Mathematical Knowledge For Teaching Research Articles

Usage of Classroom Technology and the Technological Pedagogical Content Knowledge (TPACK) of Mathematics Teachers

Technological Pedagogical Content Knowledge (TPACK) is a theoretical framework in technology integration that is highly regarded in today's digital era. Using a descriptive research design, this study investigated 81 secondary mathematics teachers' use of available classroom technology and level of competence in the eight TPACK domains. The findings revealed that classroom technology was rarely employed. This was due to a combination of external and internal factors. While along the TPACK domains, the teachers obtained the highest level of competence in CK (M = 4.29, SD = .59) and lowest in TK (M = 3.69, SD = .70). One-way ANOVA uncovered that there was a highly significant difference in the level of competence along with TPACK domains. Furthermore, correlation and multiple regression analysis unveiled that the level of usage of classroom technology was discovered to be highly significant and served as the best predictor of TK (F(6, 74) = 6.17, p<.001), TPK (F(6, 74) = 6.39, p<.001), TCK (F(6, 74) = 4.30, p<.001), and TPACK (F(6, 74) = 2.65, p =.022). Implications of the findings and recommendations are discussed.

The relationship between prospective teachers’ mathematics knowledge for teaching and their ability to notice student thinking

The relationship between prospective teachers’ mathematics knowledge for teaching and their ability to notice student thinking

Contextualizing the Mathematical Knowledge for Teaching Framework for teachers of Emergent Bilinguals

We are amid a rapid demographic shift, with Emergent Bilinguals (EBs) being the fastest growing K-12 student population. This has created an ambitious goal for teacher education programs as they must prepare mathematics pre-service teachers (PSTs) to assess the needs of EBs. As a response, this study conducted a qualitative analysis of 16 PSTs to propose a contextualized version of the Mathematical Knowledge for Teaching (MKT) framework as an emerging knowledge base of teaching that can be used to further guide the planning and enactment of teacher education programs in the mathematics education of EBs, specifically.

Pedagogical Content Knowledge Analysis of Mathematics Teachers in Developing Lesson Plans on Ratio Topic

In preparing a Lesson Plan, a mathematics teacher should pay attention to pedagogical principles, including general and mathematical pedagogy. Teacher knowledge related to these two pedagogies is called Pedagogical Content Knowledge (PCK). This study aims to analyze the PCK of a mathematics teacher at a junior high school in Kebumen when preparing lesson plans and carrying out learning activities on Ratio Topics. This study used a qualitative research method with a case study design. The teacher’s PCK analyzed in this study was divided into two parts: general pedagogical knowledge and mathematical pedagogical knowledge. The results showed teachers' general pedagogical knowledge when learning was more complete than when compiling lesson plans. Likewise, in mathematical pedagogy, the teacher's mathematical pedagogy knowledge when carrying out education is better than when compiling lesson plans. This also indicates a mismatch between the lesson plans compiled by the teacher and the learning activities he carried out. Therefore, in compiling lesson plans, teachers are advised to pour all pedagogical content knowledge that they have so that the lesson plans are by the learning activities carried out by the teacher so that the entire learning process can be carried out more optimally.

What are primary teachers’ experiences of policy on shaping a context of sustainable mathematics professional development?

ABSTRACT The author explored the extent to which policy could be a source of sustainable professional development for elementary teachers’ mathematical knowledge for teaching. The study involved three policies in England: the National Numeracy Strategy and the Primary National Strategy, introduced in response to concerns regarding mathematics teaching and student attainment, and a new National Curriculum. Professional development was offered to support teachers in the processes of changing their practice. This article focuses on the responses of eight teachers who suggest that the National Numeracy Strategy and the Primary National Strategy were useful sources of mathematical knowledge for teaching. However, the 2013 National Curriculum, along with the teaching for mastery policy, show how the teachers’ professional development had been rooted in policy enactments and was temporal. The author discusses the need for sustainable professional development to facilitate teachers’ continuous enhancement of their mathematical knowledge for teaching within a changing policy landscape.

