Challenges in deepening prospective teachers’ understanding of multiplication through justification

This study examines prospective elementary teachers' growth and development of competencies, conceptions, and perceptions of mathematical modelling in a mathematics content course for elementary teachers. A series of lessons were implemented that engaged students in the modelling process through modelling tasks. The goal was to capture prospective teachers' thoughts and perceptions on the meaning of mathematical modelling and their conceptions of teaching and learning modelling at the elementary and middle school level. The research questions were: (1) How do prospective teachers translate the mathematical modelling cycle into their practice of doing modelling? and (2) How do prospective teachers' conceptions of modelling and teaching and learning modelling evolve throughout the implementation of a series of mathematical modelling lessons? Data sources included posters, modelling reports, responses to a pre- and post-intervention questionnaire, and semi-structured interview dialogue. Data analyses included mixed methods using provisional coding, open coding, and a categorical rubric. Findings from this study indicate that (1)Prospective elementary teachers translated the modelling cycle into their practice by developing their range of modelling competencies including multiple components of the modelling cycle, and (2) They developed a professionally appropriate conception of mathematical modelling along with productive perceptions of the benefits of teaching and learning modelling.

There is compelling evidence on the effectiveness of bibliotherapy for facilitating one’s development. Arguably, in teacher education, bibliotherapy has been shown to facilitate prospective teachers’ professional development. However, teacher educators may experience difficulties in finding relevant reading to stimulate prospective teachers’ identification process, which is essential if the application of pedagogical bibliotherapy is to be successful. This study is situated in a mathematics education course for prospective elementary school teachers and explores the features of relevant pedagogical reading via analysis of four prospective elementary school teachers’ identification processes with two case descriptions. The identification here relates to the reading of the so-called true stories; prospective teachers read stories of other prospective teachers from the same teacher education context. We outline the recommendations for the selection of reading material when applying pedagogical bibliotherapy in order to assist prospective teachers’ professional development.

Local script is one of the local wisdoms that must be preserved. Primary school education plays an important role in the preservation of local writing. This study aims to determine the perception of prospective elementary school teachers towards the preservation of local writing. the intended local writing is the Sasambo script in NTB. This research uses a combined method. Data collection using questionnaires and interviews. The results of the questionnaire were analyzed using descriptive statistics. Interview results were analyzed qualitatively. This study involved the University of Mataram PGSD students as respondents. The problems studied include: how is the motivation of prospective teachers in preserving local writing? What do prospective teachers do in preserving local writing? What are the difficulties experienced by prospective teachers in preserving local writing? The results showed that the motivation of prospective elementary school teachers in preserving local writing was still quite high. However, prospective teachers have difficulty in preserving local writing. Difficulties faced by prospective teachers include: local writing is rarely used, low community interest in learning, lack of teachers, lack of facilities and infrastructure, lack of literature, low awareness and low literacy. Efforts to preserve local writing by prospective elementary school teachers include: studying local writing, conducting training, and holding competitions. Local writing preservation programs in NTB need attention. The attention of prospective teachers, the government and the community can save local writing from extinction

Epistemological beliefs refer to an individual’s thinking and beliefs about the nature of knowledge and knowing. The present study examined two research questions: (1) how do prospective elementary teachers’ epistemological beliefs in science change as a result of instruction specifically designed to improve their epistemological beliefs and (2) what role does the conceptual ecology for epistemological beliefs play in their development? The study was correlational with a sample of 161 prospective elementary teachers (148 female, 13 male). Self-report questionnaires tapping four dimensions of epistemological beliefs (certainty-simplicity, justification, source, attainability of truth) were given to prospective elementary teachers at two time points during an introductory science course. Results indicated that prospective elementary teachers became more sophisticated in their beliefs across all four dimensions of epistemological beliefs. It was found that one component of conceptual ecology for epistemological beliefs, thinking dispositions, was related to the development of epistemological beliefs. Prospective teachers with high thinking dispositions developed more sophisticated beliefs in comparison to prospective teachers with low thinking dispositions.

The history and philosophy of science course is among the very important courses for prospective teachers in terms of understanding the development of science, evaluating its social and cultural context, developing scientific thinking skills, and better understanding and teaching scientific knowledge. Studies on this subject are important in terms of teaching planning and development. This research aimed to examine prospective teachers’ opinions, attitudes and practices towards the history and philosophy of science course. The study group, conducted within the scope of a special case study, consists of 54 prospective teachers studying at a state university in different programs in the 2020-2021 academic year. An opinion form prepared by taking expert opinions, the history of science attitude scale and lesson plans prepared by prospective teachers were used as data collection tools. Additionally, semi-structured interviews were conducted and recorded with six prospective teachers. The data obtained from the opinion form, interviews and lesson plans were analyzed qualitatively and codes, categories and themes were created. The findings obtained were interpreted and supported by direct quotations. The data obtained from the attitude scale was analyzed with the SPSS program. The findings revealed that the attitudes towards the history and philosophy of science course were generally positive, the course content was sufficient, and the prospective teachers found the course fun, interesting, intriguing, and very useful in terms of questioning and developing different perspectives. In line with the results obtained, suggestions were made to educators and researchers.

