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1.
This study investigated mathematics teachers' professional knowledge among elementary school teachers exposed to a professional training program that either supported self-regulated learning (SRL) or offered no SRL support (no-SRL). The SRL support was based on the IMPROVE metacognitive self-questioning method that directs students' attention to understanding when, why, and how to solve problems (Kramarski and Mevarech, Am Educ Res J 40:281–310, 2003). Sixty-four Israeli elementary teachers participated in a month-long professional development program to enhance mathematical and pedagogical knowledge. The course was part of a 3-year professional development program sponsored by the Israeli Ministry of Education. This mixed-method study included quantitative assessments of teachers' professional knowledge in mathematical problem solving for an authentic task based on Program for International Student Assessment's framework (Program for International Student Assessment, 2003) and in lesson planning, as well as qualitative interviews and videotaped observations of two teachers. Results indicated that teachers in the SRL program outperformed those in the no-SRL program on various problem solving skills (e.g., reflection and conceptual mathematical explanations) and lesson planning (e.g., task demands and teaching approach). Videotaped observations of actual teaching indicated that the SRL-trained teacher demonstrated more teaching practices that aimed to promote students' understanding and better supported students' regulation of their own learning, compared to the no-SRL-trained teacher. We discuss educational and practical implications.  相似文献   

2.
Recent research efforts (Schmidt et al. in The preparation gap: teacher education for middle school mathematics in six countries, MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical knowledge and pedagogical knowledge. However, identifying the nature of the mathematical knowledge and the pedagogical content knowledge (PCK) required for effective teaching remains elusive (Ball et al. in J Teacher Educ 59:389–407, 2008). Building on the initial conceptual framework of Magnusson et al. (Examining pedagogical content knowledge, Kluwer, Dordrecht, pp 95–132, 1999), we examined the PCK development for two beginning middle and secondary mathematics teachers in an alternative certification program. The PCK development of these two individuals varied due to their focus on developing particular aspects of their PCK, with one individual focusing on assessment and student understanding, and the other individual focusing on curricular knowledge. Our findings indicate that these individuals privileged particular aspects of their knowledge, leading to differences in their PCK development. This study provides insight into the specific aspects of PCK that developed through the course of actual instructional practice, providing a lens for future research in this area.  相似文献   

3.
Preservice science teachers face numerous challenges in understanding and teaching science as inquiry. Over the course of their teacher education program, they are expected to move from veteran science students with little experience learning their discipline through inquiry instruction to beginning science teachers adept at implementing inquiry in their own classrooms. In this study, we used Aikenhead’s (Sci Educ 81: 217–238, 1997, Science Educ 85:180–188, 2001) notion of border crossing to describe this transition preservice teachers must make from science student to science teacher. We examined what one cohort of eight preservice secondary science teachers said, did, and wrote as they both conducted a two-part inquiry investigation and designed an inquiry lesson plan. We conducted two types of qualitative analyses. One, we drew from Costa (Sci Educ 79: 313–333, 1995) to group our preservice teacher participants into one of four types of potential science teachers. Two, we identified successes and struggles in preservice teachers’ attempts to negotiate the cultural border between veteran student and beginning teacher. In our implications, we argue that preservice teachers could benefit from explicit opportunities to navigate the border between learning and teaching science; such opportunities could deepen their conceptions of inquiry beyond those exclusively fashioned as either student or teacher.  相似文献   

4.
This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching—organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five Practices framework (Smith and Stein in Five practices for orchestrating productive mathematics discussions. Corwin Press, Thousand Oaks, CA, 2011) were implemented and studied to examine how prospective elementary teachers set goals, selected and sequenced available student work, and planned questions within a mathematical discussion. We examined prospective elementary teachers’ strengths and weaknesses in these facets through an approximation of practice set in a lesson context familiar to the prospective elementary teachers. Our results demonstrated that although prospective elementary teachers set varying goals for a discussion, their pedagogical choices in planning their discussion tended to be consistent with the goals they have set. These results support the focused development of prospective elementary teachers’ goal setting as an implication for mathematics teacher educators.  相似文献   