PENGETAHUAN TEKNOLOGI PEDAGOGI KANDUNGAN GURU MATEMATIK SEKOLAH MENENGAH

The purpose of this research was to identify the level of technological pedagogical content knowledge of secondary school mathematics teachers. This study also aimed to find out the differences in those variables from the aspect of gender and teaching experience. The questionnaire was administered to 248 mathematics teachers from 22 secondary schools in the West Coast Zone of Sabah, Malaysia. The results of the study showed that the technological pedagogical content knowledge of secondary school mathematics teachers was at high level (M=4.071, SD=0.540). The Welch t-test results showed that there was no significant difference in technological pedagogical content knowledge based on gender (p= .0560, p> .05). The one-way ANOVA analysis also showed that there was no difference in technological pedagogical content knowledge based on the teaching experience. The findings of this study are useful as a guide for stakeholders to plan relevant strategies and training for mathematics teachers in implementing teaching and learning. This study implicated that teachers regardless of gender and teaching experience, need to remain committed in planning and implementing their teaching based on the element found in the technological pedagogical content knowledge framework.

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.

Didactic-mathematical knowledge of future mathematics teachers in Ecuador when developing tasks based on ethnomathematical practices

Este trabajo pretende inferir características del conocimiento didáctico-matemático de futuros profesores de matemáticas al desarrollar tareas basadas en prácticas etnomatemáticas locales. Se identificaron las prácticas etnomatemáticas y los conocimientos matemáticos de estos futuros profesores, estudiantes de una universidad ecuatoriana y, posteriormente, se analizaron sus reflexiones con relación al llevar estas prácticas al aula de clases. Los resultados indican una contemplación positiva por parte de los futuros profesores en dos aspectos: primero, en conectar las prácticas etnomatemáticas con las actividades profesionales locales y segundo, en presentar fragilidades en las características del conocimiento tanto matemático como didáctico-matemático. Como camino a seguir, el artículo sugiere que estas percepciones deben incorporarse en la formación de los futuros profesores, además de los conocimientos didáctico-matemáticos y las perspectivas de las Etnomatemáticas.

Professed vis-à-vis Enacted Knowledge: Topic-Specific Pedagogical Content Knowledge of University Mathematics Teachers

This study aimed to determine and observe the topic-specific pedagogical content knowledge of university mathematics teachers before and during limit and continuity concept instruction, and compare the teachers’ perceptions of their teaching to what happened in their classrooms using the case study method. The study involved five university mathematics teachers who teach ‘Applied Mathematics I’ to pre-engineering students at Assosa University, Ethiopia. Classroom observation sessions and pre-lesson teacher interviews were used as data sources. The data were analyzed by identifying common themes in each of the knowledge components prior to and during the lesson, and then by comparing the two phases. The findings from the teacher cases provided detailed contextual information and revealed knowledge manifestations in their lesson design and actual teaching processes. The study’s findings revealed that teachers had a good understanding of topic-specific pedagogical content knowledge components prior to the lesson, but did not demonstrate most of these in their actual teaching of limit and continuity; their reported and enacted knowledge differed. According to this study, individual teachers varied in their implementation of what they had mentioned about various components of topic-specific pedagogical content knowledge. The study proposes that understanding teachers’ knowledge during the lesson design phase and actual teaching could help fill the gap as a means of professional development, and thereby, improve pre-engineering students’ mathematics learning.

Changes in Lesson Plans as Teachers Participate in a Professional Development on Statistical Literacy

Research on mathematics teacher knowledge has gained momentum recently; however, research on teacher planning is scarce, especially using lesson plans as the primary data source. This study examines how teachers' lesson plans change as they participate in a professional development, supporting them in implementing the Vietnamese reformed Curriculum 2018. Using a design-based research methodology, we developed a research-informed framework that assesses teachers' lesson plans for developing students' statistical literacy as emphasized in the mathematics Curriculum. Informed by research literature and data collected from teachers, the framework including seven criteria was shared and used by 61 teachers to reflect on the quality of their lessons. The analysis of 38 lesson plans shows all criteria have improved from pre- to post-lesson plans. The teachers included more explicit and comprehensive learning intentions in their post-lessons. Tasks in the post-lesson plans afforded more opportunities for students to develop statistical literacy, helped them engage in the statistical investigation using real data, and included multiple representations. Finally, the post-lesson plans tended to follow the constructivist teaching principles. Implications on ways to develop teachers' planning competence and suggestions for future studies are included.

