Examining Teacher Mathematics-related Beliefs and Problem-solving Knowledge for Teaching: Evidence from Indonesian Primary and Secondary Teachers (original) (raw)
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Secondary teachers' mathematics-related beliefs and knowledge about mathematical problem solving.pdf
This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem-solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem-solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. The analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem-solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem-solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both Platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving
Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers' responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers' work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving
Journal of Physics: Conference Series, 2016
Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers' responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers' work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
This article describes primary teachers’ beliefs, knowledge, and performance regarding mathematical problem-solving. An explorative descriptive research was undertaken involving 80 teachers from East Java Province, Indonesia. Data were obtained through questionnaires and problem-solving tasks. The results of this study indicate that the teachers have a sufficient understanding of the knowledge of problem-solving as instruction and problem-solving in teaching practice. However, they have less understanding about the knowledge of problem-solving strategies and the meaning of mathematical problems. It can be explained from the teachers’ performance in problem-solving tasks, indicating that their incorrect answers were found to be a manifestation of their difficulties in applying problem-solving strategies. Analysis of teachers’ beliefs shows that the teachers tend to view mathematics as an instrumental tool, while they tend to view teaching mathematics as a learner focused task and students should learn mathematics as an autonomous exploration of students’ own interest, which is aligned with a problem-solving view.
Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving
Journal of Physics: Conference Series, 2017
Teacher knowledge and beliefs are known to play crucial roles in shaping teacher teaching practice regarding mathematical problem-solving. Thus, assessing the teacher's quality of mathematical problem-solving can be traced through such three factors. This paper aimed at exploring the elements of mathematics-related beliefs, mathematics problem-solving knowledge for teaching, and problem-solving-based teaching practice needs to be improved by mathematics teachers. Some empirical findings of assessing those three factors from a two-year research project involving a total of 288 teachers from primary and secondary school on teacher's problem-solving were presented as the manifestation of teacher quality regarding mathematical problem-solving. More specifically, the teachers participating in such a research project were indicated to have beliefs0about natureoof mathematics, mathematics teachinggand mathematics learning ranging from Instrumentalist view to problem-solving view. Also, it was found that teacher problem-solving0content knowledge such as knowledge of mathematics problem and problem-solving0strategies was insufficient to hold a problem-solving instruction. Furthermore, the teacher's teaching practice, assessed by observing how the teacher participants guide their students to solve a mathematics problem following Polya's four stages of problem-solving, range from directive to consultative teaching. In sum, beliefs, knowledge, and teaching practice are discussed as three interdependent factors which determine the quality of teacher's mathematical problem-solving.
Journal of Physics: Conference Series
Teacher knowledge and beliefs are known to play crucial roles in shaping teacher teaching practice regarding mathematical problem-solving. Thus, assessing the teacher’s quality of mathematical problem-solving can be traced through such three factors. This paper aimed at exploring the elements of mathematics-related beliefs, mathematics problem-solving knowledge for teaching, and problem-solving-based teaching practice needs to be improved by mathematics teachers. Some empirical findings of assessing those three factors from a two-year research project involving a total of 288 teachers from primary and secondary school on teacher’s problem-solving were presented as the manifestation of teacher quality regarding mathematical problem-solving. More specifically, the teachers participating in such a research project were indicated to have beliefs about nature of mathematics, mathematics teaching and mathematics learning ranging from Instrumentalist view to problem-solving view. Also, it ...
International Conference on Elementary Education, 2021
Mathematical proficiency as a goal of learning mathematics and other skills developed by teachers in schools through a didactic and pedagogical activity. The quality of teaching mathematics in elementary education is largely determined by the teacher's perspective on Pedagogical Content Knowledge (PCK) in mathematics learning itself. This study aims to see the perspectives of elementary school teachers who are experienced in teaching mathematics regarding several things that are needed in learning mathematics in elementary schools. The study used a survey method which was conducted on elementary school teachers who have experience in teaching mathematics with various educational backgrounds and different schools (n = 65) through random sampling. The study is focused on investigating the pedagogical perspective, the perspective of mathematics learning objectives, and the perspective of mathematics content taught in elementary schools. These perspectives are arranged in a research instrument in the form of a questionnaire containing multiple answer questions and open-ended answers. Data collection was carried out with the help of google forms. The data analysis used is quantitative and qualitative approaches. The results showed that various innovative learning models were known by the teacher, although not all teachers were sure that they had implemented the learning model according to the syntax of the learning model. Also, teachers are still optimistic that innovative learning models have flexibility so that they can be applied in pandemic conditions.
Southeast Asian Mathematics Education Journal
This is a case study investigating a primary teacher’s beliefs, knowledge, and teaching practice in mathematical problem solving. Data was collected through interview of one primary teacher regarding his beliefs on the nature of mathematics, mathematics teaching, and mathematics learning as well as knowledge about content and pedagogy of problem solving. His teaching practice was also observed which focused on the way he helped his students solve several different mathematics problems in class based on Polya’s problemsolving process: understand the problem, devising a plan, carrying out the plan, and looking back. Findings of this study point out that while the teacher’s beliefs, which are closely related to his problem solving view, are consistent with his knowledge of problem solving, there is a gap between such beliefs and knowledge around his teaching practice. The gap appeared primarily around the directive teaching which corresponds to instrumental view he held in most of Poly...
Journal of Education and Practice, 2014
The level of basic numeracy achievement in Malaysian education system is a growing concern to key stakeholders. Apart from monitoring numeracy standards, no attempt has been made to explore what are the beliefs of Malaysian primary school teachers' beliefs towards mathematics teaching and learning. It is important to understand teacher beliefs since ultimately these beliefs lead to student achievement in mathematics. Thus, this research examined the beliefs about mathematics teaching and learning held by Malaysian primary school (SK, SJKC and SJKT) teachers. A quantitative approach with a survey design was used. A total of 174 primary mathematics teachers from South Seberang Perai district of Penang participated in this research. A survey instrument with 18 items (Mathematics Beliefs Scales) was adapted from Capraro, and and administered to the SK, SJKC and SJKT teachers in order to determine their beliefs regarding mathematics teaching and learning on three subscales, namely beliefs about student learning, beliefs about the stages of learning and beliefs about the teaching practices. Teachers' responses derived from participation in the survey were analyzed for formal and informal mathematics beliefs. Descriptive statistics were calculated to explore the beliefs of SK, SJKC and SJKT mathematics teachers. Results indicated that most of the teachers expressed beliefs that tended to fall in the mid-range between formal and informal mathematics beliefs. A multivariate analysis of variance (MANOVA) was conducted and statistically significant differences were found in the mean scores of the three subscales of the Mathematics Beliefs Scales between SK, SJKC and SJKT mathematics teachers. The SJKC teachers were found to favour more informal beliefs in teaching and learning mathematics than their counterparts from SK and SJKT. Conclusions suggest as the most of primary mathematics teachers, especially from SK and SJKT have a mixture of both formal and informal beliefs, professional development must address their fundamental beliefs about mathematics so that they would adopt informal beliefs to enhance their mathematics teaching and learning.