5.
This documentary account situates teacher educator, prospective teacher, and elementary students’ mathematical thinking in relation to one another, demonstrating shared challenges to learning mathematics. It highlights an important mathematics reasoning skill—creating and analyzing representations. The author examines responses of prospective teachers to a visual representation task and, in turn, their examination of school children’s responses to mathematical tasks. The analysis revealed the initial tendency of prospective teachers to create pictorial representations and highlights the importance of looking beyond the pictures created to how prospective teachers use mathematical models. In addition, the challenges prospective teachers face in moving beyond a ruled-based conception of mathematics and a right/wrong framework for assessing student work are documented. Findings suggest that analyzing representations helps prospective teachers (and teacher educators) rethink their teaching practices by engaging with a culture of teaching focused on reading for multiple meanings and posing questions about student thinking and curriculum materials.  相似文献   

6.
As teacher educators, we are tasked with preparing prospective teachers to enter a field that has undergone significant changes in student population and policy since we were K-12 teachers. With the emphasis placed on connections, mathematics integration, and communication by the New Generation Science Standards (NGSS) (Achieve in Next generation science standards, 2012), more research is needed on how teachers can accomplish this integration (Bunch in Rev Res Educ 37:298–341, 2013; Lee et al. in Educ Res 42(4):223–233, 2013). Science teacher educators, in response to the NGSS, recognize that it is necessary for pre-service and in-service teachers to know more about how instructional strategies in language and science can complement one another. Our purpose in this study was to explore a model of integration that can be used in classrooms. To do this, we examined the change in science content knowledge and academic vocabulary for English language learners (ELLs) as they engaged in inquiry-based science experience utilizing the 5R Instructional Model. Two units, erosion and wind turbines, were developed using the 5R Instructional Model and taught during two different years in a summer school program for ELLs. We analyzed data from interviews to assess change in conceptual understanding and science academic vocabulary over the 60 h of instruction. The statistics show a clear trend of growth supporting our claim that ELLs did construct more sophisticated understanding of the topics and use more language to communicate their knowledge. As science teacher educators seek ways to prepare elementary teachers to help preK-12 students to learn science and develop the language of science, the 5R Instructional Model is one pathway.  相似文献   

7.
This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, Human Development 52:109–128, 2009) to understand students’ mathematical thinking. This study challenged teachers’ pedagogical assumptions about what it means to teach for student understanding. Clinical task-based interviews opened a window into students’ knowledge, problem-solving and reasoning, and helped teachers reflect on their teaching and assessment of student learning. Teachers also learnt about what it means to establish a culture of thoughtful questioning in the classroom and developed an emerging awareness that this requires a readiness to hear students’ ideas and connect informal or invented strategies with classroom mathematics.  相似文献   

8.
Photovoice is a participatory action research tool that is grounded in the literature for critical consciousness (Wang & Burris, 1997). Four creative high school girls who reported struggles with mathematics were given cameras and asked to take photographs to answer the following questions: (1) What is mathematics? (2) What is your ideal learning environment? (3) What things impede your learning of mathematics? Within-case and cross-case analyses of the photographs and interview responses were conducted. Each individual case was analyzed using the work of Belenky, Clinchy, Goldberger, and Tarule (Women’s Ways of Knowing, 1986) who investigated women’s epistemological perspectives. The girls were either silenced (disconnected from the mathematical knowledge of the teacher), received (lacked confidence to do mathematics independently), or “fragily” subjective (viewed mathematical knowledge as personal rather than imparted by the teacher) knowers of mathematics. The use of photovoice has the power to facilitate the nurturing of silence as it moves toward the “roar which is on the other side of silence” (Belenky et al., 1986, p. 4).  相似文献   

9.
Mathematics educators and writers of mathematics education policy documents continue to emphasize the importance of teachers focusing on and using student thinking to inform their instructional decisions and interactions with students. In this paper, we characterize the interactions between a teacher and student(s) that exhibit this focus. Specifically, we extend previous work in this area by utilizing Piaget’s construct of decentering (The language and thought of the child. Meridian Books, Cleveland, 1955) to explain teachers’ actions relative to both their thinking and their students’ thinking. In characterizing decentering with respect to a teacher’s focus on student thinking, we use two illustrations that highlight the importance of decentering in making in-the-moment decisions that are based on student thinking. We also discuss the influence of teacher decentering actions on the quality of student–teacher interactions and their influence on student learning. We close by discussing various implications of decentering, including how decentering is related to other research constructs including teachers’ development and enactment of mathematical knowledge for teaching.  相似文献   

