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1.
Interpreting and responding to student thinking are central tasks of reform-minded mathematics teaching. This study examined preservice teachers’ (PSTs) interpretations of and responses to a student’s error(s) involving finding a missing length in similar rectangles through a teaching scenario task. Fifty-seven PSTs’ responses were analyzed quantitatively and qualitatively. Analysis results revealed that although the student’s errors came from conceptual aspects of similarity, a majority of PSTs identified the errors as stemming from procedural aspects of similarity, subsequently guiding them by invoking procedural knowledge. This study also revealed two different forms of address and teaching actions in PST interventions along with three categories of acts of communication barriers. The broader implications of the study for international communities are discussed in accordance with the findings.  相似文献   

2.
This study investigated eight prekindergarten teachers’ underlying assumptions about how children learn, and how these assumptions were used to inform and enact instruction. By contextualizing teachers’ knowledge and understanding as it is used in practice we were able to provide unique insight into the work of teaching. Participants focused on children’s ability to remember information, frequently through engagement and repetition. Teachers also anticipated what children would be learning in the early elementary years and taught that content, yet they did not necessarily expect children to remember the information, or even know if children learned the information. Implications for the design of both preservice and in-service teacher education are discussed. This includes helping teachers develop a strong foundational understanding of how children learn, establishing the pedagogical content knowledge relevant to teaching advanced symbol systems like literacy, and shifting pedagogical reasoning about practice. Given the link between the quality of instructional support and learning in the early years, developing the early childhood teaching force’s capacity to use knowledge to reason skillfully about teaching offers a critical lever for creating robust learning in the early years.  相似文献   

3.
This research analyses preservice teachers’ knowledge of fractions. Fractions are notoriously difficult for students to learn and for teachers to teach. Previous studies suggest that student learning of fractions may be limited by teacher understanding of fractions. If so, teacher education has a key role in solving the problem. We first reviewed literature regarding students’ knowledge of fractions. We did so because assessments of required content knowledge for teaching require review of the students’ understanding to determine the mathematics difficulties encountered by students. The preservice teachers were tested on their conceptual and procedural knowledge of fractions, and on their ability in explaining the rationale for a procedure or the conceptual meaning. The results revealed that preservice teachers’ knowledge of fractions indeed is limited and that last-year preservice teachers did not perform better than first-year preservice teachers. This research is situated within the broader domain of mathematical knowledge for teaching and suggests ways to improve instruction and student learning.  相似文献   

4.
Experimentation is a complex problem-solving process. In biology lessons, experiments involve creative thinking and open discovery; however, they still require some degree of instructional guidance. The right balance between discovery learning and instructional guidance depends substantially on students’ prior knowledge. Students with low prior knowledge in particular might have difficulties with conducting and understanding experiments. Incremental scaffolds might be a valuable tool to meditate between pure discovery and strong guidance while simultaneously taking learners’ individual knowledge and skills into account. In the current study, we examined the effects of incremental scaffolds (IncSc), no scaffolds (NoSc), and worked-out examples (WoEx) on students’ knowledge acquisition while doing inquiry-based experimentation with a special focus on students with low prior knowledge. In a pre-posttest design, 193 students (Mage?=?13.02?±?0.81 years) participated in a four-hour teaching unit on animals’ overwintering strategies. In the pre- and posttest, we assessed the students’ conceptual and procedural knowledge. Our results partially confirmed our hypotheses: Regarding the conceptual and procedural knowledge of all students, incremental scaffolds showed no additional benefit regarding students’ knowledge in the posttest when compared to working with no scaffolds or worked-out examples. For the students with low prior knowledge, working with incremental scaffolds led to higher conceptual and procedural knowledge after the teaching unit than working with worked-out examples.  相似文献   

5.
ABSTRACT— This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based approaches to understanding the ways in which children become proficient in mathematics. Task analysis indicates that executive cognitive functions likely operate in concert with procedural and conceptual knowledge and in some instances might act as a unique influence on mathematics problem-solving ability. It is concluded that consideration of the executive cognitive demand of mathematics can contribute to research on best practices in mathematics education.  相似文献   

