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1.
In the present study, we describe a participating student’s (Carol’s) distributive partitioning scheme and operations along with Steffe’s and his colleagues’ studies about children’s constructions of fraction knowledge as a particular model of mathematical learning. Analysis of Carol’s mathematical behaviors indicates that an operationally common mathematical behavior (distributive partitioning operation) was revealed in various mathematical problem situations such as fraction multiplication, fraction division, and multiplicative transformation between fractional quantities. It both provides a rationale for why becoming versed in one mathematical subject could facilitate working with another mathematical subject and also implies the necessity of describing and defining students’ mathematical behaviors from an operational view of knowledge, which might lead to building foundations of a substantial cognitive map for students’ mathematical development. 相似文献
2.
AbstractThe talking behaviors of college students enrolled in teacher training were assessed in weekly discussion groups. Students were randomly assigned to (1) a student record (SR) condition in which he recorded his own and one other group member’s initiated responses, (2) a leader record (LR) condition in which his initiated responses were recorded by the leader with the subject’s knowledge, or (3) a control condition (CC) in which the leader recorded surreptitiously. Results for subjects initially classified as reticent indicated a significant difference between LR and CC treatments. Further, SR subjects not only made more responses than LR or CC students, but increased across treatment weeks as well. 相似文献
3.
Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content knowledge, horizon content knowledge and specialised content knowledge, have been used to describe aspects of such knowledge. Purpose: This paper proposes a model for teacher knowledge in mathematics that embraces and develops aspects of earlier models. It focuses on the notions of contingent knowledge and the connectedness of ‘big ideas’ of mathematics to enact what is described as ‘powerful teaching’. It involves the teacher’s ability to set up and provoke contingent moments to extend children’s mathematical horizons. The model proposed here considers the various cognitive and affective components and domains that teachers may require to enact ‘powerful teaching’. The intention is to validate the proposed model empirically during a future stage of research. Sources of evidence: Contingency is described in Rowland’s Knowledge Quartet as the ability to respond to children’s questions, misconceptions and actions and to be able to deviate from a teaching plan as needed. The notion of ‘horizon content knowledge’ (Ball et al.) is a key aspect of the proposed model and has provoked a discussion in this article about students’ mathematical horizons and what these might comprise. Together with a deep mathematical content knowledge and a sensibility for students and their mathematical horizons, these ideas form the foundations of the proposed model. Main argument: It follows that a deeper level of knowledge might enable a teacher to respond better and to plan and anticipate contingent moments. By taking this further and considering teacher knowledge as ‘dynamic’, this paper suggests that instead of responding to contingent events, ‘powerful teaching’ is about provoking contingent events. This necessarily requires a broad, connected content knowledge based on ‘big mathematical ideas’, a sound knowledge of pedagogies and an understanding of common misconceptions in order to be able to engineer contingent moments. Conclusions: In order to place genuine problem-solving at the heart of learning, this paper argues for the idea of planning for contingent events, provoking them and ‘setting them up’. The proposed model attempts to represent that process. It is anticipated that the new model will become the framework for an empirical research project, as it undergoes a validation process involving a sample of primary teachers. 相似文献
4.
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. 相似文献
5.
AbstractIn this article I described the means of identifying teaching behaviors that have cognitive and affective learning effects on students who are taking a course in mathematics. This study was conducted on 50 mathematics teachers who were teaching in the eighth grade. I obtained the data on teaching behaviors through direct systematic observation. Multiple regression was used as the method of analysis. For the cognitive domain, the results showed that effective teaching behaviors are: (a) high-level questions put to a large group of students; (b) probing, followed by a correct student response; (c) teacher waiting after asking a question; (d) successful redirecting; and (e) all forms of positive acknowledgement. Effective teaching behaviors in the affective domain are: (a) all forms of teacher lecture/explanations; (b) probing, followed by correct student response; and (c) all forms of positive acknowledgement. More teaching behaviors have a positive effect on mathematical knowledge than have a positive effect on students’ attitude toward mathematics. 相似文献
6.
