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The behaviours of the Zinc coating would be subjected to the complex zinc anion, and also the additives, current densities and compositions of electroplating bath. In this study, the complex agents (anise aldehyde and Lugalvan P) were added into the electroplating bath to improve the anti-corrosion ability and inhibit dendritic structure on zinc coating. The Lugalvan P is added into the electroplating bath to inhibit dendritic structure during electroplating. The anise aldehyde and complex zinc ions plate a smooth zinc coating. Moreover, the crystalline structures of zinc coating analyzed by X-ray diffraction analyzer (XRD) and the surface morphology of zinc coating was observed by the scanning electron microscope (SEM). The results show that the Lugalvan P additive forms the relatively highest flatness, which inhibited the dendritic structure. High electroplating efficiency was achieved of current intensity of 3 A cm-2, and a smoothness and gloss deposited surface could be obtained. With increasing the deposition current density, it can form a better zinc coating with low plating bath resistance to form a higher anti-corrosion zinc plate.

Previous research has analyzed the meaning and value of STEM education and explored both its current possibilities and future development. However, STEM education experts have not reached a consensus on the goals of STEM education, making its promotion more challenging. Thus, this study examined which particular STEM education goals should be emphasized through a survey questionnaire. The study employed a stratified random sampling method to collect survey data from secondary teachers of STEM-related courses (i.e., science, technology, and mathematics) in Taiwan. A total of 645 valid survey responses were collected and then analyzed by independent t-test and analysis of variance to examine teachers' perceptions about 17 critical competencies proposed as education goals relevant to STEM education. The findings revealed that STEM teachers generally had positive attitudes and high levels of acceptance toward implementing the 17 proposed STEM education goals through integrative STEM education. However, the proposed goal of "cultivating students' entrepreneurial capabilities" received lower scores and should not be used at the secondary level. It may be introduced as an important education goal in tertiary STEM education. In addition, STEM teachers with different backgrounds (e.g., STEM teaching experience, perceptions of STEM teaching methods) perceived the competency goals as having different levels of importance in STEM education. Teachers' willingness to teach STEM using a transdisciplinary integration method increases when they have access to sufficient resources and support.

This study explored mathematics teachers' reasoning regarding their instructional design for technology use in teaching mathematics. Various types of qualitative data were obtained and analysed from a sample of 19 secondary and 28 primary preservice teachers. The findings showed that the purposes of technology use, teachers' conceptions of mathematics and its learning, their learning experience and knowledge of student thinking as well as mathematical cognition, and empirical inquiry were the main sources of teacher reasoning. Three levels of teacher reasoning were identified: descriptive, explanatory, and justifying. Our findings contributed to research on teacher professional development by identifying four types of technology use with a variety of pedagogical purposes, and formulating two main dimensions to characterise the three levels of teacher reasoning.

This study investigated whether the three variables of task form, squares carried, and figural complexity, for designing cube folding tasks, affect sixth graders' cube folding performance. Two task forms were used to develop two versions of "cube folding test." Each version was designed based on two levels of squares carried and three levels of figural complexity, and contained 18 multiple-choice items. The sample included 107 boys and 92 girls with an average age of 12.04 years who were randomly assigned to complete one of the two versions. A linear mixed model was carried out with three factors: task forms, squares carried, and figural complexity, in which squares carried and figural complexity were "within-subjects" factors, and task form was the "between-subjects" factor. The results showed the interaction effect of squares carried and task form, and the main effect of figural complexity, which differentiated the difficulty in cube folding tasks.

Based on an enactivist perspective on learning mathematics, we articulate three key processes of designing mathematics-grounding activities (MGAs) where students' mathematical thinking can be motivated and shaped with the interactions between their enactments and the evolving tasks in the activities. Then, evaluation criteria and design steps will be derived in terms of the key processes. The key processes of designing MGAs, the criteria for evaluating quality MGAs and the design steps also emerged from the reciprocal relationships between theories and practices in the context of the Just Do Math (JDM) program. The processes and steps of designing MGAs suggested in this article can benefit researchers and educators to develop original activities for advancing the learning of mathematics in line with the enactivist perspective. Additionally, the key processes can be further referred to for explanations of how metaphorical grounds of mathematics can emerge under systemic interactions between learners, tasks and social contexts, and how learners' motivation is integrated into the evolving tasks. Criteria could be applied for not only evaluating the potential of MGAs but also for identifying the weaknesses needed to be modified.