The effect of learning opportunity factors and efficacy belief on mathematical knowledge in the teaching process

The present study investigates the influence of opportunities to learn (OTL) and mathematics teaching efficacy beliefs (MTEB) towards mathematical knowledge for teaching (MKT). Using a structured questionnaire together with paper and pencil test adapted from the literature reviewed, data were collected from 187 pre-service elementary teachers in Institute of Teacher Education Indonesia. Data were analyzed using Smart PLS 3.0. The result of the structural equation model indicated that both OTL-Practicum (β = 0.395, p < 0.001) and OTL-Program (β = 0.324, p < 0.001) were positively related to MKT. The second regression analysis was to examine the impact of mathematics teaching efficacy belief on the MKT. The results showed that mathematics teaching outcome expectancy belief (MTOEB) (β = 0.322, p < 0.001) was positively related to MKT, whereas personal mathematics teaching efficacy belief (β = 0.017, p > 0.1) was not related to MKT. Overall, the belief and OTL factors explain a total of 54% variance in MKT. Implications from these findings to the successful teacher's education program implementation in Indonesia were further elaborated

Determination of Technology Pedagogy Content Knowledge Levels of Preservice Mathematics Teachers through Activities

It is one of the important qualifications of teachers to know contemporary instructional technologies and to use them in their lessons. However, the studies have concluded that teachers' use of technological tools and equipment is inadequate and their level of using materials is generally not at a desirable level. In this context, the aim of this study is to determine the level of Technological Pedagogical content knowledge of preservice mathematics teachers in the context of technology-supported activities they prepared. The study was conducted with 13 preservice secondary school mathematics teachers studying at a state university. Preservice teachers were given a training lasting 8 weeks. After the training, they were asked to prepare technology-supported activities including concept cartoon (Powtoon, Canva), concept map (Bubbl.us, Luchidchart), interactive worksheet (Teachermade), gamification applications (Puzzlemaker, Wordwall, Matific, ClassDojo) and digital stories (Pixton, Powtoon, StoryboardThat, Storyjumper). The activities they prepared were analyzed by document analysis method with the Technological Pedagogical Content Knowledge [TPACK] rubric developed by Lyublinskaya and Tournaki (2012) and preservice teachers' TPACK levels were evaluated in terms of purpose knowledge, instructional knowledge, curriculum knowledge and strategy knowledge components. The study has revealed that preservice teachers were able to reach the highest level of discovery, curriculum knowledge was the most successful component and they showed the lowest success in the strategy knowledge component. In this context, we suggest that course content that includes such activity design tasks should be prepared and included in the teaching process for the development of preservice teachers' Technological Pedagogical content knowledge.

유아교사의 수학적 태도와 수학교과교육학지식이 수학문해환경에 미치는 영향

Objectives The purpose of this study is to analyze the effect of early childhood teachers' mathematical attitudes and Mathematical Knowledge for teaching on the mathematical literacy environment of early childhood education institutions. Methods Data were collected from 229 teachers working at 34 kindergartens and daycare centers located in Seoul, Gyeonggi, and Incheon using a questionnaire for teachers on mathematical attitudes, Mathematical Knowledge for teaching, and mathematics literacy environment. The collected data were analyzed using descriptive statistics, frequency analysis, t-test, one-way ANOVA, and stepwise multiple regression analysis. Results First, it was found that early childhood teachers differ in their mathematical attitudes according to the age of the class they are in charge of, and Mathematical Knowledge for teaching differs according to career, academic background, and type of institution among general variables of early childhood teachers. In addition, it was found that the environment of mathematical literacy differed according to career and educational background, type of institution, and age in charge among general variables of early childhood teachers. Second, general variables of early childhood teachers, mathematical attitudes and mathematical knowledge for teaching showed positive correlations with the environment of mathematics literacy. Third, the general variables of early childhood teachers, the motivation for mathematics in the mathematical attitude, and the knowledge of teaching and learning methods in the mathematical knowledge for teaching had explanatory power in the mathematical literacy environment. Conclusions This study investigated the effects of teachers' general variables, mathematical attitudes, and mathematical knowledge for teaching on the mathematical literacy environment of early childhood education institutions. Through this, it was emphasized that teacher education should be carried out by developing a teacher education program that can improve teachers' mathematical attitude and knowledge of mathematics and pedagogy as a way to improve the quality of the environment for mathematics literacy in the early childhood education field.