6.
Besides viewing knowledge about the nature of science (NOS) as important for its own value with respect to scientific literacy, an adequate understanding of NOS is expected to improve science content learning by fostering the ability to interrelate scientific concepts and, thus, coherently acquire scientific content knowledge. However, there is a lack of systematic investigations, which clarify the relations between NOS and science content learning. In this paper, we present the results of a study, conducted to investigate how NOS understanding relates to students’ acquisition of a proper understanding of the concept of energy. A total of 82 sixth and seventh grade students received an instructional unit on energy, with 41 of them receiving generic NOS instruction beforehand. This NOS instruction, however, did not result in students having higher scores on the NOS instrument. Thus, correlational analyses were performed to investigate how students’ NOS understanding prior to the energy unit related to their learning about science content. Results show that a more adequate understanding of NOS might relate to students’ perspective on the concept of energy and might support them in understanding the nature of energy as a theoretical concept. Students with higher NOS understanding, for example, seemed to be more capable of learning how to relate the different energy forms to each other and to justify why they can be subsumed under the term of energy. Further, we found that NOS understanding may also be related to students’ approach toward energy degradation—a concept that can be difficult for students to master—while it does not seem to have a substantive impact on students’ learning gain regarding energy forms, transformation, or conservation.  相似文献   

7.
This study examined the effectiveness of 3 curriculum interventions focused on strengthening children’s ability to solve area measurement problems and explored the instructional perspectives of the instructor who implemented the interventions. The interventions involved various degrees of emphasis on area measurement and knowledge of 2-dimensional geometry. Participants were 131 fourth graders, recruited from a city in northern Taiwan, and 1 instructor. The results confirmed the effectiveness of an enriched curriculum integrating knowledge of 2-dimensional geometry in enhancing children’s conceptual understanding of area measurement. The group that received the enriched curriculum outperformed the other groups that received the curricula stressing only 2-dimensional geometry or numerical calculations for area measurement in solving the area problems requiring mathematical judgments and explanations. The curriculum also facilitated children’s reasoning in distinguishing between the perimeter and area of a rectangle, which required higher-order mathematical thinking. Interview data revealed that approximately all children from the 3 intervention groups could identify the mathematical subject-matter components highlighted in the curricula. Interviewees tended to consider the use of formulae to solve area measurement problems to be important, despite some differences in learning gains among the 3 groups. In interviews, the participating instructor revealed a change of perspective regarding the importance of offering students opportunities for manipulation and geometric operations when teaching area measurement, prompted by curriculum enactment.  相似文献   

8.
In evaluating teachers' instructional decisions during instruction, it is clear that the nature of their elicitation is crucial for student learning. When instructional decisions are informed by information about students' conceptual understanding, significant learning is possible. This article examined the elicitation practices of two high school science teachers who indicated that they made instructional decisions based on the elicited evidence of students' knowledge but whose elicitation practices were characteristic of low-level elicitation. The teachers focused on students' responses that used canonical terms and expressed acceptable knowledge. The teachers demonstrated low-level responsiveness because they did not have full access to students' knowledge. The elicited evidence of students' knowledge that was used in making instructional decisions was not representative of students' conceptual understanding. There was, thus, a mismatch between the teachers' perspectives about their formative assessment practice and what is considered effective formative assessment.  相似文献   

9.
This study investigated preservice elementary science teachers’ (PSTs) informal reasoning regarding socioscientific issues (SSI), their epistemological beliefs, and the relationship between informal reasoning and epistemological beliefs. From several SSIs, nuclear power usage was selected for this study. A total of 647 Turkish PSTs enrolled in three large universities in Turkey completed the open-ended questionnaire, which assessed the participants’ informal reasoning about the target SSI, and Schommer’s (1990) Epistemological Questionnaire. The participants’ epistemological beliefs were assessed quantitatively and their informal reasoning was assessed both qualitatively and quantitatively. The findings revealed that PSTs preferred to generate evidence-based arguments rather than intuitive-based arguments; however, they failed to generate quality evidence and present different types of evidence to support their claims. Furthermore, among the reasoning quality indicators, PSTs mostly generated supportive argument construction. Regarding the use of reasoning modes, types of risk arguments and political-oriented arguments emerged as the new reasoning modes. The study demonstrated that the PSTs had different epistemological beliefs in terms of innate ability, omniscient authority, certain knowledge, and quick learning. Correlational analyses revealed that there was a strong negative correlation between the PSTs’ certain knowledge and counterargument construction, and there were negative correlations between the PSTs’ innate ability, certain knowledge, and quick learning dimensions of epistemological beliefs and their total argument construction. This study has implications for both science teacher education and the practice of science education. For example, PST teacher education programs should give sufficient importance to training teachers that are skillful and knowledgeable regarding SSIs. To achieve this, specific SSI-related courses should form part of science teacher education programs.  相似文献   

