Mathematical Content Knowledge Research Articles

Comparison of prospective mathematics teachers’ problem posing abilities in paper-pencil test and on dynamic geometry environment in terms of creativity

This study aims to investigate the similarities and differences between prospective mathematics teachers’ creative thinking skills in paper-pencil test and on a Geogebra-supported environment in terms of problem-posing. This case study used purposive sampling method for determining the participants. Findings revealed that the activities carried out in the GeoGebra-supported environment were insufficient to produce creative problems, and GeoGebra’s main utility to prospective teachers was in identifying their mistakes related to mathematical concepts and discrepancies among numerical values of the problems posed. The reasons for the low achievement in posing problem were discussed: These were; (i) lack of problem-posing experience, (ii) the structure of problem-posing activity, and (iii) prospective teachers’ mathematical content knowledge.

Systems approaches to professional and decisional mathematics capital

PurposeThis study aims to explore how the theories of professional capital and decisional capital can be extended to introduce “professional mathematics capital” and “decisional mathematics capital”.Design/methodology/approachProfessional development (PD) efforts in one school district in elementary mathematics education are described to illustrate these extensions and to contemplate ways to enhance teacher learning of mathematics pedagogy.FindingsBoth theoretical extensions provided useful frameworks for conceptualizing mathematics PD. Preliminary evidence suggests that participants demonstrated the emergence of professional and decisional mathematics capital.Research limitations/implicationsWhile there were observed and reported changes to teacher practice, further research is needed to explore the implications of these theoretical extensions on student learning.Originality/valueThis study serves to enhance the literature related to PD and teachers' mathematical content knowledge. The theoretical extensions of professional and decisional mathematics capital are a novel and promising concept that allows for a unique approach to be laid out for those designing PD in mathematics.

Unpacking Mathematics Pedagogical Content Knowledge for Elementary Number Theory: The Case of Arithmetic Word Problems

“Number” is an important learning dimension in primary mathematics education. It covers a large proportion of mathematical topics in the primary mathematics curriculum, and teachers use most of their class time to teach fundamental number concepts and basic arithmetic operations. This paper focuses on the nature of mathematics pedagogical content knowledge (MPCK) concerning arithmetic word problems. The aim of this qualitative research was to investigate how well the future primary school teachers in Hong Kong had been prepared to teach mathematical application problems for third and sixth graders. Nineteen pre-service teachers who majored in both mathematics and primary education were interviewed using two sets of scenario-based questions. The results revealed that innovative approaches were suggested for teaching third graders while the strategies suggested for teaching sixth graders were mostly based on a profound understanding of mathematical content knowledge. Many participants demonstrated sound knowledge about the sixth grader’s mathematical misconception, but most of them were unable to precisely indicate the third grader’s error in presenting a complete solution for a typical mathematics word problem. A deep understanding of elementary number theory seems to be a precondition for developing pre-service teachers’ MPCK in teaching arithmetic word problems.

A measurement model of technological pedagogical content knowledge (TPACK) in Indonesian senior mathematics teachers’ scenario

The TPACK is one of the primary knowledge for teachers understanding technology in the era of the industrial revolution 4.0. In education, teaching technology in the classroom can apply by looking at the TPACK stages teachers have. Teachers who have high stages in TPACK will facilitate their steps and movements in exploring technology in the classroom. This study aims to validate the TPACK measurement model, which consists of 30 items. A quantitative method of the cross-sectional survey is applied in this study. We used the questionnaire for gaining the data. TPACK instruments were distributed to 235 respondents. The analysis of this TPACK measurement model testing uses exploratory factor analysis (EFA) and confirmatory factor analysis (CFA). All constructs revealed acceptable internal consistency reliability. A good model fit found for measurement models of TPACK using several fit index tests like CMINDF, GFI, CFI, TLI, and RMSEA. The findings showed that all fit indices criteria were fulfilled. It is concluded that the TPACK measurement model pictures the TPACK level of the senior mathematics teachers in the Indonesian scenario.