Having cognitive competence in mastering learning theory and designing learning is one of the important competencies for prospective teachers to have. The description of prospective teacher competence is important for lectures to follow up. One approach to learning in mathematics is Realistic Mathematic Education (RME). RME is a student-centered approach to learning mathematics adopted from the Netherlands and holds to the principle that mathematics is a human activity. This learning approach has been implemented massively in the last few decades in Indonesia and has had a positive impact so this approach is important to teach. However, there are still many prospective elementary teachers who do not know and understand what and how to implement RME itself. Because of the importance of the cognitive competence that prospective elementary teachers must have regarding this RME approach, further research is needed on this matter. The aim of this study is to describe how the cognitive abilities of prospective elementary teachers on RME approach with the application of cooperative learning. The method used in this study was descriptive qualitative with observation and survey data collection techniques which were analyzed using cognitive levels according to PISA and Anderson on 50 prospective elementary teachers in Yogyakarta State University or in Bahasa Universitas Negeri Yogyakarta (UNY) 4th semester students. The results of this study were that most students had a fairly good theoretical understanding of RME. Although to apply it in learning mathematics requires more training, especially in designing contextual problems and how to evaluate them with various other approaches in learning mathematics.

Introduction A common response when questioning in-service mathematics teachers about their mathematical preparation for teaching is that their college mathematics courses did not adequately prepare them to teach school mathematics because the college courses often failed to connect the mathematics they were learning with the school mathematics that they would be teaching. Though the courses were rich in mathematical ideas, their connections to important concepts in school mathematics were not always explicitly detailed. Several factors contributed to this deficiency, but the most prominent one was the lack of high quality textbooks that identify and explain the critical connections. Without such materials, it is challenging and time consuming for mathematicians, who primarily teach content courses for pre-service teachers and who are typically unfamiliar with school mathematics curricula, to make these critical connections. To help address the need for specialized courses and materials for pre-service mathematics teachers, the Conference Board of Mathematical Sciences, and the Mathematical Association of America (with funding provided by the United States Department of Education), developed the Mathematical Education of Teachers Report(MET) , [2]. It gives a framework for mathematics content courses for prospective teachers that is built on the premise that “The mathematical knowledge needed for teaching is quite different from that required by college students pursuing other mathematics-related professions. Prospective teachers need a solid understanding of mathematics so that they can teach it as a coherent, reasoned activity and communicate its elegance and power.”

Prospective elementary teachers may enter their teacher education program having experienced science more as a collection of definitions and facts than in ways that support rich engagement with scientific phenomena. As a result, their visions of themselves as science teachers may not align with the most recent understandings about how to teach science to support student learning. Science methods courses are settings that have the potential to shift prospective teachers’ visions of science teaching. We used an explanatory sequential mixed methods approach with collection of survey data followed by interviews with selected participants. We analyzed how prospective elementary teachers’ visions of science teaching shifted over the course of a one-semester science methods course and what experiences they felt most influenced their visions of teaching science. We found that the visions of science teaching shifted towards or maintained alignment with the principles of science teaching introduced in the science methods course. Additionally, the prospective teachers identified model science activities and explicit connections between these activities and how students learn science as having influenced them in terms of how they thought about teaching science.

The PISA data results show that computational thinking abilities are still lacking. Computational thinking ability is influenced by gender. This research aims to analyze patterns of computational thinking skills of prospective elementary school teachers based on gender at 8 universities in Indonesia. In this research, the components of computational thinking skills analyzed are abstraction, algorithmic, decomposition, and pattern recognition. This research is a mix method research with research subjects as many as 234 prospective elementary school teachers at 8 higher educational institutions. The instruments used were test and interviews. The data analysis technique used is a quantitative data analysis technique using SEM PLS and for qualitative data analysis using miles and Huberman. The research results show that computational thinking skills are still low on the decomposition and pattern recognition components. Based on the SEM PLS test results, it shows that computational thinking abilities are related to gender. In general, the computational thinking ability of female students is slightly higher in all sub-indicators than men and there are differences in the pattern of computational thinking ability between male and female elementary school teacher prospective. The ability of prospective female elementary school teachers to answer in more detail and more structured, while the answers of male prospective teachers are shorter and less comprehensive. Recommendations for developing computational thinking skills by developing problem-based learning, contextual project-based learning and STEAM based learning.

It is important for students to connect with real life in mathematics courses. The aim of this study is to investigate the activities which are written by prospective primary school teachers in the context of Realistic Mathematics Education. This research is a case study of which data were collected by qualitative methods. The participants of the research included 81 prospective primary teachers who are junior students attended primary teacher department. It was asked them to write an activity suitable for primary mathematics curriculum by considering Realistic Mathematics Education principles. They were given one month to write the activities. The activities written by prospective teachers analyzed by descriptive methods in terms of learning domains, types of context and principles of Realistic Mathematics Education. Totally 36 activities were written by prospective teachers. Based on the analysis, it was observed that not all the contexts were exactly real life contexts. It was determined that prospective teacher could not distinguish routine word problems from real life problems. It can be said that theoretical knowledge of Realistic Mathematics Education is inadequate for writing activities and prospective primary teachers need to practice on writing activities regarding the mentioned theory.