AbstractSexuality has an essential part in human lives and can be affected by changes in one’s health status. Since the nursing profession delivers holistic care for patients, nurses must have the knowledge and skills to deliver care concerning sexuality. Evidence from the professional literature demonstrates that nurses do not address sexuality care consistently, mainly due to different factors such as lack of knowledge, skills, and cultural attitudes. This study’s purpose was to learn about the factors that affect nursing students’ willingness to grasp the nurse’s role as a sexuality educator in practice prior to establishing a specified course in sexual education for BSN students. A quantitative study was conducted in a college at the center of Israel, with a convenience sample of nursing students in a BSN program ( n?=?214). The research tool was a questionnaire designed to assess the knowledge, attitudes, and willingness of nursing students to practice sexuality education in the future. The study’s approach was based on Ajzen’s Theory of Planned Behavior. Results indicated that self-efficacy is the main mediator between attitudes and intentions. There is a need to reinforce nursing student’s self-efficacy on the subject to increase their intention to practice it in the future. 相似文献
7.
AbstractAs part of Middle Tennessee State University’s (MTSU’s) initiative to improve retention of at-risk STEM majors, they recruit first-time, full-time freshman STEM majors with mathematics ACT scores of 19 to 23 to participate in MTSU’s “Mathematics as a FirstSTEP to Success in STEM” project (FirstSTEP). This article overviews MTSU’s FirstSTEP research approach and demonstrates that introductory, early research experiences can be successful for mathematics projects. At the end of their freshman year, mathematics students can develop a foundation to conduct mathematical research, increase depth of content knowledge, and build confidence in their technical abilities. 相似文献
8.
The activity of reasoning-and-proving is at the heart of mathematical sense making and is important for all students’ learning as early as the elementary grades. Yet, reasoning-and-proving tends to have a marginal place in elementary school classrooms. This situation can be partly attributed to the fact that many (prospective) elementary teachers have (1) weak mathematical (subject matter) knowledge about reasoning-and-proving and (2) counterproductive beliefs about its teaching. Following up on an intervention study that helped a group of prospective elementary teachers make significant progress in overcoming these two major obstacles to teaching reasoning-and-proving, we examined the challenges that three of them identified that they faced as they planned and taught lessons related to reasoning-and-proving in their mentor teachers’ classrooms. Our findings contribute to research knowledge about major factors (other than the well-known factors related to teachers’ mathematical knowledge and beliefs) that deserve attention by teacher education programs in preparing prospective teachers to teach reasoning-and-proving. 相似文献
9.
AbstractWe present a first-hand, longer-term account of one student’s (Christine’s) experiences in and after a mathematics inquiry course. In this course, students actively posed problems, conducted their own mathematical explorations, and wrote journal entries about their experiences. During the course, Christine found that inquiry helped her develop mathematical content knowledge and a deeper understanding of the nature of research. After the course, Christine became a mathematics education faculty member in a mathematics department and reports that the course impacted the way she teaches mathematics. This provides an illustrative case of the potential long-lasting benefits of an inquiry course. 相似文献
10.
Abstract Curriculum design might appear to be a project for a pure educational theory. An example of such a theory is Paul Hirst's deduction of distinct forms of knowledge’ upon which rests his advocacy of the liberal curriculum’. Hirst's theory, though immune to many of the attacks that have been directed at it, fails to consider how (if at all) the structure of knowledge maps on to the structure of our mental (learning) faculties. The partitioning of the manifold of knowledge may correspond not at all to the optimum curricular partitioning of the teaching manifold. Further, as a curriculum proposal, Hirst's account needs to be underwritten by an account of the purpose of education. Accounts of the latter sort normally invoke considerations of a political nature. Such considerations, together with the influence of other forces, tend to pull curricula in directions which many educationalists regard as undesirable. Can pure educational theory reassert itself as the controlling force behind curriculum planning? I argue that there is little prospect of its so doing. 相似文献
11.
ABSTRACTBackground: In Slovakia, no relevant information is available about the scientific literacy levels achieved by secondary school students. Purpose: The objective of the research was to identify the levels of scientific literacy among students in the last year of grammar school and examine to what extent this determined the subject chosen for a school-leaving exam, which is related to a student’s personal preferences, as well as to the student’s profile and preparation for university education. Sample: The research sample consisted of 221 students from 17 grammar schools located in various regions of Slovakia. Design and methods: To identify the level of scientific literacy, we applied the Test of Scientific Literacy Skills. Results: The students achieved the lowest success rate in the skill focused on the identification of the research design elements and its strengths and weaknesses. A comparably low success rate was also observed in the skill focused on the justification of the conclusions based on quantitative data. Other difficulties were identified in the field of understanding the basics of statistics, thus indicating an insufficient level of mathematical literacy of the students in the abovementioned field. By contrast, the highest success rate was achieved in the skill focused on the correct application of the scientific results for social purposes. Conclusions: At the end of secondary school studies, the scientific literacy among Slovak students is at the average level. No differences were observed in terms of gender. In terms of the subjects chosen by the students for their school-leaving exams, we observed that those students who took a school-leaving exam in Biology or Chemistry achieved significantly better results in the test. By contrast, the students who reported on Geography and Civics as the subject of their school-leaving exam achieved significantly worse results in the test. 相似文献
12.