10.
Although interim assessments are currently promoted as a mechanism for improving teaching and student learning, we know little about how teachers use this data to modify instruction. This article presents findings from a larger study on teachers’ use of interim assessment information in elementary mathematics. We address the following questions: (a) How do the Philadelphia teachers in our sample analyze benchmark assessment results, (b) how do they plan instruction based on these results, and (c) what are their reported instructional responses to such results? To answer these questions, we interviewed all 3rd- and 5th-grade teachers in five average- and above-average-performing elementary schools three times during the 2006–07 school year. We found that although the teachers in our study used interim assessment results to gain information about students’ learning in mathematics, teachers did not use interim assessments to make sense of students’ conceptual understanding. Furthermore, teachers’ tendency to interpret student errors as procedural missteps was paralleled by a trend toward procedural instructional responses.  相似文献   

11.
The ability to analyze and understand classroom situations through the eyes of not only teachers but also students can be seen as a crucial aspect of teachers’ professional competence. Even though video case-based learning is considered to have great potential for the promotion of analytical competence of teachers (i.e., becoming immersed in student and teacher perspectives as well as applying conceptual knowledge to better understand classroom situations), only a few studies have investigated the effects of corresponding instructional support. This empirical field study examines the effects on analytical competence of two types of instructional support—hyperlinks to multiple perspectives and hyperlinks to conceptual knowledge—by using a 2 × 2 factorial design in a computer-supported video case-based learning environment inspired by cognitive flexibility theory and participatory design. The study examines collaborative learning processes to discover what specific kind of instruction may help to counteract some of the known deficits of case-based learning and teacher thinking, such as limited perspective-taking. From a participatory design point of view, training novices to become immersed in teacher and student perspectives can be considered as an alternative for direct involvement of teachers and students in the design process. The study was realized as a four-day university course for pre-service teachers (N = 100). ANCOVAs of learning processes (small-group discussions) and outcomes (written case analyses) provide evidence that both types of instructional support (i.e., hyperlinks to multiple perspectives and conceptual knowledge) are beneficial. In particular, hyperlinks to multiple perspectives affected small-group case discussions and written post-tests as they led to increased immersion (i.e., perspective-taking). Hyperlinks to conceptual knowledge furthered the application of this knowledge, especially in the written post-tests. Implications for teacher education, participatory design, and further research are discussed.  相似文献   

12.
Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics.  相似文献   

13.
ABSTRACT

This paper offers pedagogical content knowledge (PCK) rubrics, that is, guides providing criteria for grading that are potentially applicable to a range of science topics and levels of teacher experience. Grading criteria applied in the rubrics are based on qualitative analyses of planned topic-specific professional knowledge (TSPK) and content knowledge (CK). Data were collected via three topic-specific vignettes from 239 pre-service science teachers (PSTs) starting a university-based, full-time, one year teacher education programme in England. The statements were analysed for TSPK and CK. PSTs’ statements proposed instructional strategies comprising demonstrations, explanations, illustrations and analogies, classified as Relevant to the science topics, others Irrelevant. Some Relevant strategies missed an aspect that may, if enacted, help students’ learning, so were judged Incomplete. Statements were also analysed for evidence of relevant and correct CK. CK and TSPK statements are aligned into grids, creating PCK rubrics. These demonstrate the precise nature of knowledge likely to lead to instruction that impacts positively on student learning. The rubrics present the possibility of PCK repertoires that contribute clarity and precision to teaching instruction. Although findings cannot be generalised, the methodology offers a strategy for supporting out-of-field teachers, and those seeking instructional strategies to add to existing repertoires.  相似文献   

14.
Elementary mathematics curriculum materials can serve as a lever for instructional change. In this paper, we promote a particular kind of instructional change: supporting teachers in learning to integrate children’s multiple mathematical knowledge bases (MMKB), including children’s mathematical thinking and children’s home and community-based mathematical funds of knowledge, in instruction. A powerful means of supporting pre-service teachers in integrating children’s MMKB in instruction may be to scaffold teachers’ noticing of potential spaces in elementary mathematics curriculum materials for connecting to children’s MMKB and then developing practices for leveraging these spaces during instruction. We focus on existing and potential spaces in written curriculum materials, or curriculum spaces, so as to better support teachers in enacting curriculum that opens spaces for connecting to children’s MMKB.  相似文献   

15.
This study explored whether pre-service teachers’ (PSTs’) lesson analysis skills during a teacher education course in the country of Turkey were related to their skills of lesson planning. PSTs’ lesson analysis skills during fieldwork were assessed by their attention to and interpretation of student thinking and learning, and how it is influenced by the teachers’ instructional decisions. The PSTs’ lesson analysis scores were significantly and positively correlated with scores in lesson planning task focusing on student thinking. The findings contribute to the literature on whether PSTs’ lesson analysis skills may be transferred to one of the core activities of teaching.  相似文献   

