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Abstract: Abstract The present study investigated if the argument-driven inquiry (ADI) model with embedded explicit-reflective teaching of NOSI improved pre-service science teachers’ (PSTs) comprehension of the nature of scientific inquiry (NOSI). The study employed the qualitative experiment method with 16 PSTs. The PSTs working in small groups conducted seven ADI laboratory activities. During the activities, NOSI aspects were made explicit, and reflective discussions were conducted to provide the PSTs with opportunities to discuss and deepen their understanding of NOSI. A Views About Scientific Inquiry questionnaire and follow-up interview were applied to understand participants’ understandings about NOSI before and after the instruction. The PSTs displayed a promising understanding about NOSI before the instruction. Some of the PSTs already had informed views on some NOSI aspects before the instruction, and “inquiry process is instructed by the question” was the most well-known aspect of NOSI. After the instruction, the PSTs developed their views on almost every aspect of NOSI. The most well-understood aspects of NOSI were that “scientific research all starts with a question” and “no single scientific method.” The results provided evidence that the PSTs performed significantly better after the ADI laboratory instruction with embedded explicit-reflective teaching of NOSI. PubDate: 2022-06-01
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Abstract: Abstract The purpose of this study is to investigate how languages in a multilingual classroom come to participate in the objectification process in the context of pattern generalization. Data came from the transcription of 10 videotaped sessions in grade 7. A mixed quantitative-qualitative approach was adopted for the analysis. The significance of triadic dialog (teacher initiation – student response – teacher feedback) (Sinclair & Coulthard, 1975) as the dominant mode of interaction and the multilingual nature of language were presented as unique aspects of classroom talk in this study. The multilingual classroom (teacher and students) repertoire, which includes aspects of colloquial Arabic and English, was a resource of meaning-making for objectification in different generalization level episodes during classroom talk. Crucial words in home language played various roles in the process of objectification. The teacher and students used colloquial Arabic to refer to deictic means, adverbs of generative action, and pronouns in addition to other linguistic functions. Those linguistic means prove to be central to the process of objectification. The study analyzes three episodes. The first two episodes present how the teacher and students used code-switching and colloquial Arabic for various functions in almost all utterances to objectify near generalization tasks. The third episode focuses on how languages come to participate in the objectification process in a far generalization task. The findings show that natural movements between languages helped in the objectification process of generalization. The findings also show that the relational, diverse, stratified, and agentive aspects of languages helped in the objectification process during various generalization level episodes. PubDate: 2022-06-01
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Abstract: Abstract In this article, we examine how 10th graders make use of different intertwined representations when solving algebraic word problems. It is structured in a quantitative phase, with 61 students and a subsequent follow-up case study with nine pairs of students. We found that drawings and tables, used as auxiliary representations within variants of the algebraic solving method, were useful in the construction of situation and/or problem models. However, this did not entail a higher rate of correct solutions, because students made errors in the subsequent conversion to equations due to misconceptions about the notion of equation. Teaching implications are discussed. PubDate: 2022-06-01
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Abstract: Abstract The study aims to analyze student responses to chemistry constructed response items to obtain detailed information on science NAEA (National Assessment of Educational Achievement) in South Korea and to draw suggestions for enhancing curriculum, teaching, and learning. For this purpose, we analyzed 7444 answers that could be generalized as 1.29% of the 9th grade students by the two-stage stratified cluster sampling method. The types of answers to constructed item were classified, and the response rate distribution curve according to the achievement score for each achievement level was drawn and analyzed. In this way, analyzing the descriptive answers is an advantage of the constructed response items; that is, students’ responses vary widely, and they can systematically analyze the various types of misconceptions they have. As a result, students at the basic level tended to have misconceptions about the quantity of thermal energy, whereas students above proficient level had misconceptions about thermal equilibrium. Therefore, both the understanding and misconceptions of students differed according to achievement levels, so customized teaching and learning based on achievement levels should be developed. And the implications for curricula and improvement of teachers’ expertise in assessment of constructed items are suggested. PubDate: 2022-06-01
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Abstract: This research explored the interrelationship among Taiwanese high school students’ conceptions of learning science (COLS), self-regulated learning science (SRLS), and science learning self-efficacy (SLSE). A total of 309 students participated in the study, and the self-report survey data were collected to measure these three constructs. Four COLS factors (Testing, Calculating and practicing, Application, and Understanding and seeing in a new way), two SRLS dimensions (Preparatory SRLS [task definition, goal setting, planning] and Enactment SRLS [controlling, monitoring, reflecting]), and two SLSE factors (Conceptual understanding and Higher-order cognitive skills), which adhere to the cognitive learning dimensions, were included for analysis. The results revealed a direct relationship between Testing and SLSE without going through any of the SRLS constructs. However, no direct relationship was built among other COLS components and the two SLSE dimensions. There are direct relationships among Calculating and practicing, Application, and the two SRLS constructs, but Understanding and seeing in a new way solely links to Enactment SRLS and not to Preparatory SRLS. In the end, the two SRLS constructs are directly associated with the students’ SLSE dimensions. These results have the important implication that learners’ COLS have a significant impact on their SRL engagement, which eventually leads to their beliefs about their cognitive abilities in learning the abstract concepts and critical thinking tasks in science. PubDate: 2022-06-01