AbstractIn this paper, we present a collaboration project within one urban Puerto Rican classroom, focused on constructing a critical literacy inquiry curriculum grounded in the students’ out-of-school literacy practices in their communities, including their experiences with media and popular culture. We focused on a critical literacy and media inquiry unit centered on the students’ self-selected subject of the telenovela. Here, we examine one student’s work to highlight two overarching findings: (1) the visibility of the students’ complex understanding of the media landscapes in telenovelas, particularly the construction of dominant social discourses across telenovela worlds, and (2) the ways that bringing children’s mediatized cultural imaginaries in their creative work supports an approach to literacy in classrooms, where explorations of discourses of power emerge from the students’ knowledge. In order to articulate how children actively examine and construct discourses across multiple social worlds, we examine these findings using the Four Resource Model, and elements of discourse analysis, as theoretical and analytical frameworks, focusing on the construction of identities, worlds and meanings in relation to the social discourses of telenovelas. 相似文献
13.
Adaptability refers to the capacity to adjust one’s thoughts, behaviors, and emotions in order to manage changing, new, or uncertain demands. Although preliminary research has highlighted its relevance for positive student outcomes, there remain several important empirical questions to be examined. In particular, research on adaptability has used domain-general measures (i.e., not tied to a particular domain such as a school subject) and has focused only on self-reports of adaptability (not, for example, reports by significant others). The aim of the current study was to advance knowledge of adaptability by addressing these gaps. We examined students’ domain-specific adaptability in mathematics as reported by students themselves and by their mathematics teachers ( n = 371). We examined the extent to which the two reports of mathematics adaptability are associated with students’ mathematics engagement, mathematics achievement, and literacy achievement (the latter a test of discriminant validity). Well-known covariates were included as controls (e.g., gender, prior achievement). Results revealed that student-reported adaptability predicted students’ mathematics engagement. Moreover, student-reported and teacher-reported adaptability uniquely predicted mathematics achievement. In terms of discriminant validity, (mathematics-based) student and teacher reports of adaptability were not associated with students’ literacy achievement. Together, findings advance knowledge of the adaptability construct, including providing preliminary evidence of domain-specificity and the complementary nature of self- and teacher-reports for assessing adaptability. Implications for practice are discussed. 相似文献
14.
According to the big-fish-little-pond effect (BFLP) model, high individual academic performance in a particular subject is related to high self-concept in that subject, whereas high average classroom performance has a negative effect on self-concept. In the present study, data from Finnish primary school students in grade 3 (504 students), grade 4 (487 students), and grade 6 (365 students) are used to examine whether the assumptions of the BFLP effect model hold already in primary school. Furthermore, we examined gender differences in BFLP effect. The results showed that as expected students’ high performance in literacy and in mathematics was related to high self-concept in the same subject. Support for the negative classroom effect was small and it depended on the school subject and student’s gender. That is, a high average classroom performance already in grade 3 had a negative but small effect on boys’ self-concept in mathematics. In literacy and among girls, only little support was found for the negative classroom effect. 相似文献
15.
In order to teach mathematics effectively, mathematics teachers need to have a sound mathematical knowledge, but what constitutes sound mathematical knowledge for teaching is subject to debate. This paper is an attempt to unpack what constitutes teacher knowledge of the concept of a function which is a unifying idea in the mathematics curriculum. The central components of the framework, which will be elaborated on in this paper, are: teachers’ subject matter knowledge, teachers’ pedagogical content knowledge, teachers’ technological pedagogical knowledge, technological content knowledge, and technological pedagogical content knowledge in relation to the concept of a function. The framework is informed by Shulman’s (Educational Researcher 15:4–14, 1986) Types of Teachers Knowledge Framework, Ball, Bass &; Hill 29:14–17, 20–22, 43–46 (2005) Mathematical Knowledge for Teaching Framework, and Mishra &; Koehler’s (Teachers College Record 108:1017–1054, 2006) Technological Pedagogical Content Knowledge (TPACK) framework. 相似文献
16.
