Mathematical Knowledge For Teaching Research Articles

Numeracy Training: Applying Jarimatika Method in Elementary School Students of Border Area Nunpene East Nusa Tenggara

The numeracy skill of elementary school students in border area Nunpene East Nusa Tenggara is still relatively low. This is caused by the students’ habit use counting aid such as calculators. Therefore, it is necessary to have a Lecturer activity in the community to help elementary school students which aim to improve their numeracy skills. Because mathematics teaches various skills, one of which is counting. So that the ability to count is a fundamental thing that must be mastered by students when they learn mathematics. One of learning method that can be done to improve students' numeracy skills is by applying the Jarimatika method which involves the students' own organs directly. Indirectly cognitive and psychomotor abilities will develop simultaneously so as to increase the efficiency of students' counting speed. As for the steps of the service, the method are including the introduction of the counting method, assistance during the learning process, then providing an evaluation. The results of this training are that after the training, it can be seen from the posttest results that students have increased their numeracy skills using the Jarimatika method. As well as increasing the knowledge of mathematics teachers regarding the use of the Jarimatika method as an alternative method of numeracy

Providing Support and Examples for Teaching Linear Equations in Secondary School: the Role of Knowledge of Mathematics Teaching

Providing Support and Examples for Teaching Linear Equations in Secondary School: the Role of Knowledge of Mathematics Teaching

The influence of mathematical knowledge for teaching towards elementary teachers’ mathematical self-efficacy

This research study investigates how elementary teachers’ mathematical knowledge for teaching (MKT) relates to their mathematical self-efficacy (MSE) and whether the MKT can predict the MSE. Researchers administered the MSE scale and the MKT test to 86 in-service elementary mathematics teachers. Two-step regression analyses results indicated that MKT and its proxy measures (teaching experience, training type, and hours) were significant predictors of elementary mathematics teachers’ MSE level; however, the MKT was the strongest. Considering these results, the research recommends aligning the MKT and the MSE when building teacher preparation and professional development programs. The implications for teacher preparation and developmental programs are further discussed.

The Growth of Teacher’s Mathematical Knowledge for Teaching as Participating in a Primary School Teacher’s Professional Learning Community

Teacher’s Professional Learning Community (PLC) should effectively operate through sharing teaching resources, professional dialogues, and collaboration to reduce pupil’s learning achievement gaps and make teaching close to their learning experiences through providing learning scaffolding. This study adopts a qualitative research method to investigate the change of participants’ Mathematics Knowledge for Teaching (MKT) of a primary school teacher PLC which has been running for three years. The three research subjects are experienced teachers and none of whom are mathematics or science majors. According to the framework of the MKT (Hill et al. 2008), the qualitative data which include PLC meeting videos, lesson observation sheets, interviews, and learning feedback are analyzed and triangulated by the researchers and other mathematics educators. The results show that PLC may help teachers improve their MKT. At the beginning of the PLC, the discourse was mainly related to the teacher’s Knowledge of Special Content Knowledge (SCK) and Knowledge of Content and Teaching (KCT). It reveals that the participants ought to be energized in SCK and KCT, and the PLC activities should be specially arranged in these two aspects. After the continuous professional dialogue and teaching practices, the teacher’s KCC, Knowledge of Content and Student (KCS), and Special Content Knowledge (SCK) are improved most significantly, which also promotes the student learning achievements. Keywords: mathematics teaching, teacher professional development, teacher professional learning community, mathematics knowledge for teaching

We train, but how well? Assessing mathematical knowledge for teaching of future Turkish teachers