Analysis of Mathematical Content Knowledge of Elementary Teachers in Lampung Utara Regency: A Baseline Study

According to TIMSS 2015 and PISA 2018 reports, Indonesian students’ knowledge and skills of mathematics are still far from adequate compare to other countries. Therefore the efforts to improve the condition need to done, not just by government but also educational institutions and movements. One of new movement is Gerakan Nasional Berantas Buta Matematika (GernasTastaka, 2018). This baseline study aims to describe and analysis the mathematical content knowledge of 100 elementary teachers from Lampung Utara regency that joined the workshop of mathematics teaching and learning which was developed and facilitated by team from Gernas Tastaka. The eight-question multiple choice pre-test covers Number and Operation, Measurement, Data Analysis, and Probability. Each question is related to specific mathematical content knowledge and skill that are supposed to be mastered by grade 6 students. The quantitative descriptive for each question was conducted to give more details on specific mathematical content knowledge. The result displays that only 36% of the participants can answer correctly 50% of the questions. The low competency of teachers gives impact to their students’ achievement. It is correspondent with the data from Indonesian National Assessment Program (INAP, 2012); mathematics competency of elementary students in Lampung province is below Indonesian national level. One of the teachers’ competencies is their mastery of content knowledge. This study recommends that future developmental workshops/ program for the participants must cover all mathematical content knowledge and skills of elementary level. Besides that, detailed data of participants should be provided in order to attain more reliable analysis.

Differences in teacher education programmes and their outcomes across Didaktik and curriculum traditions

ABSTRACT Teacher education is of vital importance for what teachers are capable to do for their pupils, but little is known about student teachers’ pedagogical knowledge. The Didaktik and the curriculum traditions are two main education approaches underpinning formal schooling and teacher education programmes (TEPs) in the Western world. The main difference between the two traditions lies in the content and objectives of teacher education, which are either theoretical or action-oriented. Two questions are addressed quantitatively: How do teacher education programmes and their outcomes vary across Didaktik and curriculum traditions? How do opportunities to learn and beliefs about teaching methods affect mathematical content knowledge (MCK) and mathematical pedagogical content knowledge (MPCK) scores? Empirical data from the Teacher Education and Development Study in Mathematics (TEDS-M) are used, with samples from Norway, Germany, Switzerland, and the US. The study offers alternative explanations for variations of TEPs’ outcomes within the Western world.

Learning to teach for mathematical proficiency: Behavioural changes for pre-service teachers on teaching placement

This study reports on an investigation of how field experiences in teaching prepares pre-service teachers (PSTs) to effectively deal with the challenges and complexities of teaching mathematics in Zimbabwean secondary schools. The study was premised on the view that improvement in learning secondary school mathematics in the classroom is related to practitioner development in teaching. However, despite overwhelming research on mathematics knowledge for teachers, the problem of mathematics failure in high schools has not been addressed. A mixed methods approach, based on the perspectives of PSTs on teaching practice (TP) was employed to depict how their practices impact on their knowledge development for teaching mathematics. The study, found that a proficient mathematics PST is considered one who embraces knowledge of mathematics content and the ability to teach it. Hence, the development of mathematics knowledge for PSTs requires them to be mentored and workshopped by mathematics subject specialists who are well positioned in terms of mathematics pedagogy and mathematics content knowledge.

The Challenges of South African Teachers in Teaching Euclidean Geometry

The current study identifies challenges confronting teachers in the teaching of Euclidean geometry in schools. This qualitative case study purposefully selected ten schools situated in the Motheo District of Education, Free State, South Africa. Data was generated using classroom observations and focus group interviews. The findings revealed that the majority of the teachers lacked mathematical subject content knowledge as well as pedagogical content knowledge to teach geometry effectively. In many cases, redeployment of teachers led to teachers being ill-equipped to teach specific subjects, such as mathematics. Recommendations have been made to enhance effective teaching and learning of mathematics (geometry in this case) in schools. https://doi.org/10.26803/ijlter.19.8.16

Understanding primary school children’s learning on addition of fractions

Fractions are universally known to be difficult to learn. Learning basic fractions may not be sustainable if one is to apply it to more advanced mathematical content knowledge as it is interlinked with other mathematics topics. In the effort to understand how children grasp the learning of fractions additions, a study was carried out with a random sampling of Years 4, 5 and 6 children in Brunei Darussalam. The research participants consisted of 33 children who are currently studying at government and private primary schools in Brunei. A pen-and-paper self-designed test was used as an instrument in collecting the data. The quantitative data was analysed by using a descriptive analysis method. The overall reliability of the self-designed tests indicated that the items have relatively high internal consistency with a Cronbach alpha of .859. The findings revealed that the children’s understanding is stronger on questions with answers regarding proper fractions rather than improper fractions. This could be further explored through future studies employing a qualitative approach.