10.
In the broadest sense, the goal for primary science teacher education could be described as preparing these teachers to teach for scientific literacy. Our starting point is that making such science teaching accessible and desirable for future primary science teachers is dependent not only on their science knowledge and self-confidence, but also on a whole range of interrelated sociocultural factors. This paper aims to explore how intersections between different Discourses about primary teaching and about science teaching are evidenced in primary school student teachers’ talk about becoming teachers. The study is founded in a conceptualisation of learning as a process of social participation. The conceptual framework is crafted around two key concepts: Discourse (Gee 2005) and identity (Paechter, Women’s Studies International Forum, 26(1):69–77, 2007). Empirically, the paper utilises semi-structured interviews with 11 primary student teachers enrolled in a 1-year Postgraduate Certificate of Education course. The analysis draws on five previously identified teacher Discourses: ‘Teaching science through inquiry’, ‘Traditional science teacher’, ‘Traditional primary teacher’, ‘Teacher as classroom authority’, and ‘Primary teacher as a role model’ (Danielsson and Warwick, International Journal of Science Education, 2013). It explores how the student teachers, at an early stage in their course, are starting to intersect these Discourses to negotiate their emerging identities as primary science teachers.  相似文献   

11.
Research on teachers’ professionalism and professional development has increased in the last two decades. A main focus of this line of research has been the cognitive component of teacher professionalism, i.e., professional knowledge. Most of the previous studies on teacher knowledge—such as the Learning Mathematics for Teaching (LMT) (Hill et al. 2004), the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students´ Mathematical Literacy (COACTIV) (Baumert et al. 2010), and the Mathematics Teaching in the 21st Century (MT21) (Schmidt et al. 2007) studies—have been conducted in the field of mathematics teachers’ pedagogical content knowledge (PCK) and content knowledge (CK). There have been few comparable studies conducted with science teachers, especially biology teachers. To fill the gap, this study examines the development and use of instruments to measure biology teachers’ CK and PCK. In particular, this study describes a method to develop reliable, objective, and valid instruments measuring teachers’ CK and PCK in four steps by the use of empirical data of students. Additionally, the study explores whether CK and PCK might be measured as separate knowledge categories by using a paper-and-pencil test. This paper presents a theoretical model that guides test development and provides steps to develop and validate the instruments. Details are also provided regarding the computation of the Rasch scale score measures for 158 biology teachers. The results indicate that the instruments measured teachers’ CK and PCK in an objective, valid, and reliable way. This suggests that the new instruments can be used in combination with classroom observations to examine teaching quality and further its relation to student learning.  相似文献   

12.
How do practicing mathematics teachers continue to develop the knowledge and habits of mind that enable them to teach well and to improve their teaching over time? The question of how (and what) teachers learn lies at the crux of any effort to provide high-quality mathematics teaching for all students. This article reviews 106 articles written between 1985 and 2008 related to the professional learning of practicing teachers of mathematics. We offer a synthesis of this research, guided by Clarke and Hollingsworth’s (Teach Teach Educ 18(8):947–967, 2002) dynamic model of teacher growth. Their model emphasizes the recursive nature of teachers’ learning and suggests that growth in one aspect of teachers’ knowledge and practice may promote subsequent growth in other areas. We report the results in six major areas of teacher learning, identify several crosscutting themes in the literature, and make recommendations for future research aimed at understanding teachers’ professional learning.  相似文献   

13.
Mathematics education researchers have investigated mathematics anxiety in prospective elementary teachers. While many of these studies have focused on the bodily sensations and emotions of mathematics anxiety, particularly those felt in assessment situations, opportunities remain to investigate how prospective elementary teachers interpret their experiences with mathematics anxiety and connect them over time to compose personal histories of mathematics anxiety. Currently, over 90 % of elementary teachers in US schools are women, and women have been shown to suffer more from mathematics anxiety than do men. In this article, I analyze how one woman prospective elementary teacher described, explained, and related her experiences of mathematics anxiety across her personal narratives of learning mathematics as a K-12 student and of learning to teach mathematics as a college student in a teacher preparation program. My research demonstrates that experiences of mathematics anxiety may persist beyond assessment situations to influence women prospective elementary teachers’ larger mathematical histories. I also show that women prospective elementary teachers may interpret mathematics anxiety as specific fears (e.g., loss of opportunities for social participation) and may develop particular coping strategies related to those fears. Finally, I point out that while a coping strategy may be used consistently across K-12 mathematics learning and undergraduate teacher preparation, and may even offer a woman prospective elementary teacher some relief from mathematics anxiety, it may also limit her mathematics learning and professional development. To conclude, I present implications of my research for mathematics teacher educators.  相似文献   