This study aims to assess and compare–at the national and regional sizes–mathematical knowledge for teaching of pre-service elementary mathematics teachers (PEMTs). Participants of the study were composed of 1,367 pre-service teachers selected among 21 universities in 12 regions of Turkey. Mathematical knowledge for teaching (MKT) test, which were developed by TEDS-M project were used to collect the data. The instruments were adapted into Turkish by the researchers. According to results, while there wasn’t much differentiation among the regions in terms of the MKT, pre-service teachers in the West Marmara, Mediterranean, and Northeast Anatolia regions are more successful than the other regions. PEMTs’ mathematics pedagogical content knowledge (MPCK) performance was close but somewhat better than their mathematics content knowledge (MCK) performance, in terms of both regions and universities. In the case of the MPCK test, the regions exhibited a more homogeneous picture, while in the case of MCK, the universities did so. Algebra content domain is where the PEMTs’ performance is lowest. When we compared the results obtained from this study with published international averages from TEDS-M study, Turkish PEMTs had appreciably higher performance on both MCK and MPCK components.

Teacher Evaluation, Ambitious Mathematics Instruction, and Mathematical Knowledge for Teaching: Evidence from Early-Career Teachers

Teacher evaluation policies have been central to policy efforts to enhance teaching quality. At the same time, ambitious mathematics instruction has been emphasized by teacher education programs as well as by the Common Core State Standards. Drawing on observation and survey data from early-career teachers, this study examines how teachers’ perceived pressure of teacher evaluation policies shape their ambitious mathematics instruction. We found that teachers who perceived a strong pressure of teacher evaluation on their instructional practices tended to move further away from enacting ambitious mathematics instruction. Moreover, the negative association between the pressure of teacher evaluation and ambitious instruction was stronger for teachers with a high level of mathematical knowledge for teaching.

Mathematics Teachers’ Perceptions on the Implementation of the Quizizz Application

Quizizz is an application proposed by the Ministry of Education Malaysia that can be used to obtain information about pupils’ learning acquisition throughout lessons. Quizizz integrates technology and gamification concepts that captivate students’ desire to learn. For home-based learning, Malaysian teachers were advised to guide pupils using communication mediums and applications so that the pupils would not be left behind in their learning. This study investigated the prior knowledge and perceptions of mathematics teachers regarding Quizizz, and their attitudes towards using this application. Furthermore, this study aimed to discover the interests among primary school mathematics teachers with different years of teaching experience in integrating the Quizizz application into their classes. We adopted a quantitative research method, using a questionnaire as research instrument. Fifty primary school teachers teaching mathematics in Johor were selected as respondents. The data obtained were analyzed using descriptive statistical analysis and inferential statistical analysis. Findings showed that more than half of the respondents (68%) had followed a course on using Quizizz, and 94% felt that they could access the Quizizz website easily. Most of the respondents (mean > 3.67) had a positive attitude towards the Quizizz application. This study showed that teaching experience does not influence the teacher’s decision in implementing the Quizizz application in the teaching and learning process. Teachers are willing to learn new teaching methods.

KORELASI BELIEFS DENGAN PEDAGOGICAL CONTENT KNOWLEDGE CALON GURU MATEMATIKA

Beliefs and Pedagogical Content Knowledge are important things for prospective mathematics teachers to have. The purpose of this study is to analyze the correlation of beliefs with Pedagogical Content Knowledge of prospective mathematics teachers. The research method used quasi-experimental with purposive sampling technique. The research sample is students majoring in Mathematics Education at Institut Pendidikan Indonesia. Data was collected by giving written tests and questionnaires which were then analyzed using Spearman correlation. The results of the study show that there is a correlation between beliefs and Pedagogical Content Knowledge of prospective mathematics teachers.

Revealing Implicit Knowledge of Pre-Service Mathematics Teachers in Lesson Planning: Knowledge of Infinity

The study aims to explore how pre-service mathematics teachers reveal their knowledge of infinity during the lesson planning process in the context of limit. Specifically, we adopted the dimensions of mathematics teachers’ specialized knowledge, which are related to mathematical knowledge and its relation with teaching. We conducted an exploratory case study design in a two-cycle lesson planning process with three senior pre-service mathematics teachers. The findings indicated that in the first planning process the participants did not use infinity as a way of thinking, rather they focused on paradoxes and potential infinity. After they taught their lesson plan, they started to think about the complexity of infinity not only in the context of limit but also in the concept itself during the lesson planning process. The findings did not cover the knowledge of infinity; rather, they yield important implications for lesson planning process to reveal teachers’ knowledge for teaching.