Identification of characteristics of didactic and meta-didactic mathematical knowledge of novice and expert teachers when reflecting on class episodes

This article describes the didactic analysis carried out by an expert teacher and a novice teacher, based on the didactic suitability criteria (DSC) of the Onto Semiotic Approach (OSA) when analyzing episodes of a high school mathematics class in Costa Rica. This is a qualitative investigation with an interpretive hermeneutic approach. First, a questionnaire was applied to the two participants, to classify them as novice and expert, based on certain defined characteristics. Both teachers then analyzed three video segments using a guide for didactic analysis and, finally, an interview was conducted to elaborate on the reflections previously obtained. The data analysis focused on identification, classification, and comparison of elements in each of the video segments with reference to the OSA’s DSC indicators. The results show that there are differences and similarities between the didactic analysis carried out by these teachers. It is concluded that the novice teacher provides a more descriptive analysis, in which errors are not specified, and focuses on the activities carried out by his students, while the expert teacher, who provides a thoughtful evaluative analysis of, identifying errors in the concepts and focusing his analysis on the teacher’s actions and performance in the video segments.

Investigating the Effects of Integration on the Development of Mathematical Knowledge for Teaching: A Case of Pre-Service Teachers in the Colleges of Education in Ghana amidst Curriculum Changes

The study examined the effects of integration on the development of Mathematical Knowledge for Teaching (MKT) among pre-service teachers while enrolled in a math program at the colleges of education in Ghana in the face of the new curriculum. In all, two hundred and forty-seven (247) pre-service teachers (PSTs) were sampled for the study. The experimental group comprised one hundred and thirty (130) PSTs who were taught both Mathematics content and method courses in an integrated manner, while the control group, comprised of one hundred and seventeen (117) PSTs, was taught Mathematics content and method courses separately. The non-equivalent static-group comparison design was used for the study. Both groups of PSTs were post-tested after they had received instruction in mathematics courses up to the point where they were ready to go for their macro teaching (Off Campus Teaching Practice) to compare their achievements in terms of their mathematical knowledge for teaching. Analysis of data using the independent sample t-test revealed that the control group had a mean score lower than the experimental group, and the standard deviation showed that the scores of the control group were far from their mean score. That is, the scores of the control group were more heterogeneous than that of the experimental group. The experimental group scored higher than the control group on the post-test, and their scores were more homogeneous than the control group. At a significant level of 0.05, there was a statistically significant difference between the means of the two groups on the post-test. With a mean difference of 5.042, the experimental group performed better than the control group on the post-test. Hence, the students in the experimental group turned out to achieve better on MKT components than the students in the control group. It was recommended, among others, that the use of the integrated approach in the teaching and learning of Mathematics should be encouraged, monitored, and supported throughout the Colleges of Education in Ghana.

Specialised Knowledge of the Mathematics Teacher to Teach through Modelling using ICTs

Background: The study of the knowledge of the mathematics teacher has focused attention on differentiating mathematics preservice teachers from other types of professionals who know the area to establish specific characteristics that can identify the professional licensed for the teaching of mathematics. Objectives: To characterise the specialised knowledge of the teacher who incorporates information and communication technologies (ICT) in the teaching of mathematics using modelling. Design: Qualitative research based on an instrumental case study. Setting and participants: The study is carried out in a secondary basic education course, with a teacher with training and experience in teaching mathematics with technological resources. Data collection and analysis : The analyses focused on three subdomains of the mathematics teacher’s specialized knowledge model, namely: knowledge of the topics, knowledge of mathematical practices, and mathematical knowledge for teaching, by adapting indicators to the categories of knowledge of these subdomains, integrated with aspects of modelling. Results: The relationships that arise between categories of the subdomains were found and are evidence of the need for the teacher who teaches mathematics to know the subject discipline in depth and to relate it to their didactic-pedagogical knowledge to develop mathematical modelling processes using the ICTs. Conclusions: The construction of knowledge indicators of the KoT, KMP, and MKT allowed us to understand and interpret the specialised knowledge of the teacher when teaching conics, particularly, the circumference, through mathematical modelling with the specialised GeoGebra software.