In order to teach mathematics effectively, mathematics teachers need to have a sound mathematical knowledge, but what constitutes sound mathematical knowledge for teaching is subject to debate. This paper is an attempt to unpack what constitutes teacher knowledge of the concept of a function which is a unifying idea in the mathematics curriculum. The central components of the framework, which will be elaborated on in this paper, are: teachers’ subject matter knowledge, teachers’ pedagogical content knowledge, teachers’ technological pedagogical knowledge, technological content knowledge, and technological pedagogical content knowledge in relation to the concept of a function. The framework is informed by Shulman’s (Educational Researcher 15:4–14, 1986) Types of Teachers Knowledge Framework, Ball, Bass & Hill 29:14–17, 20–22, 43–46 ( 2005) Mathematical Knowledge for Teaching Framework, and Mishra & Koehler’s (Teachers College Record 108:1017–1054, 2006) Technological Pedagogical Content Knowledge (TPACK) framework. 相似文献
17.
ABSTRACTThis study aimed to explore the features of mobile learning behaviors among Chinese elementary school students, and relationships between mobile learning behaviors and personal characteristics in mobile learning environment. The current study designed and developed a game-based educational mobile environment and conducted an experimental research. Eighty-three elementary students participated in this study. The results revealed the features of elementary school students’ mobile learning behavior including: 1) the students had reasonable login frequencies and learning time duration with appropriate guidance from the teachers, and satisfying learning performance by self-learning; 2) higher grade, learning style with active information processing and higher test scores in the conventional Chinese subject course had positive impacts on the mobile learning behaviors, but no gender difference was found. Regrettably, students showed more digital consuming than digital creating in the current study. The results could provide necessary suggestions on mobile learning for young learners. 相似文献
18.
AbstractThis paper describes the use of Mathematics Action Research Projects (ARPs) as a capstone experience in lieu of a Master’s Thesis in a Master’s program for in-service secondary teachers. The ARPs include two primary components: (i) each teacher participant conducts mathematical research that is new to them on a topic that is connected in some way to the material they teach in one of their classes; and (ii) each teacher participant also creates an in-class innovation related to the mathematical research they have been doing, and implements it in their own classroom. Ten teacher participants have completed such ARPs with the author over the last 3 years. In completing their ARPs, teacher participants not only learn how to conduct mathematical inquiry themselves, but also most often choose to implement some kind of inquiry-based classroom innovation that allows them to share some of this experience with their own students. This course structure has had the effect of encouraging teachers to decide to try more inquiry-based teaching methods, and at the same time, has given them the knowledge and tools to be successful in doing so. 相似文献
19.
Over the years, a variety of frameworks, models and literacies have been developed to guide teacher educators in their efforts to build digital capabilities in their students, that will support them to use new and emerging technologies in their future classrooms. Generally, these focus on advancing students’ skills in using ‘educational’ applications and digitally-sourced information, or understanding effective blends of pedagogical, content and technological knowledge seen as supporting the integration of digital resources into teaching, to enhance subject learning outcomes. Within teacher education institutions courses developing these capabilities are commonly delivered as standalone entities, or there is an assumption that they will be generated by technology’s integration in other disciplines or through mandated assessment. However, significant research exists suggesting the current narrow focus on subject-related technical and information skills does not prepare students adequately with the breadth of knowledge and capabilities needed in today’s classrooms, and beyond. This article presents a conceptual framework introducing an expanded view of teacher digital competence (TDC). It moves beyond prevailing technical and literacies conceptualisations, arguing for more holistic and broader-based understandings that recognise the increasingly complex knowledge and skills young people need to function ethically, safely and productively in diverse, digitally-mediated environments. The implications of the framework are discussed, with specific reference to its interdisciplinary nature and the requirement of all faculty to engage purposefully and deliberately in delivering its objectives. Practical suggestions on how the framework might be used by faculty, are presented. 相似文献
20.
This paper is a part of an extensive project on the role of intuitive rules in science and mathematics education. First, we described the effects of two intuitive rules ‐‐ ‘Everything comes to an end’ and ‘Everything can be divided’ ‐‐ on seventh to twelfth grade students’ responses to successive division tasks related to mathematical and physical objects. Then, we studied the effect of an intervention, which provided students with two contradictory statements, one in line with students’ intuitive response, the other contradicting it, on their responses to various successive division tasks. It was found that this conflict‐based intervention did not improve students’ ability to differentiate between successive division processes related to mathematical objects and those related to material ones. These results reconfirmed that intuitive rules are stable and resistant to change. Finally, this paper raised the need for additional research related to the relationship between intuitive rules and formal knowledge. 相似文献
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