, preservice and in-service teachers were asked to determine whether the given numbers 0.444…,√2, 𝜋 and e can be located on the number line, they cannot be located on the number line or they do not have exact places on the number line. Additionally, they were asked to justify their responses to each of the questions in the questionnaire. Open coding was performed while analysing data. Findings indicated that while majority of the participants stated that given repeating decimal, i.e. 0.444…, can be located on the number line, for the given irrational numbers, i.e. √2, 𝜋 and e, only small number of participants considered that they can be located on the number line. The main sources of the consideration that the given numbers do not have an exact place or they cannot be located on the number line were identified as approximation, infinity, irrationality and uncertainty in the justifications.

Prospective and In-Service Mathematics Teachers’ Attention to a Rich Mathematics Task While Planning its Implementation in the Classroom

This study explores secondary mathematics teachers’ attention to the three components of Jaworski’s (1992) “teaching triad” (i.e., mathematical challenge, learning management, and sensitivity to students) as they planned a lesson revolving around a rich mathematics problem and assessed pre-designed student solutions for that problem. Written work was gathered from 17 cohorts. Qualitative analysis generated categories. Quantitative analysis revealed that some components of the teaching triad were attended to in both activities, some were not attended to in either activity, and some were attended to in one activity but not in the other. Findings are interpreted in light of theory.

Exploring In-Service Mathematics Teachers’ Perceived Professional Development Needs Related to the Strands of Mathematical Proficiency (SMP)

The National Research Council developed the concept of mathematical proficiency as being described by five strands: conceptual understanding, procedural fluency, strategic competency, adaptive reasoning, and productive disposition. The purpose of this study is to explore in-service mathematics teachers’ perceptions of professional development needs related to the five strands of mathematical proficiency and to investigate the effect of teachers’ demographic factors on their perceived needs. Participants included 342 teachers with varying qualifications and years of experience teaching at multiple grade levels (elementary, preparatory, and secondary) in Qatar’s government schools. The study uses a 35-item questionnaire to evaluate teachers’ professional development needs within the five strands.

Teachers’ Beliefs about Mathematics, Learning, Teaching, Students, and Teachers: Perspectives from Chinese High School In-Service Mathematics Teachers

This study serves two purposes. The first purpose is the development and validation of a Mathematics Teachers’ Beliefs Scale (MTBS). In addition to providing a valid and reliable MTBS instrument, this study provides information on the process of developing and validating the instrument, which shall be useful for the development and validation of similar instruments. The second purpose of this study is to explore the relationship between teachers’ beliefs and their teaching experience. Using a validated MTBS, this study assessed the beliefs of four groups of Chinese high school mathematics teachers with varying years of professional teaching experience: 1–5 years (n = 25), 6–10 years (n = 70), 11–20 years (n = 48), and 21+ years (n = 28). The MTBS is composed of 26 items distributed across five subscales spanning beliefs about mathematics, learning, teaching, students, and teachers. Among the four groups, the results of this study indicate that there were no significant differences in scores on beliefs about mathematics, mathematics learning, mathematics teaching, students, and teachers. Further item analysis revealed that longer teaching experience does not necessarily mean that a teacher holds reform-oriented views. However, teachers with 6–10 years of experience were most likely to hold a more dialectic view of mathematics.

In-service Secondary Teachers' Teaching Approaches and Views Towards Integrating Ethnomathematics Approaches into Geometry Teaching

Abstract Geometry teaching and learning ought to mirror and embrace the social diversity found in the geometry learning environment as well as the increasingly connected world. For that reason, ethnomathematics approaches that relate geometry teaching and learning to the learners' cultural experiences and background should be used when teaching geometry. The aim of this study was to find out the teachers' teaching approaches in geometry as well as their views towards the incorporation of ethnomathematics into the geometry teaching. A convergent mixed methods design was used in this study. Focus group discussions and questionnaires were used as data gathering instruments. The sample comprised of 40 in-service mathematics teachers. Findings show that both teacher-centered and learner-centered approaches were used in geometry teaching and learning. The study also revealed that teachers had the opinion that ethnomathematics approaches should be integrated into geometry teaching. The study recommends that teachers should be trained to use ethnomathematics approaches when teaching geometry.

Minding the nouns and verbs: definitions that respect knowledge development

The definition of function varies from textbook to textbook at the introductory level. Though the definitions are often mathematically equivalent, there are linguistic features that may make some definitions more accessible to beginning learners. In particular, students who see functions as actions or processes rather than objects may be better served by definitions which facilitate the use of meaningful verbs. This study examines the impact of definition choice on the mathematics work of graduate students, all of whom were mathematics majors and pre- or in-service mathematics teachers. Their work with three definitions of function is interpreted within the commognitive framework and frames a discussion of features of mathematical definitions that may help learners.