In this paper we report the results of a study in which we investigated how formal education and shadow education in Taiwan provide students opportunities to learn mathematics. Based on the conceptual framework of Opportunity to Learn (OTL), aspects specific to formal education, including mathematics curriculum, mathematics textbooks, and teachers' competence, and their teaching, were reviewed. Two national projects identified under shadow education were examined. The results revealed significant features of the mathematics curriculum, textbook design, and the quality of mathematics teachers in Taiwan that constitute a lived space where teachers with their knowledge and beliefs, curriculum, textbooks, and school settings, can generate cognitive and affective learning outcomes in students. Further analyses of the two above-mentioned projects showed how Taiwan extended learning opportunities to motivate students to learn and understand school mathematics. Based on the review, challenges were also identified.

To solve mathematical modelling problems, students must translate real-world situations, which are typically presented in text form, into mathematical models. To complete the translation process, the problem-solver must first understand the real-world situation. Therefore, reading comprehension can be considered an essential part of solving modelling problems, and fostering reading comprehension might lead to better modelling competence. Further, ease of comprehension and involvement have been found to increase interest in the learning material, and thus, improving reading comprehension might also increase interest in modelling. The aims of this study were to (a) determine whether providing students with reading comprehension prompts would improve the modelling sub-competencies needed to construct a model of the real-world situation and their interest in modelling and (b) analyze the hypothesized effects in two different educational environments (Germany and Taiwan). We conducted an experimental study of 495 ninth graders (201 German and 294 Taiwanese students). The results unexpectedly revealed that providing reading comprehension prompts did not affect the construction of a real-world model. Further, providing reading comprehension prompts improved students' situational interest. The effects of providing reading comprehension prompts on the construction of a real-world model were similar in Germany and Taiwan. Students' interest in modelling improved more in Germany. An in-depth quantitative analysis of students' responses to reading prompts, their solutions, and their interest in the experimental group confirmed the positive relation between reading comprehension and modelling and indicated that the reading comprehension prompts were not sufficient for improving reading comprehension. Implications for future research are discussed.

This review study synthesises the literature on how computational thinking (CT) and mathematical thinking (MT) are integrated into mathematics education research with a focus on tasks. A review of 28 relevant articles on the Web of Science Core Collection database indicated that (1) CT helps students develop and apply mathematical concepts and competence using software or programming; (2) MT helps students solve problems in CT, not necessarily including programming; (3) a reciprocal relationship between CT and MT embeds CT into mathematics learning, where CT is involved in problem-solving, and MT is developed to improve student performance on debugging or reflection; (4) tasks rarely involve creative thinking for creating computational artefacts in CT practices; and (5) tasks rarely involve critical thinking for constructing viable arguments and critiquing the reasoning of others in MT practices. Subsequently, features (including relationship, entry, and what to do) of tasks for integration between CT and MT are proposed.

The values of mathematics in STEM education have become an issue that needs to be considered by mathematics educators. To address this issue, this qualitative study explores four Indonesian high school mathematics teachers' values of the relationships between mathematics and integrated STEM education. The phenomenography research approach was adopted as this study investigated participants' perceptions of the relationship between mathematics and integrated STEM education. The primary research tool was semi-structured interviews. To analyze the data, qualitative content analysis was performed using an abductive thematic approach. Three main findings were obtained in this study: (1) there were three categories of teachers' orientations of the values of the relationships between mathematics and STEM education: core, peripheral, and reciprocal; (2) there were six types of values of STEM education for mathematics education: application, integration, interest, performance, usefulness, and implementation; and (3) there were four types of values of mathematics education for STEM education: resolvable, supported, modellable, and thinkable. Additionally, it was interesting to see the teachers' different perspectives on the importance of highlighting mathematics in STEM education. Three teachers agreed that mathematics should be displayed explicitly, while one teacher believed that STEM activities are more successful if mathematics is only implicitly included. The findings and discussions contribute to the further design of an instrument to measure a variety of teachers' values of mathematics in STEM education.