This study aims to determine how prospective elementary teachers' attitudes about technology-based mathematics assessment determine whether there are attitude differences between first and third-year prospective elementary teachers about technology-based mathematics assessment. This research is a comparative study with quantitative methods. The research data was conducted through an online survey, namely a questionnaire using Google Form. The populations of this study were 236 prospective elementary teachers with a sample size of 70 prospective elementary teachers. We use the proportion stratified random sampling technique to select the sample of this study. The results showed that the prospective elementary teachers have good attitudes toward technology-based mathematics assessment. This study also shows no difference between first and third-year prospective elementary teachers' attitudes towards the technology-based mathematics assessment.

Traditional teaching methods have become obsolete in modern society, especially in preparing prospective elementary school teachers to face the challenges of the 21st century. Therefore, a new educational approach is needed that is able to develop globally relevant knowledge, skills, and character values. This study aims to analyze the effect of science, technology, engineering, and mathematics (STEM)-based hybrid learning on the 21st-century skills and character values ​​of prospective elementary school teachers. This study uses a mixed-methods method with an explanatory sequential design, where quantitative data is collected first and then continued with qualitative data to deepen the findings. The sample consisted of 156 students from four universities in Indonesia: Universitas PGRI Yogyakarta, STKIP Majenang, Universitas Islam Sultan Agung, and Universitas PGRI Semarang. The validity of the instrument was tested through expert judgment, while reliability was tested using Cronbach's alpha. The research instruments included an essay test to measure critical thinking skills and creativity, as well as a Likert scale questionnaire (1–5) to assess communication, collaboration, and character. Data were analyzed using Multivariate Analysis of Variance (MANOVA), with results showing significant F values ​​for all indicators (Pillai’s Trace = 7.709; Wilks’ Lambda = 8.115; Hotelling’s Trace = 8.344; Roy’s Largest Root = 14.295; p < 0.001), indicating that the hybrid-STEM model has a significant effect on improving 4C skills (critical thinking, creativity, collaboration, and communication) and students’ character values. Surveys and observations also showed a positive response to this model, which was proven to improve conceptual understanding, problem-solving skills, and active involvement in learning. This study recommends strengthening STEM-based learning in higher education as a strategy to produce prospective teachers who excel academically and in character. The limitations of the study lie in the scope of the institution and the number of samples, which are still limited, so it is recommended to conduct further studies with a broader context to strengthen the generalization of the findings.

Features of two lesson study contexts, one with prospective secondary teachers engaged in microteaching lesson study and one with prospective elementary teachers engaged in field experiences, were investigated for providing US prospective teachers with opportunities for growth as teachers of mathematics. In both contexts, the prospective teachers (PTs) exposed their knowledge, beliefs and practices to the scrutiny of peers and other experts, developing and reconsidering their thinking and practices through the shared teaching experiences. Similarities and differences in features of the two contexts are discussed with respect to PT learning. Similarities included the importance of negotiation during teaching cycles as catalysts for PT learning, the value of the cooperative nature of the experiences for sharing varying ideas and perspectives among PTs, the merits of overarching student learning goals for PT lesson planning, and the contributions of the group products (written or oral reports of the lesson study) to the learnercenteredness of the experiences. Differences influencing prospective teacher learning included the extent of focus on mathematics knowledge, extent of focus on classroom processes and management, use of videotaped lessons as part of formative feedback, and participation of knowledgeable advisors during or at the end of the cycles.

ABSTRACTThis research utilized self-study methodology to examine my experience as a novice elementary mathematics teacher educator whose foundation was a high school mathematics teacher and graduate training in secondary mathematics education. By analyzing video data of the weekly mathematics methods course, I relived moments in which I masked my uncertainties through engaging the class in discussion, putting up a wall of defense, and through walking away or leaving the discussion unresolved. However, my perspective of these moments was reframed through stimulated recall interviews with two of the prospective elementary teachers enrolled in the course. Our experiences were similar in terms of our tensions and professional growth, our understanding of mathematical concepts, student thinking, and appropriate instructional practices. The insights from this study raised questions regarding a community of learners among teacher educators and prospective teachers.

ABSTRACTThe aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich insights into the types of mathematical knowledge that a particular item requires and prospective teachers’ difficulties in using these knowledge types. A sample of 52 prospective teachers worked the mathematics test, and 12 of them were interviewed afterwards. The data-sets were complementary: the quantitative data showed that PISA items could be categorized under contextual, conceptual, and procedural knowledge and indicated the most frequent difficulties in the combined contextual, conceptual, and procedural knowledge items. The qualitative data revealed that few prospective teachers could give mathematical explanations for conceptual knowledge items, and that their contextual knowledge was fragmented. Educational implications were discussed.