Mathematics Teachers Understanding of the Concept of Radian

Trigonometry is among the mathematics subjects that students have difficulty in understanding due to the lack of proper understanding of the basic concepts. Research on radian, a concept that is among the fundamental concepts of trigonometry, has revealed that teachers, pre-service teachers and students lack, in some regards, proper conceptual knowledge about the subject term. Accordingly, studies on the issue bear particular importance. In the relevant literature, studies on the concept of radian focus mainly on students and pre-service teachers. However, there are not any national and contemporary studies that are conducted with teachers. In view of these, the current study aims to analyze mathematics teachers’ ways of understanding of the concept of radian. In this regard, the study attempts to explore the reasons behind teachers’ lack of conceptual knowledge regarding the concept of radian and to propose solutions that would help eliminate these reasons. The study employs case study method. The sample group consists of 41 in-service mathematics teachers who work in different types of schools. General Information Form and Concept Test developed by the researchers of the study as well as unstructured face-to-face interviews were utilized as data collection tools. As a consequence, majority of the participant teachers were found to lack an accurate and complete understanding of the concept of radian and to have some conceptual misunderstandings regarding the subject. In the conclusion section, findings of the study are discussed in relation to the relevant literature and some recommendations are made for teaching the concept of radian more efficiently.

Competence Measurement in (Mathematics) Teacher Education and Beyond: Implications for Policy

Teacher education and the professional development of teachers has become a prominent topic in recent policy discussions worldwide. However, many educational changes have been carried out without clear reference to the results of empirical studies evaluating the efficiency of teacher education programs. This paper aims to contribute to this discussion. It provides an overview on the current knowledge derived from empirical research on the structure of the professional competence of teachers and competence development during teacher education. First, a description of a theoretical framework for the professional competence of teachers and their impact of competence measurement with pre- and in-service mathematics teachers is given. Then, the competence development of teachers at the transition from teacher education into teaching practice and the relation to instructional quality and student learning gains is described. Finally, implications for policy are outlined, emphasizing the necessity of a sound knowledge base in teacher education, which has to be complemented by professional noticing accounting for situated facets of teacher competence. Due to the dynamic acquisition of teacher competence through practical learning opportunities in early career teaching, strong professional development measures are needed.

The Development of In-Service Mathematics Teachers' Integration of ICT in a Community of Practice: Teaching-in-Context Theory

The goal of the present research is to describe five lower-secondary in-service mathematics teachers' development of ICT (Information Communication Tech-nology) integration in their teaching as a result of mentoring pre-service teachers who practiced the integration of technology in their mathematics teaching. This is done through the combination of Schoenfeld's Teaching-in-Context theory and Goos' community of practice framework. To collect the research data, the re-searchers used semi-structured interviews with the in-service teachers at the be-ginning and end of the academic year. In addition, several observations of lessons taught by the in-service teachers with the assist of pre-service teachers were rec-orded towards the end of the intervention. The research findings indicate that the community of practice context can serve as an escalator that supports the decision of in-service mathematics teachers to integrate ICT in their mathematics teaching. However, these decisions were conditioned by taking care of the students' formal procedural mathematical knowledge.

Application of Logistic Differential Equation to Investigate The Extent of Emphasizing Stimulus Variation in Mathematics Instruction

The knowledge and skills in mathematics processes can be provided in an effective and systematic manner only by teaching mathematics in schools. Stimulus variation as a teaching skill is used to stimulate students’ interest and attract their attention to the lesson presentation. Therefore, this study investigated the extent of emphasizing stimulus variation in mathematics instruction using logistic differential equation. The study adopted a developmental survey design where a cross-section of in-service mathematics teachers in Imo State numbering 94 were continuously observed and surveyed to decipher their extent of emphasizing stimulus variation in the classroom to promote teaching excellence. The observations were carried out for 14 days and the data were generated based on direct observational technique (using observation schedule). The result revealed inadequate and inconsistent emphasis of stimulus variation teaching skill in mathematics instruction. This implies that pre-service mathematics teachers seldom emphasize stimulus variation when teaching mathematics. It was recommended that mathematics teachers should always employ the skill of stimulus variation in class during instructional delivery so as to enhance students’ learning experience and satisfaction thereby promoting teaching excellence. DOI: https://doi.org/10.31235/osf.io/rthj2

Mathematics Teachers Technological Content Knowledge (TCK) in using Dynamic Geometry Software

Technological content knowledge (TCK) is a framework that describes the knowledge required by teachers to represent material using technology. This paper reveals the knowledge of mathematics teachers in representing geometry material in software called GeoGebra. We analyzed the process of constructing geometrical objects in geometry problems by teachers who participated in a workshop on the use of GeoGebra in teaching mathematics. The approach used is a qualitative case study. 47 in-service mathematics teachers participated on training on the use of Geogebra in mathematics teaching. Researchers distributed questionnaires to 47 participants, and determined 7 subjects representing high, medium, and low questionnaires of Technological Pedagogical Content Knowledge (TPACK). Subject were given a task, to find out Technological Content Knowledge (TCK) of teachers in using geogebra, and observed them while they were doing the task. Observation was made when the process of constructing geometric objects into geogebra was taking place. Interviews were conducted to obtain more in-depth information that was not found by researchers in the observation process. Teachers’ knowledge in representing the geometry material in GeoGebra was reviewed based on how the knowledge supports the problem solving process. The results show that the knowledge can be divided into two groups: Constructive TCK and Obstructive TCK.