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Abstract: Abstract In this article, we describe a case study that was conducted within a study aiming to diagnose grade 5 students’ concept images of parallelograms. The theoretical framework that we adopted for this study was that of concept definition–concept image as reported by Tall and Vinner (Educational Studies in Mathematics 12:151–169, 1981), a theory that is widely used in mathematics education. The occurrences during our interviews with one of the first students that we interviewed led us to identify a need to extend this theory. This manuscript suggests to add two new constructs to the theory of concept definition–concept image: missing concept images and mis-in concept images. Missing concept image defines a situation in which an example of a concept is erroneously categorized as a non-example of the concept. Mis-in concept image is the somewhat complementary case, in which a non-example of the concept is mis(takenly) in(cluded) in the set of examples of the concept and consequently this non-example is erroneously identified as an example of the concept. In this manuscript, we introduce these two constructs. We also describe two possible sources of students’ decisions regarding their ways of sorting figures into examples and non-examples of parallelograms that were detected during the interviews. To the best of our knowledge, these sources were not reported in the related literature. PubDate: 2022-06-01
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Abstract: Abstract Canonical coherence occurs when subject matter in school is organized to align with the logical structures of an academic discipline. Even though it is highly desired, this condition is an assumption that must be empirically tested, which was the rationale behind our examination of the coherence of topics from middle-school (grades 7–9) integrated science textbooks from Taiwan and Korea. We wanted to determine if textbooks here were able to present science in a way that made it conceptually easier for students to learn and the means whereby coherence was achieved. Based on a list of “standard” science topics from Third International Mathematics and Science Study (TIMSS) research, our comparative study found that while the number of science topics varied by grades and region, their total numbers did not differ significantly. Both regions also focused strongly on physical science topics based on textbook page coverage even as different topics were emphasized (or not). In Taiwanese textbooks, topics were strongly grouped by disciplines in each middle-school grade (a specialist approach) whereas topics from the three main science disciplines were dispersed within each middle-school grade over an academic year in Korea (a generalist approach). Coherence of topics in both regions was found to be supported through a mix of desirable upper triangular patterns within the main science disciplines as well as buttress topics that develop disciplinary ideas over time. The results from our study can create greater awareness of the significance as well as challenges of achieving canonical coherence of topics in science textbooks, especially with respect to integrated science subjects that are extremely common worldwide. PubDate: 2022-06-01
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Abstract: Abstract In this qualitative study, the researchers explored the ways in which 21st-century skills (specifically communication and critical thinking) are enhanced by Grade 10 beginner Physical Sciences teachers while teaching Particulate Nature of Matter (PNM) through the implementation of problem-based learning (PBL). The study was conducted in one of the four educational districts of the North West province, South Africa. The district was selected due to its geographical proximity and accessibility to the researchers. Two participants were purposively selected from two rural government secondary schools. Research instruments for the study comprised an open-ended questionnaire and a reflective portfolio. The data were analyzed manually using Saldaña’s model and Smith et al.’s assessment rubric. The findings show that PBL enhances communication and critical thinking skills. It is recommended that a teacher professional development (TPD) training program be presented for beginner Physical Sciences teachers which targets the formulation of PBL problems, the promotion of 21st-century skills (communication and critical thinking), and the implementation of PBL in other topics in Chemistry. PubDate: 2022-06-01
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Abstract: Abstract This article explores three attributes of teachers’ understanding of fraction magnitude: the accuracy and reasonableness of teachers’ estimations in response to fraction arithmetic tasks as well as the alignment of the estimation strategies they used with the concept of fraction magnitude. The data were collected from a national sample of mathematics teachers in grades 3–7 in which fraction concepts were taught (N = 603). The results indicated the teachers’ estimations were only partially accurate and reasonable, particularly when fraction division was involved. Furthermore, teachers’ credentials and the grade level at which they taught mathematics were significantly related to teachers’ understanding of fraction magnitude. PubDate: 2022-06-01