SELF-EFFICACY BELIEFS AMONG SCHOOL MATHEMATICS TEACHERS OF NEPAL

Self-efficacy belief of the teacher is widely accepted construct in the professional development of the teacher. In this context, I as a mathematics teacher interested to study the efficacy beliefs of mathematics teachers in Nepal, which is a major contributing factor for teaching mathematics effectively. In this research, I, specifically, focused on exploring the self-efficacy beliefs of mathematics teachers in three aspects: student engagement, instructional strategy, and classroom management and to analyze the different contributing factors in the development of efficacy beliefs by using explanatory sequential mixed-method research. I chose 214 mathematics teachers randomly from Kathmandu district for a survey and 15 mathematics teachers from 214 mathematics teachers who participated in survey purposively for interviews. Adjusted Teacher’s Self-Efficacy Scale containing 15-items were used for survey and semi-structured interview schedule for interview. Descriptive as well as inferential statistics were used to analyze the self-efficacy beliefs of teachers and inductive approached used for the data obtained from interview. At last, I integrated both quantitative and qualitative results to deduce the findings and conclusion of the study. The result shows that teachers have good efficacy beliefs in teaching mathematics. Teachers have better efficacy beliefs in instructional strategy than in the other two. Experienced teachers have significantly higher self-efficacy beliefs than novices. Despite the huge investment of government in the teachers of public school, institutional school’s teachers have better self-efficacy beliefs in teaching mathematics. Teaching experience, teacher’s engagement in professional activities, mathematical and pedagogical content knowledge, and working environment of the school are major contributing factors in the development of the self-efficacy beliefs in mathematics teachers. There are so many factors in the development of self-efficacy of mathematics besides professional training, so stakeholders should focus on other aspects as well.

What skills and knowledge do university mathematics teacher education programs give future teachers in Costa Rica?

High-quality teaching is crucial for improving mathematics education. Teaching mathematics requires specific knowledge, including knowledge of both content and pedagogy. In this study, we analyzed the knowledge for teaching mathematics among 80 future teachers from four mathematics teacher education programs in Costa Rica. Using the Teacher Education and Development Study in Mathematics (TEDS-M) questionnaire, we studied the opportunities to learn the programs provide and the participants’ performance in tests of their mathematical content and pedagogical knowledge. The results showed that all the teaching programs involved gave more emphasis to the topics covered in tertiary level mathematics than to aspects of general and mathematics pedagogy. Moreover, the results highlighted the variation among universities in the participants’ performance in the tests and demonstrated that the number and content of the courses taken was not correlated with the participants’ performance. These findings offer insights to the Costa Rican government and policymakers into the actual structure, variability, and characteristics of teacher education programs, which could serve as a tool for making decisions on measures to improve the quality of teaching.

What do teachers need? Math and special education teacher educators’ perceptions of essential teacher knowledge and experience

Special education and mathematics education are becoming increasingly intertwined in inclusive classrooms. However, research and practice in these two fields are not always aligned. We discuss, in the context of extant research on pedagogical theory, concepts of access, and the findings of an exploratory study, how these two education sub-fields view teacher expertise. Teacher educators (from math and special education) were asked to rank the importance of different types of expertise for effectively posing purposeful mathematical questions. The groups differed significantly in their rankings of the importance of knowing individual students and general teaching experience. There were also notable differences between the groups’ rankings of the importance of knowing the needs of students with disabilities and mathematical content knowledge. The possible reasons for this are discussed, along with suggestions for improving professional collaboration.