Students' negative affective performance in mathematics learning is a global problem, and the situation is especially challenging in high-achieving East Asian countries. Taiwan's Just Do Math (JDM) program was launched to resolve this problem and to serve as an example of successful scaling up with regard to implementation of innovation. We developed a framework consisting of a synthesis of the literature on essentials for successful implementation and for scaling up, and applied this framework for the purpose of identification of the factors contributing to the success of the JDM program. The identified factors include the following: the development of low-complexity sources for teachers' use and the low degree of adaptation required to sustain fidelity; the consideration of characteristics of adopters to promote innovation outside schools; construction of communication channels to ensure the dissemination of the core ideas of JDM; the feedback mechanism through which participating teachers can acknowledge the relative advantages of innovation as realized in the program; the consideration of the influence of historical, social, political, and economic factors on program implementation; and the efforts to ensure teachers' in-depth learning, acknowledgment of the promoted principles, and the sustainability of implementation through implementation of JDM activities in regular mathematics classes.

This article develops an analytical framework for analysing college (tertiary) statistics textbooks in terms of text accessibility by integrating the text, the reader, and the content into the framework. Five accessibility attributes of science texts were adapted to conceptualize the accessibility of statistics texts. For each accessibility attribute, two components were proposed by referring to the literature on the readability of mathematics texts as well as the characteristics of statistics. The feasibility of the framework is demonstrated by analysing sample statistics texts. The contributions and potential of the framework are discussed.

Possessing the mathematical competence to encounter the challenges under globalisation and the ubiquity of digital technology is an important goal of education. Herein, we propose a broad conceptual framework for understanding and developing mathematical competence. The framework comprises four non-overlapping but interlinked cores: "learning," "knowing," "applying," and "viewing." Our framework encompasses ontological, epistemological, and pedagogical dimensions based on a multi-dual perspective. The proposed framework serves as a foundation for generating different learning paths to develop mathematical competence. Examples of learning paths are provided to illustrate the correlative and complementary relationships among the cores of mathematical competence.

Mathematization is critical in providing students with challenges for solving modelling tasks. Inadequate assumptions in a modelling task lead to an inadequate situational model, and to an inadequate mathematical model for the problem situation. However, the role of assumptions in solving modelling problems has been investigated only rarely. In this study, we intentionally designed two types of assumptions in two modelling tasks, namely, one task that requires non-numerical assumptions only and another that requires both non-numerical and numerical assumptions. Moreover, conceptual knowledge and procedural knowledge are also two factors influencing students' modelling performance. However, current studies comparing modelling performance between Western and non-Western students do not consider the differences in students' knowledge. This gap in research intrigued us and prompted us to investigate whether Taiwanese students can still perform better than German students if students' mathematical knowledge in solving modelling tasks is differentiated. The results of our study showed that the Taiwanese students had significantly higher mathematical knowledge than did the German students with regard to either conceptual knowledge or procedural knowledge. However, if students of both countries were on the same level of mathematical knowledge, the German students were found to have higher modelling performance compared to the Taiwanese students in solving the same modelling tasks, whether such tasks required non-numerical assumptions only, or both non-numerical and numerical assumptions. This study provides evidence that making assumptions is a strength of German students compared to Taiwanese students. Our findings imply that Western mathematics education may be more effective in improving students' ability to solve holistic modelling problems.

This study documented the process of evolution of the continuous design and revision of the tools of a novice mathematics teacher educator--researcher (MTE-R) as he planned and implemented design-based professional development workshops for in-service mathematics teachers in Taiwan. In order to effectively facilitate teachers designing and implementing their own conjecturing activities during the workshops, the MTE-R fostered their professional learning and growth through reflection upon students' performance. From the perspective of activity theory, this study examined the evolution of the MTE-R's mentoring activities and tools whose design gradually changed from being based on the literature content toward being learner-centered activities with teachers as learners. Such evolution not only enhanced teachers' learning outcomes, but also facilitated the MTE-R's own professional growth in different areas, including mathematics, mathematics learning, mathematics teaching, teacher education, and, in particular, the extrapolation of generic examples for understanding mathematical concepts.