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Abstract: Abstract Network analysis is a topic in secondary mathematics education of growing importance because it offers students an opportunity to understand how to model and solve many authentic technology and engineering problems. However, very little is known about how students make sense of the algorithms typically used in network analysis. In this study, I used the Hungarian algorithm to explore how students make sense of a network algorithm and how it can be used to solve assignment problems. I report the results of a design-based research project in which eight Year 12 students participated in a teaching experiment that spanned four 60-min lessons. A hypothetical learning trajectory was developed in which students were introduced to the steps of the Hungarian algorithm incrementally. The results suggest that students made sense of the intermediate steps of the algorithm, the results of those steps, and how the algorithm works to solve assignment problems. The difficulties that students encountered are also discussed. PubDate: 2022-06-01
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Abstract: Abstract Growing research evidence indicates student learning gains from guided representation construction/invention in school science and mathematics. In this inquiry approach, students address challenges around what features of a phenomenon/problem to attend to, what data to collect, how and why, and make collective judgments about multimodal accounts of phenomena. However, researchers to date have tended to focus on student learning rather than on the teacher’s role in guiding various phases of inquiry. In this paper we report on (a) analysis of Grade 1 students’ engagement in interdisciplinary mathematics and science inquiry practices in a classroom sequence in ecology; (b) the teacher’s role in guiding such inquiry; and (c) interpretation of these practices in terms of support of student transduction (connecting and remaking meanings across representations in different modes). Data from our study included video capture of two case study teachers’ guidance of tasks and classroom discussion and student artefacts. We examine the classroom processes through which the teachers used students’ invention and revision of data displays to teach the concepts of living things, diversity, distribution and adaptive features related to habitat in science. Mathematical processes included constructing and interpreting mapping, measurement and data modelling, sampling and using a scale. The analysis offers fresh insights into how teachers support student learning in these two subjects, through discrete stages of orienting, representation challenge, building consensus and applying and extending representational systems. PubDate: 2022-05-18
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Abstract: Abstract This cross-national study examined students’ evaluation of strategies for solving linear equations, as well as the extent to which their evaluation criteria were related to their use of strategies and/or aligned with experts’ views about which strategy is the best. A total of 792 middle school and high school students from Sweden, Finland, and Spain participated in the study. Students were asked to solve twelve equations, provide multiple solving strategies for each equation, and select the best strategy among those they produced for each equation. Our results indicate that students’ evaluation of strategies was not strongly related to their initial preferences for using strategies. Instead, many students’ criteria were aligned with the flexibility goals, in that a strategy that takes advantages of task context was more highly valued than a standard algorithm. However, cross-national differences in strategy evaluation indicated that Swedish and Finnish students were more aligned with flexibility goals in terms of their strategy evaluation criteria, while Spanish students tended to consider standard algorithms better than other strategies. We also found that high school students showed more flexibility concerns than middle school students. Different emphases in educational practice and prior knowledge might explain these cross-national differences as well as the findings of developmental changes in students’ evaluation criteria. PubDate: 2022-05-16
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Abstract: Abstract This report focuses on the ways in which 36 Grade 4 students recognized, explained, described, and employed variation during interviews conducted 1 month after participating in STEM-based activities in which they tested, adjusted, and re-tested catapults. An inductive thematic methodology was used for analysis of the interview transcripts to capture the ways in which students discussed their analyses and justified their conclusions from the activity. The results were based on 1080 instances of variation in student responses to the interview questions, which evidenced three ways students characterized variation: contextual variation, specific variation, and general variation. Findings point to the essential nature of context in building statistical understanding in relation to both specific and general aspects of variation as well as decision-making in that context. PubDate: 2022-05-14
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Abstract: Abstract Mathematical literacy is a keystone of contemporary mathematics education research. We collectively, thoroughly explore this set of literacy practices from the perspectives of mathematical writing and mathematical discussion. Mathematical literacy practices, of course, include a third component—reading—which takes a number of forms. This document explores the mathematical reading processes of 22 middle school students, identifying the strategies most and least used by these students, and the ways in which strategy implementation aids their reading process. From this study, we can begin to identify how this knowledge can be used by teachers, curriculum designers, and educational researchers in an effort to aid their students. PubDate: 2022-05-14
