Development of prospective elementary teachers’ knowledge to teach early algebra through case discussions

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.

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.

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.

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.

Developing algebraic thinking in elementary school has gained consensus among mathematics educators. The objective of this study is to understand the developmental trajectory of early algebraic thinking in elementary school students so as to assist teachers and curriculum developers in implementing instruction that aligns with students' cognitive development. This study adopted a cross-sectional survey approach, involving 526 students from grades three to five in Shanghai, who were tested using a 12-item assessment that measured three aspects: "generalized arithmetic", "functional thinking", and "quantitative reasoning". Latent class analysis was used to analyze students' response strategies, and, in conjunction with individual interviews, this study identified potential developmental pathways in students' early algebraic thinking, progressing from "arithmetic thinking" to "concrete algebraic thinking", "generalized algebraic thinking", and finally to "symbolic algebraic thinking". As thinking levels advanced, significant differences in students' response strategies emerged, with notable improvements in "generalization abilities" and "symbolization abilities". This study suggests that educational practices should encompass content in elementary arithmetic curricula that fosters generalization abilities. Additionally, providing students with opportunities for diverse representations can effectively stimulate the development of early algebraic thinking.

The effects of cooperative and individualistic learning on the achievement and attitudes of prospective elementary school teachers (non-music majors) in a course in music teaching methods were examined. Forty-three American college students were randomly assigned to conditions stratified on the basis of previous musical experience. Cooperation promoted higher achievement than did individualistic efforts on assignments for which each student's grade was affected by the quality of groupmates' work. In addition, students in the cooperative condition were off-task academically (such as walking around the room) less frequently, initiated fewer interactions with the instructor, perceived the instructor to be more supportive, perceived the grading system to be fairer, and perceived the feedback received as being more helpful.

Notwithstanding long term efforts to differentiate between domains of mathematics-related teacher knowledge, there is no doubt that different forms and aspects of teacher knowledge are interrelated and mutually influence each other. However, the nature of this relation is still open to scholarly debate. First, we give an overview of empirical studies that investigated the relation between different domains of mathematics teachers’ knowledge, notably, the domains of “content knowledge” and “pedagogical content knowledge”. We demonstrate that the research on the relationship turns out to be multifaceted and we point to the need of cognitive orientated research on the integration of knowledge domains. Second, we present our own ongoing research on the integration of prospective elementary teachers’ math-specific knowledge domains by describing our use and analysis of task-based interviews. Preliminary findings indicate that our approach can help to identify mental processes that illuminate the integration of math-specific knowledge domains.

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.

This study aims to investigate and compare mathematics teachers’ knowledge of pedagogical content, knowledge of students’ understanding and knowledge of instructional strategies, subcomponents of pedagogical content knowledge, student errors in the relationship between perimeter and areas in rectangles, squares, and parallelograms. 10 pre-secondary school in-service mathematics teachers and 10 prospective mathematics teachers participated in the study. The qualitative case research approach was used. To collect the data, an interview form consisting of four questions showing student errors related to perimeter and area was prepared. The participants were asked to comment on the questions given in the form, and their answers were recorded. Later, they were asked to write down their answers to these questions. According to the outcomes, there is a lack of knowledge of students’ understanding and knowledge of instructional strategies, which are the subcomponents of the pedagogical content knowledge of prospective mathematics teachers. Moreover, prospective teachers are found to be incompetent as regards the necessary mathematical subject matter knowledge. To prevent difficulties, when the concepts of perimeter and area are taught, instead of giving formulae initially, concrete materials or real-life examples about these concepts should be provided. Keywords: pedagogical content knowledge, perimeter, area, mathematics teachers, prospective mathematics teachers.

In this introduction to the Special Issue Early algebraic thinking: studies from different perspectives, approaches and regions we provide readers with the main motivation and interest underlying research on early algebraic thinking. We then introduce the five papers that make up this Special Issue. Each of these studies, coming from various countries around the world, has a different theoretical framework, methodological approach and perspective regarding teachers, students, instructional practices and curricula. In this introduction, we summarize some of the main themes throughout the different papers, including interviewers’ practices that can promote early algebraic thinking; the kinds of practices that teachers can implement to have a positive impact on students’ early algebraic thinking; and the use of physical models to explore and promote aspects of early algebraic thinking. The Special Issue also includes an additional Prospectives piece by Analúcia Schliemann and David Carraher, in which they examine the algebraic thinking research in elementary school in light of the current mathematics standards in the United States.

Teacher quality is one of the most influential factors in student learning. In-depth material knowledge (content) is very important for prospective teachers who will one day become teachers. Thus, analyzing and describing the Content Knowledge (CK) of prospective teachers needs to be done. The purpose of this study is to describe the CK of prospective elementary school teachers (SD/MI) on the material of fractional arithmetic operations. The subjects of this study were three students from Ar-Raniry State Islamic University of Banda Aceh. This research includes qualitative descriptive research, so that the data were analyzed using qualitative data analysis, namely data reduction, data presentation, and drawing conclusions. Data collection in this study was carried out through tests and combined with interviews so that the instruments used were test questions and interview guidelines. The study results indicate that the content knowledge of the three elementary teacher candidates was still weak, there were teacher candidates who did not understand the arithmetic operation hierarchy and still made carelessness in the concept of fractional arithmetic operations.

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.

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

Mathematics achievement in senior high schools (SHS) in Ghana is not encouraging and this has become a concern for major stakeholders. Several studies have been conducted to provide information to understand the issue of poor mathematics achievement. Of all the studies, areas regarding the joint influence of experience, pedagogical content knowledge (PCK) and subject matter knowledge (SMK) have been less explored in Ghana. In this study, the interplay among these variables is examined in an attempt to explain the variances in students’ mathematics achievement. To achieve this purpose, 210 SHS teachers and 8,400 students in SHS across the country were surveyed and subsequently administered tasks on algebra taking into consideration the variables of interest. The study revealed that teacher knowledge and teaching experience significantly influenced students’ mathematics achievement. It was discovered that PCK had a significant indirect effect on students’ mathematics achievement through teachers’ SMK. The findings also showed that experience did not significantly moderate the relationship between teachers’ SMK and students’ mathematics achievement. The study, based on the outcome, made conclusions and recommendations for practice. Suggestions for the implementation of future studies were also highlighted.

This study examines the ways prospective elementary teachers (PSTs) made connections to children’s mathematical thinking and children’s community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that asks PSTs to visit community settings and develop problem solving mathematics lessons that connect to mathematical practices in these settings (Community Mathematics Exploration Module). Using analytic induction, we identified three distinct levels of connections to children’s mathematical thinking and their community funds of knowledge evidenced in PSTs’ work (emergent, transitional, and meaningful). Findings describe how these connections reflected different points on a learning trajectory. This study has implications for understanding how PSTs begin to connect to children’s mathematical funds of knowledge in their teaching, a practice shown to be effective for teaching diverse groups of children.