Using Concept Cartoons to investigate future primary school teachers’ pedagogical content knowledge on addition

This paper introduces an exploratory empirical qualitative study that has been carried out with two diverse groups of future primary school teachers (before vs after the attendance of a course on didactics of mathematics). The study uses an educational tool called Concept Cartoons accompanied by a set of six indicative questions as a means of collecting data on pedagogical content knowledge (PCK) in mathematics. In particular, the study focuses on future teachers’ written responses to virtual pupils’ opinions in a virtual classroom situation related to the algorithm of written addition of natural numbers. The findings reveal ten different code categories of displays of PCK related to knowledge of pupils (three categories), knowledge of tasks (one category) and knowledge of instruction (six categories), some of them related to strong PCK, others to weak PCK. According to the findings, all the categories related to knowledge of pupils occurred in the post-didactic group only, all the categories that appeared only in the pre-didactic group are connected to weak PCK, and all the categories that occurred only in the post-didactic group are connected to strong PCK.

Pre-service teacher’s mathematical knowledge for teaching in problem-based learning

Mathematical Knowledge for Teaching (MKT), comprising Mathematics Content Knowledge (MCK) and Mathematics Pedagogy Content Knowledge (MPCK), is essential for pre-service teachers. However, numerous studies have shown that pre-service teachers are weak in content and difficult to plan to teach. Therefore, a shifting effort dealing with the learning activities within the teacher training program from a teacher-centered to student-centered approach should be made. One learning model succeeding in the student-centered approach is Problem-Based Learning (PBL). Studies on PBL as an effort to improve the MCK and MPCK of pre-service teachers have never been done before. There were two models of PBL applied in this experimental study: PBL with authentic problems (PBL1) and PBL with authentic problems and teaching practices (PBL2). The aspects of MCK studied are knowing, applying, and reasoning. While the aspects of MPCK are creating representation for the explanation, understanding mathematical structures, and anticipating students' thinking. The results of the study showed that there were significant differences between MCK and MPCK achievements in PBL1, PBL2, and conventional learning classes conventional. PBL1 and PBL2 classes were considered superiors since the pre-service teachers predominantly control the learning activities and were active in finding solutions. Hence, there were differences in the effect of the learning models on the aspects of MCK and MPCK.

ANALISIS KEPERLUAN PENGETAHUAN ISI KANDUNGAN DALAM PENGAJARAN MATEMATIK

Education transformation in Malaysia recently requires teachers to equip themselves with the highest knowledge in line with national education development needs. Based on the foundation, this study aimed to study the level of content knowledge among mathematics teachers in secondary schools in the state of Kedah. This study employs a cross-sectional survey design using a quantitative approach involving 343 mathematics teachers. Descriptive analysis with the mean score was used to explain the level of variables studied. Results from the descriptive analysis found that the average (min) content knowledge score was high (mean = 3.88). This shows that mathematics teachers were equipped with mathematics content knowledge. The findings of this study can be a guideline to the Ministry of Education Malaysia to develop ongoing training programs related to the knowledge of teachers.

Pre-service Secondary Teachers’ Mathematical Pedagogical Content Knowledge Self-concept related to their Content Knowledge of Functions and Students

Pre-service teachers’ beliefs, attitudes, and values about mathematics have a significant influence on their self-concept about mathematics as a subject and determine how confident they are to teach it. The purpose of this study was to examine Zambian pre-service secondary mathematics teachers’ pedagogical content knowledge self-concept about the function concept in relation to their knowledge of content and students. Data was collected from 150 pre-service teachers using a sequential approach in two phases. The first, quantitative phase, involved 150 pre-service teachers who responded to a functions survey and a mathematical pedagogical content knowledge survey. The second, qualitative phase, involved two pre-service teachers who were purposively selected from phase one to respond to vignettes and interviews for an in-depth understanding of their knowledge. Results of the study revealed that pre-service teachers’ level of their pedagogical content knowledge self-concept was low. They would not be confident enough to teach the function concept in secondary school. Results further revealed that their knowledge of content and students was weak. A weak correlative relationship between pre-service teachers’ KMLS and KM was revealed whereas a moderate correlative relationship of their KL and KC was revealed. It was further revealed that there was no significant correlative relationship between KTS and their knowledge of the function concept Thus, pre-service teachers needed to improve before leaving university for them to effectively teach secondary school concepts.