Teacher Moves and Knowledge in Preparing Students for General Certificate of Education Examination

This study investigated an experienced teacher’s moves in preparing high school students for an end of year certificate examination. Six consecutive lessons taught by this teacher were observed and videotaped in the second term of the 2020/2021 academic year. These lessons were transcribed and coded for teacher moves as well as teacher knowledge deployed in any of the moves. First, the two researchers coded teacher moves independently and agreed on them. Second, interviews were used to obtain justification for teacher moves used. Third, Ball, Thames and Phelps’s (2008) categorizations of mathematical knowledge for teaching was used to determine which teacher knowledge motivated the move. Results revealed that this teacher, Ngwa, a pseudonym, deployed the following moves: reading through all the topics to identify key concepts and determine connections between and among them, connecting ideas from one topic to another, returning to previous chapters or units for review of mathematical ideas, reinforce understanding by modifying problems, adoption/adaptations and extension of problems to generate the use of more ideas, withdrawal of the teacher and creation of space for interaction, announcing or advertising what will be learned in the next lesson, and learners designing their own questions for the class to engage with. The findings also revealed that understanding the structure of an examination might be a form of specialized content knowledge as it drives teaching. In addition, teaching and learning was found to be forward and backward to review concepts and reinforce learning in learners. Furthermore, teachers must intentionally create space for student-student interaction which provide opportunities for learners to make sense of what is being taught. The findings of this study might be beneficial to teacher educators and professional development experts to focus training on productive teaching moves. Classroom teachers can also use the outcome of this study for the improvement of their practice of teaching.

Primary teachers’ perceptions of their mathematical knowledge for teaching and the effects of policy on their mathematics teaching

ABSTRACT The mathematical knowledge for primary teachers has been guided by policy since the National Strategies Programme was introduced in 1999. Research regarding the National Strategies focussed on the outcomes of the policy rather than in terms of teachers’ mathematical knowledge for teaching (MKT). Teachers respond to policy in a variety of ways according to how they make sense of it within their current practice. This paper focusses on teachers’ perceptions of the effect of their policy enactments on their MKT and vice versa. A qualitative methodology included semi-structured interviews in order to explore the perceptions of thirteen primary teachers from five schools in a borough of London. Tension occurred when teachers considered that policy superseded their MKT or they perceived that they needed guidance to teach the new National Curriculum. There are implications for teachers who associate MKT with policy, which is subject to change and therefore temporal in nature.

Teacher time out as a site for studying mathematical knowledge for teaching

The special mathematical knowledge that is needed for teaching has been studied for decades but the methods for studying it have challenges. Some methods, such as measurement and cognitive interviews, are removed from the dynamics of teaching. Other methods, such as observation, are closer to practice but mostly involve an outsider perspective. Moreover, few methods tap into the tacit and often invisible demands that teachers encounter in teaching. This article develops an argument that teacher time outs in rehearsals and enactments might be a productive site for studying mathematical knowledge for teaching. Teacher time outs constitute a site for professional deliberation, which 1) preserves the complexity and gets inside the dynamics of teaching, where 2) tacit and implicit challenges and demands are made explicit, and where 3) insider and outsider perspectives are combined.

Modelling of Student Teachers’ Mathematical Conceptions According to Ck¢ Theory: The "Knowledge Transfer" Conception

This study aims to examine the basic mathematical knowledge of primary education student teachers according to the Ck¢ theory. The data of this qualitative study is collected through exams applied and clinical interviews undertaken with student teachers. To determine mathematical conceptions of student teachers, examinations on the subjects of Sets, Equations, Functions, and Numbers were applied to 61 classroom teachers , and then 26 of them were interviewed. A detailed analysis of the exam questions was undertaken and all types of knowledge that student teachers used whilst solving these problems were identified. Student teachers’ general mathematical conceptions were revealed through the classification of the related parts of such knowledge that were expressed as “operator” in the conception phase of Ck¢ theory. In this study, the conception of knowledge transfer is presented as one of the determined conceptions. It has been identified that student teachers use the knowledge they have previously experienced as effective in problems, whilst they solve problems, and that they thus think that they will be effective in future problems as well. Operators involving such knowledge underpin the ‘knowledge transfer’ conception. Yet, it has also been found that this knowledge transfer leads students to make mistakes as they usually rely on the idea that a rule leading them to the correct result in a situation, which occasionally leads them to the correct result, will be applicable in any other situations. This conception shows that students tend to use the knowledge that seems appropriate for their logic, their existing knowledge, and their mathematical thinking, even if they notice that what they do in solving problems does not have any mathematical validity. Therefore, this study contributes to the literature in terms of revealing students’ ways of mathematical thinking and addressing the important areas to be covered by teachers in designing learning environments.