Development of the STEM-Pedagogical Content Knowledge Scale for Pre-service Teachers: Validity and Reliability Study

This study aims to develop a valid and reliable scale to determine the STEM-Pedagogical Content Knowledge (STEM-PCK) levels of pre-service teachers. This study was conducted in the 2018-2019 academic year with 322 pre-service teachers in Turkey. In the study, one of the mixed method typologies, Exploratory Sequential Design was applied. The scale was submitted for evaluation by four experts to determine the content and face validity. Exploratory Factor Analysis (EFA) and Confirmatory Factor Analysis (CFA) was performed to determine the construct validity of the scale. As a result of EFA, the scale had five factors including STEM Pedagogical Knowledge, Pedagogical Knowledge, Engineering Pedagogical Knowledge, Mathematics Pedagogical Knowledge and Science Pedagogical Knowledge.As a result of CFAχ ² / df = 2.7085, RMSEA = .073, RMR = 0.0420, SRMR = .0667, NFI = .940, NNFI = .960, CFI = .961, IFI = .962, RFI = .938 values were reached and the factor structure determined to be suitable.To determine the reliability of the scale, internal consistency and test-retest reliability analyzes were made. Internal consistency reliability value of the scale was found as .977. The final form of the STEM-PCK scale is a 5-point Likert type that includes 57 items and 5 factors.

Investigating secondary mathematics teachers’ analogies to function

This study investigates the analogies used by a sample of secondary mathematics teachers when they described the concept of function. The study is concerned with understanding what analogies were used by the participant teachers and conceptions of functions positioned in those analogies. Using examples from a set of responses to five open-ended questionnaire items, the article presents the main analogies found in the descriptions of the participant teachers and examines ways in which these are structurally mapped to function by applying Gentner’s structure-mapping theory of analogy. Among those discussed are the child–mother linkage and machine/factory analogies. Of interest is the predominance of illustrations that show a correspondence approach to functions (mappings and input-output machines), while a covariation approach is entirely absent. The article makes the case for using the concept of analogy as a tool in research on teachers’ Mathematical Knowledge for Teaching (MKT).

Providing Online Learning Situations for In-Service Mathematics Teachers' External Transposition Knowledge During COVID-19 Pandemic: Case of Indonesia

Updating mastery of mathematics scholarly knowledge is vital for mathematics teachers' professional development in Indonesia. External transposition refers to the transposition of mathematics scholarly knowledge to the school curriculum. During the COVID-19 pandemic, online learning becomes the primary strategy for strengthening the external transposition knowledge of mathematics teachers in Indonesia. This study aims to describe the process of providing online learning situations in lifting the in-service mathematics teachers' external transposition knowledge during the COVID-19 pandemic. The online learning involved 57 in-service high school mathematics teachers in Indonesia as participants. The scholarly knowledge to be delivered was the visualization of matrix multiplication. This qualitative study is a didactical design research that includes a prospective learning situation analysis, a meta-technopedadidactic analysis, and a retrospective analysis. In the prospective learning situation, the solutions for re-situating face-to-face learning to online learning were disclosed. Moodle was used as the Learning Management System, and GeoGebra Classroom was used as the Task Response System. A meta-technopedadidactic is an educator's ability to comprehensively analyze pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in using technology in a learning situation. The finding in the meta-technopedadidactic analysis showed the role of technology as a visualization tool in online learning, evidence of participants' external didactic transposition, constraints, and collaboration in learning. Finally, the retrospective analysis suggested some future improvements for better online learning situations. This study contributes to the comprehensive organization of e-learning courses in Indonesia for mathematics teachers' professional development based on pedagogic interaction, didactic interaction, and didactic pedagogy anticipation in the use of technology. Despite some of the study's limitations, the findings have the potential to be an advantage for the long-term sustainability of e-learning as a new norm for teachers' professional development programs, rather than just a foreshadowing of the pandemic.