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Abstract: Abstract The history of science (HOS) has played an important role in science curricula for teaching about science. However, historical information in science textbooks is often de-contextualized, coupled with limited class time and teaching barriers, and thus fails to help students understand the dynamic process of scientific development. This research effort was then directed to design nontextbook, supplemental reading materials that include scientific historical vignettes and guiding questions to elicit views about nature of science (NOS). The homework notebook was designed as a carrier to provide students after-school learning opportunities with the HOS-NOS approach. In the large-scale implementation study, 18 middle school homeroom teachers voluntarily adopted the designed HOS-based notebook for the regular purpose of homework recording and teacher-parent communication over a semester. They were interviewed about homework policies. Their students’ scientific epistemological beliefs and individual interests in science and reading were assessed at the beginning and end of the semester to evaluate the effectiveness of the notebook. Quantitative results indicated that these 7th and 8th grade students had significant improvements in epistemic understandings of the source and the (un)certainty of scientific knowledge after using this notebook. Students’ individual interest in science and reading was interrelated with their epistemic views about the evolving nature of science and justification methods in science. Further explorations on the quality of students’ reflective writings in the notebook suggested that students’ reading experiences were affected by the homework policies and writing requirements their homeroom teachers adopted. This research provides implications on the design of reading materials for improving students’ scientific literacy. PubDate: 2022-05-12
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Abstract: Abstract Literacy, specifically reading mathematical text, is an essential component of developing deep mathematical understanding. Given the role that textbooks play in classroom instruction around the globe, it is useful to consider how features of curriculum design might influence classroom practice related to reading. Results from studies of a curriculum series in which reading mathematics is an embedded design feature provide insight on teachers’ and students’ perceptions on the importance and frequency of reading in mathematics and on the strategies used. The results have implications for curriculum developers as they design mathematics textbooks. PubDate: 2022-05-12
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Abstract: Abstract We examined widely used popular calculus textbooks to explore opportunities to learn the limit concept. Definitions, worked problems, and exercise problems were coded to examine if these tasks allow students to use informal thinking to coordinate domain and range processes to understand the infinite process of limit. Results revealed many exercise problems are step 1 tasks in genetic decomposition, where students only need to evaluate a function at one point. Such tasks prevent students from using their informal thinking productively. Recommendations and implications to calculus students and instructors are also mentioned. PubDate: 2022-05-06
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Abstract: Abstract In high school geometry, proving theorems and applying them to geometry problems is an expectation for students. An essential part of most geometry proofs is the diagram because it not only helps encapsulate the claim being proved but can also be a tool in reasoning or communicating an argument. This interview-based study investigated how high school students interpret and use diagrams during the process of proving geometric claims. Particular attention is given to the semiotic resources such as symbols, visuals, and gestures that students employ in relation to the diagrams. Study participants were nine students from grades 10 to 12 and data was collected through one-on-one task-based clinical interviews with tasks that varied with regard to diagrammatic features. The findings suggest that, in general, some visual resources such as drawing a new figure occurred regularly in particular tasks such as tasks that did not adhere to the typical diagrammatic register or that had unknown truth values. Gesturing with justifications were the most frequently used proving actions in all tasks. Moreover, in all valid proof arguments produced by students, they engaged in all three semiotic resources (symbols, visuals, and gestures). PubDate: 2022-05-04
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Abstract: Abstract The present study aims to describe and characterize the insights of elementary school students during the collaborative solving of mathematics problems. A total of 10 elementary school 60-min math classes were analyzed, with each session documented by videotaping the interaction of groups of 3 to 6 children. The study included 41 students in total (14 boys and 27 girls aged from 7 to 10). Group interaction was analyzed by taking spontaneous insights as queues. The results distinguish full insight—where students suddenly discover the answer to the problem—from partial insight—where students realize they have been following an incorrect procedure. Data shows that most insight takes place during interaction and not individually. An in-depth description of such insights shows a junction between the semantic content in verbal explanations and proto-symbolic content involved in gestures. The described insights also show in situ emergence of joint rhythmicity among participants. Results suggest that it is possible to clearly identify insight in spontaneous interaction among school children. PubDate: 2022-05-03
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Abstract: Abstract Recent research on teacher education has highlighted the importance of teachers’ noticing of students’ mathematical thinking. Much remains unknown about the ways in which teachers develop noticing abilities in professional development settings. This study examines changes in teachers’ noticing in the context of peer discussions in a video club. The study identified critical incidents of noticing, ranging from attending and interpreting to deciding on pedagogical responses. Furthermore, the study divided attending in the noticing framework into selecting and recognizing. Findings indicate that peer discussions about a video showing students’ statistical variability reasoning catalyzed change in teachers’ attending. Other catalysts include (1) participants’ assumption of the proposer role in the video club, (2) participants’ peers as the coadjacent speakers, and (3) participants’ use of an analytical framework as professional knowledge. The study discusses the ways in which participants’ individual focal components of noticing emerge and develop through a video club as professional development. PubDate: 2022-05-02
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