This study explored the perspectives of mathematics teacher educator-researchers (MTE-Rs) on the use of theory in facilitating teacher growth. We adopted the framework of the theory-centered scholarship triangle (Silver & Herbst, 2007) to probe the underlying meanings of perspectives on theory use expressed by MTE-Rs. Qualitative analysis revealed three distinct types of perspectives: a perspective focusing on research, a perspective focusing on practice, and a perspective on the connection between research and practice. For the perspective on the connection between research and practice, two sub-categories were identified: connection with consideration of context and that without consideration of context. Different perspectives that MTE-Rs possess may influence their actions taken in professional development and consequently influence teachers' learning of theory. Specifically, the cyclic process of decontextualizing and recontextualizing theory between research and practice domains is the key to the development of MTE-Rs' educative power so that they can better facilitate teachers in learning theory.

This study investigates one issue related to reading mathematical texts by presenting a two-dimensional framework for assessing reading comprehension of geometric construction texts. The two dimensions of the framework were formulated by modifying categories of reading literacy and drawing on key elements of geometric construction texts. Three categories of reading mathematical texts were recognized and then cross-tabulated with three key elements of geometric construction texts to create a nine-category assessment framework, which was used to design an instrument. After reporting on the validation of the instrument, we conclude by discussing the implications of the framework for assessing students' reading to learn mathematics and for improving the learning of geometric constructions by reading.

The new-type stainless steel–concrete–carbon steel double-skin tubular (SCCDST) members, characterized by their exceptional corrosion resistance and mechanical bearing capacity, have promising applications in ocean engineering, particularly in deep-water engineering. The external hydraulic pressure and interfacial action of various materials intensify the complexity of composite performance of SCCDST members. This paper describes an analytical investigation on the concentric compressive performance of SCCDST members under external hydraulic pressure. The full-range mechanism, including load–displacement response, bearing capacity contribution, and contact pressures, was investigated through the finite element (FE) model that was validated by the failure mode, bearing capacity, and response of axial load versus strain. Subsequently, influences of key geometric–physical parameters were analyzed, e.g., diameter-to-thickness ratios (Do/to, Di/ti), material strengths (fyo, fyi, and fc), hollow ratios (χ), and water depths (H). Typical results indicate that: the initial active confinement action derived from the hydraulic pressure can enhance the interfacial contact pressure and axial compression capacity of SCCDST members due to the tri-axial compression state; the enhancement of confinement effect is mainly from the interfacial interaction between outer stainless steel tube and concrete infill; influence of water depth on bearing capacity cannot be ignored, e.g., the bearing capacity of an SCCDST member with larger hollow ratio (χ = 0.849) is not enhanced under a higher hydraulic pressure (H = 900 m) because of the cross-sectional buckling failure risk. Finally, a modified method considering the effect of water depth was proposed and verified for SCCDST members under hydraulic pressure. [ABSTRACT FROM AUTHOR]

This article reports the results of a mixed-methods approach to develop and validate an instrument to measure Indonesian pre-service teachers' conceptions of statistics. First, a phenomenographic study involving a sample of 44 participants uncovered six categories of conceptions of statistics. Second, an instrument of conceptions of statistics was developed on the basis of findings from the phenomenographic study. The instrument was initially piloted with 63 participants. Subsequently, an exploratory factor analysis involving 116 participants, followed by a confirmatory factor analysis involving 232 participants, was executed, suggesting a three-factor structure. In addition, three different types of conceptions of statistical data were identified from the integration of qualitative and quantitative studies. Contributions of the study and implications of the findings for further research and statistics education are discussed.