Knowledge of mathematics teachers in initial training regarding mathematical proofs: Logic-mathematical aspects in the evaluation of arguments

The objective of this study is to characterize the knowledge of mathematics teachers in initial training (MTITs) at the Universidad Nacional (Costa Rica) on the logic-syntactic and mathematical aspects involved in proving, when evaluating mathematical arguments. The research is positioned in the interpretive paradigm and has a qualitative approach. It consists of two empirical phases: in the first, a questionnaire regarding logic-syntactic aspects was applied to 25 subjects, during the months of September and October 2018 and; in the second phase, a second questionnaire covering mathematical aspects was applied to 19 subjects, during the months of May and June 2019. For the analysis of the information, knowledge indicators were proposed. Knowledge indicators are understood as phrases to determine evidence of knowledge in the responses of the subjects. It was appreciated that the vast majority of future mathematics teachers show knowledge to discriminate when a mathematical argument corresponds or not to a proof by virtue of the logic and syntactic aspects, and of mathematical elements associated with propositions with the structure of universal implication. In general, subjects displayed greater evidence of knowledge on the logic-syntactic aspects than on the mathematical aspects. Specifically, they evidenced that consideration of a particular case or the proof of the reciprocal proposition does not prove the result; likewise, subjects evidenced knowledge about the direct and indirect proof of the universal implication. In the case of the mathematical aspects considered as hypotheses, axioms, definitions and theorems, it was appreciated that subjects could have different levels of difficulties to understand a proof.

Teacher Reflection on a Teaching-Learning Situation Regarding the Concept of Relation in Secondary Education

This study is part of the research in didactics of mathematics on teacher training. In particular, the study focuses on the knowledge of mathematics teachers, taking as a reference the theoretical approaches of the Mathematics Teacher’s Specialized Knowledge (MTSK) model and teacher reflection as a professional competence. The study corresponds to a descriptive-qualitative research, based on an instrumental study of cases, whose purpose is to describe and analyze the manifestations of mathematics teachers of Secondary Education when they observe a teaching-learning situation that shows a teacher of mathematics teaching the concept of relation. For this, narratives written by seven Secondary Education mathematics teachers in service were used, which indicate some aspects identified by them as relevant from the observed situation. The analysis of the gathered information was carried out by defining categories, subcategories, and analysis units based on the components of the MTSK model. The results indicate that participating teachers accentuate, in their manifestations, attributes mainly associated with didactic knowledge of mathematical content. The reflection of this group of teachers is characterized by three specific aspects of the MTSK model: teaching, learning, and knowledge of the topics. It is interpreted that teacher reflection has been influenced by the professional experience of the teachers participating in the study.

Algebra Teaching Knowledge of Professional and Non-professional Basic School Mathematics Teachers

Algebra Teaching Knowledge of Professional and Non-professional Basic School Mathematics Teachers

It is necessary to know a specific mathematics to teach mathematics

In this theoretical essay we problematize the statement “To teach mathematics one must know a specific mathematics for teaching” of the discourse of specific mathematical knowledge to teach. The study was inspired by Foucaultian concepts and the analysis focused on studies in the area of Mathematical Education that mobilize discourses regarding Mathematical Knowledge for Teaching, Mathematics Teacher’s Specialized Knowledge and Mathematics for Teaching. The analysis showed that the discourses operate under two truth regimes about the mathematical knowledge needed to teach. Analyzing the enunciative intertwining, we observe an approximation with: i) the educational discourse, which deals with the inseparability between theory and practice; and ii) the capitalist economic discourse, which associates of economic development with the mathematical proficiency of a country.