16.
It is considered important for students to participate in scientific practices to develop a deeper understanding of scientific ideas. Supporting students, however, in knowing and understanding the natural world in connection with generating and evaluating scientific evidence and explanations is not easy. In addition, writing in science can help students to understand such connections as they communicate what they know and how they know it. Although tools such as vee-maps can scaffold students?? efforts to design investigations, we know less about how these tools support students in connecting scientific ideas with the evidence they are generating, how these connections develop over time, or how writing can be used to encourage such connections. In this study, we explored students?? developing ability to reason scientifically by examining the relationship between students?? understanding of scientific phenomena and their understanding of how to generate and evaluate evidence for their ideas in writing. Three high school classes completed three investigations. One class used vee-mapping each time, one used vee-mapping once, and one did not use vee-mapping. Students?? maps and written reports were rated for understanding of relevant science procedural and conceptual ideas. Comparisons between groups and over time indicate a positive relationship between improved procedural and conceptual understanding. Findings also indicate that improved procedural understanding preceded improved conceptual understanding, and thus, multiple experiences were needed for students to connect evidence and explanation for science phenomena.  相似文献   

17.
This study examined the relationship among declarative, conceptual, and procedural knowledge in the acquisition of ruler measurement skills. Sixth-grade industrial arts students were taught how to use a ruler with one of two instructional methods; the fractional method was based on an understanding of fractions, whereas the line identification method required no understanding of fractions. Results indicated that the line identification method was superior overall to the fractional method, both for the initial acquisition as well as retention of skills. This superiority occurred for questions measuring understanding of fractions but not for ruler skills, indicating that students were able to use procedural knowledge to infer conceptual knowledge. Results are discussed in terms of several models of learning that address how declarative, conceptual, and procedural knowledge interact in the learning process.  相似文献   

18.
Like their students, teachers may hold a variety of naïve conceptions that have been hypothesized to limit their ability to support students’ learning. This study examines whether changes in elementary students’ conceptions are related to their teachers’ content knowledge, attitudes, and understanding of conceptual change. The study takes place in the context of the adoption of a new unit on seasonal change in which students build and use sundials to observe seasonal differences in the apparent motion of the Sun across the sky. A mixed-method approach is used. Data sources include pre- and post-tests for students and teacher interviews and questionnaires. Results indicate that changes in students’ conceptions may be related to their teachers’ knowledge of the content, attitudes toward science, and understanding of conceptual change. One teacher had low attitude toward science and limited knowledge of conceptual change. After instruction, her students’ responses became less accurate but more homogeneous than before instruction. The other teacher had high attitude and moderate knowledge of conceptual change. Her students showed gains from pre- to post-test, including responses that were more scientifically accurate than the teachers’ initial answers.  相似文献   

19.
This article explores why art education after modernism needs to engage with and assess two forms of knowledge. It distinguishes procedural knowledge or ‘knowing how’ from declarative knowledge or ‘knowing that’, and argues that current classroom practice and more general thinking in art education in the UK confuses evidence of procedural knowledge with evidence for declarative knowledge. A corollary is that assessment evidence for ‘knowing how’, which is shown or demonstrated, is confused with assessment evidence for ‘knowing that’, which requires spoken or written forms of reporting. This conceptual confusion is currently embedded in the national, flagship examination known as the General Certificate of Secondary Education, taken by students at the age of 16, resulting in that examination requiring evidence of understanding the meaning of art in its socio‐historical context while at the same time denying the necessity of written or spoken work to reveal such knowledge. The article advocates a Wittgensteinian, socio‐cultural solution to the confusions of current practice.  相似文献   

20.

This paper explores the nature of prospective teachers’ noticing of students’ understanding as they analyze and discuss middle school students’ understandings of trapezoids in micro-case videos in the context of geometry. In this exploratory study, the data were obtained from eight prospective middle school mathematics teachers through individual video analysis, reflection papers, and group discussions. The results indicated that the use of purposeful micro-case video designs based on prospective teachers’ background knowledge of quadrilaterals allowed them to be productive in video analyses and discussions. In individual video analyses, prospective teachers attended to various mathematical elements to identify students’ responses but did not always use them to make interpretations of each student’s understanding of trapezoid. In the group discussions of the micro-case videos, in contrast, prospective teachers could provide alternative interpretations of students’ understanding by identifying links between the mathematical elements in students’ responses and the characteristics of students’ understandings. In the group discussions, they provided more detailed and specific instructional actions to support each student’s understanding of trapezoid than their individual video analyses. This study suggests practical implications for teacher education programs on how to use video cases (e.g., firstly, working individually and then having group discussions about the videos) to explore prospective teachers’ professional noticing skills. Considering prospective teachers’ background knowledge of related mathematical contents, this study can also inspire future studies on how to design effective videos about students’ mathematical understanding.

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