Previous research has revealed that teaching self-efficacy could play a critical role in engaging students in integrated STEM education; however, teachers' multiple identities in STEM education (i.e. implementers, disseminators, and designers) and their commitment with respect to the different identities have not been considered and examined. This study aimed to investigate STEM teachers' self-efficacy and commitment as implementers, disseminators, and designers, and to explore the relationships between teachers' self-efficacy and commitment with respect to the three identities. 629 secondary STEM teachers completed a questionnaire that included the items of teachers' background information and 46 items to measure their self-efficacy and commitment with respect to the three identities. To compare the differences in teacher self-efficacy and commitment with respect to the three identities, repeated measures analyses of variance were used. A mixed-model analysis was conducted to examine the effects of both identity and experience with self-efficacy as a covariate on teacher commitment. Also, the structural equation modelling (SEM) method was employed to investigate the structural relationships within and between teacher self-efficacy and commitment with respect to the three identities. The results indicated that STEM teachers' self-efficacy and commitment were influenced by their identities as well as their STEM teaching experience. STEM teachers' self-efficacy and commitment to being implementers and designers were significantly higher than their self-efficacy and commitment to being disseminators. Additionally, the results of structural equation modelling indicated that teachers' self-efficacy for the three identities was highly related, as was their commitment to the three identities. Self-efficacy of being disseminators had the largest impact on teacher commitment to being disseminators, designers and implementers. The results highlight the importance of researching STEM teachers' multiple identities, and suggest that STEM teachers' different identities lead to different levels of self-efficacy and commitment. [ABSTRACT FROM AUTHOR]

This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic tool. The results show that Taiwanese textbooks intended to develop the object through the variation among the levels of generality as well as between more and less familiar connections. The procedural diagrams were less provided than the conceptual diagrams, and the diagrams required more processing were less provided than the diagrams required less processing. Nonetheless, there were differences among the three textbooks. On the basis of similarities and differences, we discuss issues related to the learning and teaching of mathematics.

In this study, we aimed at examining Indonesian In-Service primary Teachers' Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK) for teaching ratio and proportion. The instruments were administered to 271 in-service primary teachers with various education background. There were three underlined factors on MCK and MPCK instrument classified by item analysis and factor analysis. Three teachers' categories (Good, Middle, and Low) were established by cluster analysis methodology. The most teachers' challenge on MCK was figural representation. For MPCK, Indonesian teachers need more opportunity to learn the factor of Knowing students conceptual understanding. The state of teachers' MCK and MPCK and related components are worthy to suggest the design of Indonesian In-service Teachers Professional Development Program.

This paper aims to explore the educative power of an experienced mathematics teacher educator-researcher (MTE-R) who displayed his insights and strategies in teacher professional development (TPD) programs. To this end, we propose a framework by first conceptualizing educative power based on three constructs--communication, reasoning, and connection--and then we extend the conceptualization with another two dimensions: the reciprocal facilitator-learner relationships involving educators, teachers, and students, as well as a bridge between research and practice. Based on both self-study and case-study approaches, we further elaborate features specific to the MTE-R's educative power which includes communication using an approach of creating educative phenomenology, reasoning by mapping teachers' ideas onto emergent models to solve problems in educative challenges, and connection between research and practice by coordination. In particular, the core of the educative power that supported the MTE-R to initiate at-the-moment actions was his insights into the essence of mathematics, and the learning of students and teachers. We believe that the conceptual framework in this study offers a powerful tool that could guide the analyses of educative power, especially for those studies related to the initiation of at-the-moment actions and the implementation of TPD programs.

In this study, we developed an instrument for assessing teachers' mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher's MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences. Teachers' responses were analyzed by factor analysis and cluster analysis. The MCK instrument was found to have good acceptability in the reliability analysis with 3 factor components--"meaning of proportional and non-proportional situations," "number structures in situation," and "figural representation"--which was the main result of the study. With respect to the 3 factors, the teachers in the 3 assigned categories ("Good," "Middle," or "Low") showed consistent performance on the items of the 3 factors. In particular, our results indicated that Indonesian in-service primary teachers had difficulty with the factor on figural representation, but they performed best on number structures in situation representing products of proportional reasoning.

This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and epistemological beliefs in the literature. We also conducted a survey of 22 mathematics teachers who responded to open-ended questions for comparing and justifying the findings from the interview data. We found that the characteristic features of the categories and dimensions of these teachers' conceptions were different from those in the relevant literature. All of the mathematics teachers' conceptions of school mathematics, school statistics, and their differences could be identified by these categories and dimensions as reflected by their characteristic features. We discuss our findings and their implications for further research and teacher education programs.