Pre-service versus in-service mathematics teachers’ opinions of mathematics reform in post-primary schools in Ireland

A new approach to the teaching and learning of mathematics has been introduced on a phased basis in post-primary education in Ireland. As part of the OECD PISA 2012, a survey was undertaken of in-service mathematics teachers in Ireland, with the aim of gathering data on the opinions of teachers about this reform. Here, a modified version of the survey was distributed to pre-service teachers immediately before and after a four-month teaching placement to ascertain if there were differences in the views expressed by pre-service and in-service teachers in relation to the teaching and learning of mathematics, and also if there were differences expressed by the pre-service teachers before and after their placement in post-primary schools. Analysis of the results showed considerable levels of agreement between all groups, with some exceptions in relation to confidence in teaching the reformed curriculum, emphasis on various teaching and learning activities, and usage of ICT in the classroom.

In-Service Mathematics Teachers’ Beliefs About Teaching, Learning and Nature of Mathematics and Their Mathematics Teaching Practices

The aim of this study is four fold: (a) to investigate the beliefs of elementary (grades 1-3) and middle school (4-6 grades) math teachers about teaching, learning and nature of mathematics; (b) to explore their teaching practices of mathematics; (c) to study the impact of their educational qualifications, years of experience, major on their beliefs toward teaching, learning and nature of mathematics, and; (d) to explore the relationship between their beliefs about teaching learning and nature of mathematics and their teaching practices. Data were collected using two questionnaires: the Math Teacher Beliefs Scale and the Mathematics Teaching Practices Scale. The study sample consisted of 101 teachers who teach in 11 private schools located in Amman, Jordan. The result of this study showed that teachers’ beliefs towards teaching and learning mathematics are more inclined towards being constructive or mixed in between. It was also concluded that the teaching practices lean towards constructivism. There were no significant differences attributed to years of experience, academic level, major, or at what stage they teach, whether it revolves around the their beliefs towards teaching and learning mathematics or towards teaching practices (from teachers’ perspective). The study results revealed a statistically significant correlation between what the teachers believe and what teaching practices they put into use.

In-Service Mathematics Teachers' Integration of ICT as Innovative Practice

The Professional Development School (PDS) can serve as a catalyst for the professional development of mathematics pre-service as well as in-service teachers. In the present research, we describe lower-secondary in-service mathematics teachers' development of ICT integration in their teaching. This is done through the Innovation Diffusion Model of Rogers, which consists of five stages: knowledge of an innovation, (2) forming an attitude toward the innovation, (3) taking a decision to adopt or reject, (4) implementation of the innovation, and (5) confirmation of the decision by affirming or rejecting it. In the present research, ICT integration in mathematics teaching is considered as an innovation candidate for adoption by mathematics in-service teachers, where this adoption is facilitated by a community of inquiry consisting of in-service teachers, pre-service teachers and researchers. Five in-service middle school mathematics teachers participated in the present research. We used two data collecting tools: observations and semi-structured interviews to collect data about different issues related to the integration of ICT in the lessons of the participating in-service teachers. The categories of the innovation diffusion model were used to analyze the participants' adoption of ICT for their teaching before and after our intervention through the implementation of the PDS model for the period of one academic year. The research findings indicate that the participating in-service mathematics teachers' attitudes and beliefs regarding the benefits of ICT for mathematics teaching were positive at the beginning of the experiment as well as at its end. At the same time, teachers' knowledge and experience of using ICT tools in mathematics teaching improved, which contributed positively to the confirmation of their decision to adopt these tools for their classrooms. Specifically, the research results indicate that the PDS can support the in-service mathematics teachers in their adoption of new innovations, specifically when this innovation is practiced by the pre-service teachers in the training school.

Argumentative Knowledge Construction in an Online Graduate Mathematics Course

The authors report on three students' argumentative knowledge construction in an asynchronous online graduate level geometry course designed for in-service secondary mathematics (ISM) teachers. Using Weinberger and Fischer's framework, they analyzed the ISM teachers' a) geometry autobiography and b) discussion board posts (both comments and attached work including solutions to assigned problems and Geometric Sketchpad explorations) throughout an 8-week summer course. The goal was to better understand the key similarities and differences in the nature of their interaction with each other and the course content that may have contributed to the differences in their knowledge construction. Findings led researchers to re-conceptualize a rubric to (1) assist instructors in facilitating productive interaction among students, (2) prepare students to better utilize the discussion board with a critical eye, and (3) provide specific guidelines for a more productive engagement among students, using the framework as a guide.