Mathematical Knowledge of Pre-Service Early Childhood and Primary Education Teachers: an Approach Based on the Design of Tasks Involving Patterns

This study analyzes the mathematical knowledge of 40 pre-service Chilean Early Childhood and Primary Education teachers when designing mathematical tasks on patterns, in the context of teaching early algebra. Based on the domains of the Mathematical Knowledge for Teaching (MKT) model, we have adopted a descriptive qualitative methodological approach that relies on the content analysis technique. The results show that pre-service teachers exhibit little mathematical knowledge in the description of the mathematical tasks they pose, addressing partial aspects of the subdomains of specialized content knowledge and knowledge of content and teaching. We conclude that training experiences should be given that allow students to further their acquisition of mathematical knowledge in order to achieve effective learning of the contents that early algebra promotes, such as patterns, in Early Childhood and Primary Education classrooms.

Pedagogical Content Knowledge of Mathematics Teachers: A Focus on Identifying and Correcting Sources of Students’ Misconceptions in Linear Programming

Pedagogical Content Knowledge of Mathematics Teachers: A Focus on Identifying and Correcting Sources of Students’ Misconceptions in Linear Programming

Enhancing Pre-service Mathematics Teachers' Technology Integrated Competency: Cooperative Initiation and Open Lesson Observation

Technology became considerably more critical for mathematics teachers during the Covid-19 pandemic era. Apart from examining pre-service mathematics teachers' knowledge about technology integration, which failed to reflect the unique characteristics of mathematics and underrated teachers' perception toward using technology in mathematics classrooms, this study aims to examine pre-service mathematics teachers' technology integrated competency through an enhancement program. Data were gathered from 25 pre-service mathematics teachers at Lampang Rajabhat University through journals, artifacts, and focus group interviews. Quantitative and qualitative analysis was by the research analytic framework's categories to define changes in participants' technology integrated competency. The primary finding was that participants gained a better knowledge of technology integrated lesson design during a four-month period. Most participants moved their emphasis away from technology as a teaching aid and toward providing students with mathematical learning instruments. Additionally, they emphasized the significance of their courage. They did not overlook the necessity of adequate mathematical knowledge for teaching when it came to improving mathematics teachers' roles in creating a successful technology integrated mathematics lesson. It was discovered in this study that the cooperative initiation and open lesson observation of pre-service mathematics teachers had a direct effect on their lesson preparation.

An Investigation of the Factors That Contribute to Poor Problem-Solving Skills in Grade 8 Mathematics Learners in Namibia

The study seeks to investigate the factors that contribute to poor problem-solving skills in Grade 8 Mathematics learners at three combined schools in the Ongha circuit. A case study design was used within the qualitative approach. A theory of Vygotsky’s social constructivism theory of cognitive development was used as the theoretical framework of this study. The population for this study comprised all 19 Grade 8 Mathematics teachers from three combined schools in Ongha Circuit, in the Ohangwena region. A sample comprising six Grade Eight Mathematics teachers was then chosen purposively from the three combined schools in Ongha Circuit. An interview guide was used to collect data from the Mathematics teachers. Data were analyzed using themes that were discussed later. The literature and the theoretical framework were used to compare and contrast the study findings. Participants revealed that problem-solving skills have a long-term effect on learners’ learning. The study uncovered that learners with poor problem-solving skills experience difficulties in solving mathematical problems and in daily life. The study also unveiled that the factors that contribute to poor problem-solving at the combined school were language problems, lack of resources, lack of mathematical pedagogical knowledge, lack of involvement of parents, lack of motivation and support, and lack of training and workshops. It can therefore be suggested from the results of this study, that some of the strategies that can be applied to enhance learners’ problem-solving skills in mathematics are such as allow learners to do more practice, designing suitable examples and activities, using different teaching strategies, using key mathematical terms and use more teaching aids. The study further recommends the school management to provide teaching and learning resources, organize min-trainings and monitor compensatory programs. The study also suggests that the education regional directorate should supply adequate textbooks, give professional support, and organize training and workshops to help teachers to improve problem-solving skills among learners.