Pre-service primary teachers have a say on genericism in mathematics curriculum preparation

The purpose of this paper is to document pre-service primary school teachers’ responses to manifestations of genericism in mathematics teacher preparation. Specifically, it documents their responses to curriculum units that focus on developing mathematical content knowledge and specific mathematical pedagogical knowledge. Contextualised in an Australian initial teacher education program, the pre-service teachers (n = 789) were surveyed at the commencement of their units to gain insights into what they considered important to learn in their forthcoming mathematics curriculum units. Qualitative responses to the survey were categorised using thematic analysis and then used to guide the development of tailored units. The mathematics curriculum units focused on attempting to ensure depth of school mathematics content knowledge and specific pedagogy associated with this mathematics. A second survey, administered through post-course evaluations (n = 405), suggests that pre-service teachers overwhelmingly valued the modelling of specific pedagogies and scaffolding of the teaching and learning of school mathematics concepts. The results have implications for the teaching of mathematics in initial teacher education programs, particularly in Australia but also elsewhere where there is an increasing emphasis on pre-service teachers being classroom ready at graduation. This includes a deep and connected knowledge of the mathematics and range of pedagogies for the mathematics they will soon be certified to teach.

Latent Profiles of Korean Preschool Teachers Three Facets of Pedagogical Content Knowledge in Early Mathematics

Existing research primarily focused on only one aspect of preschool teachers pedagogical content knowledge (PCK) in early mathematics. With a...

Teacher Expertise and Professional Vision: Examining Knowledge-Based Reasoning of Pre-Service Teachers, In-Service Teachers, and School Principals

Classroom professional vision is a teaching skill that refers to the ability of teachers to rapidly notice information in class and engage in knowledge-based reasoning about the noticed information. Knowledge-based reasoning includes three interrelated processes: description, explanation, and prediction. The present study aimed to examine how pre-service teachers, in-service teachers, and school principals differed in these three reasoning processes after viewing classroom photographs with varying presentation time and interactional complexity. A 3×2×4 factorial design was used. Teacher expertise (pre-service teachers vs. in-service teachers vs. school principals) was a between-group factor, presentation time (1 sec vs. 3 sec) and complexity (teacher vs. dyad vs. small group vs. whole class) were within-group factors. Analysis of verbal reports suggested that in-service teachers and school principals used significantly more episodic knowledge, content knowledge, and pedagogical content knowledge in their reasoning than pre-service teachers did. Explanations with mathematical content knowledge were more frequent for in-service teachers, for shorter rather than longer presentation times, and for photographs showing the teacher only. Explanations with pedagogical content knowledge were more frequent for in-service teachers, for shorter rather than longer presentation times, and for photographs showing a small group. Across time and complexity, school principals verbalized less frequently what they noticed. In-service teachers and school principals verbalized significantly more self-monitoring and more predictions of teacher actions than pre-service teachers. The study findings contribute to the growing body of evidence on classroom professional vision, teacher noticing, and visual teacher expertise, and provide initial evidence on expert teachers’ frequent metacognitive self-monitoring.

Workshop Pemanfaatan Lingkungan Belajar di Sekitar Sekolah dalam Pembelajaran Matematika bagi Guru Sekolah Dasar di Gugus IV Kecamatan Siak Hulu, Kampar

WORKSHOP OF UTILIZATION OF LEARNING ENVIRONTMENT AROUND SCHOOLS IN MATHEMATICS LEARNING FOR ELEMENTARY SCHOOL TEACHERS IN SIAK HULU, KAMPAR. The workshop on the utilization of learning environment was motivated by the lack of teachers' mathematical and didactical knowledge. Teachers tend to explain techniques or procedures for solving mathematical problems without explaining the real context or situation of the problem, and this is contrary to the theories of mathematical learning that develop, such as the cognitive development theory, the realistic mathematics education, and the didactic situation theory. In addressing this problem, the team held a week workshop consisting of the lectures, observation, lesson plans, and implementation of learning by the teachers participating in the workshop, and reflection and evaluation of workshop activities. The data collection instrument consists of a questionnaire measuring the attitudes and beliefs of teachers towards mathematics, students learning mathematics, and mathematics learning based on real environments, photos, video recordings, and documents produced by the participants. The results of the implementation of this workshop show an increase in teachers' beliefs and attitudes towards students learning and mathematics learning based on real-life situations. Some participants were able to present the potential of the school environment as a source of learning mathematics, compile lesson plans, and carry out environment-based mathematics learning. The recommendation from this activity is that in the future it is necessary to have a service program that focuses on strengthening the teachers' mathematics content knowledge and making mathematics learning media and/or teaching aids.