14.
Why are some teachers more effective than others? The importance of understanding the interplay between teacher preparation, pedagogy and student achievement has motivated a new line of research focusing on teacher knowledge. This study analyses the effects of teacher mathematics knowledge on student achievement using longitudinal data from rural Guatemalan primary schools. After presenting a conceptual framework for linking the work of the teacher with student learning in mathematics together with an overview of the different forms of teacher knowledge, the paper introduces the Guatemalan context and the analytical framework including the sample, data and methods. Overall, the results provide some empirical support for a widely held, if infrequently tested, belief in mathematics education: effective teachers have different kinds of mathematical knowledge. The results also suggest specific mechanisms by which effective teachers can make substantial impacts on student learning, even in extremely poor contexts.  相似文献   

15.
The report is a translation of part of a Swedish paper entitled “On Students' Achievement in Mathematics after Finishing Comprehensive School”. The intention of the investigation was to

  • - diagnose the retention of some basic skills in some topics in algebra and geometry,
  • - reveal difficult steps in the learning processes in these topics.
    • Starting with a complicated question, e.g. the equation \(\frac{{3x - 2}}{2} = \frac{x}{3}\) a sequence consisting of 5–15 problems were constructed. Each new problem followed by the preceding one by taking away one or two details. \(\begin{gathered} 3(3x - 2) = 2x \\ {\text{ 9}}x - 6 = 2x \\ {\text{ 7}}x - 6 = 0 \\ {\text{ 7}}x = 6 \\ \end{gathered} \) is an example of a sequence belonging to the equation above. From about 10 complicated problems (“top-items”) and their sequences, in all 130 items, 10 sub-tests were put together in such a way that the pupils who took the test were not aware of the sequences but found no connection between the problems. Many surprising results were found, e.g., that the students scored higher on 14/(x+2)=2 than on 4/x=3, that the difficulty in finding the area of a triangle depended on the position of the triangle and that the problems “Simplify a/a 2, a2/a, a/a” were of quite unequal difficulty. A discussion about the students' thinking in patterns and mechanically learning ends the report.  相似文献   

    16.
    Although skilled mathematics teachers and teacher educators often “know” when interruptions in the flow of a lesson provide an opportunity to modify instruction to improve students’ mathematical understanding, others, particularly novice teachers, often fail to recognize or act on such moments. These pivotal teaching moments (PTMs), however, are key to instruction that builds on student thinking about mathematics. Video of beginning secondary school mathematics teachers’ instruction was analyzed to identify and characterize PTMs in mathematics lessons and to examine the relationships among the PTMs, the teachers’ decisions in response to them, and the likely impacts on student learning. These data were used to develop a preliminary framework for helping teachers learn to identify and respond to PTMs that occur during their instruction. The results of this exploratory study highlight the importance of teacher education preparing teachers to (a) understand the mathematical terrain their students are traversing, (b) notice high-leverage student mathematical thinking, and (c) productively act on that thinking. This preparation would improve beginning teachers’ abilities to act in ways that would increase their students’ mathematical understanding.  相似文献   

    17.
    This paper reports on a teacher’s and his students’ responsiveness to a new tetrahedral-oriented (Mahaffy in J Chem Educ 83(1):49–55, 2006) curriculum requiring more discursive classroom practices in the teaching of chemistry. In this instrumental case study, we identify the intentions of this learner-centered curriculum and a teacher’s development in response to this curriculum. We also explore the tensions this teacher experiences as students subsequently respond to his adjusted teaching. We use a Chemistry Teacher Inventory (Lewthwaite and Wiebe in Res Sci Educ 40(11):667-689, 2011; Lewthwaite and Wiebe in Can J Math Sci Technol Educ 12(1):36–61, 2012; Lewthwaite in Chem Educ Res Pract. doi:10.1039/C3RP00122A, 2014) to assist the teacher in monitoring how he teaches and how he would like to improve his teaching. We also use a student form of the instrument, the Chemistry Classroom Inventory and Classroom Observation Protocol (Lewthwaite and Wiebe 2011) to verify the teacher’s teaching and perception of student preferences for his teaching especially in terms of the discursive processes the curriculum encourages. By so doing, the teacher is able to use both sets of data as a foundation for critical reflection and work towards resolution of the incongruence in data arising from students’ preferred learning orientations and his teaching aspirations. Implications of this study in regards to the authority of students’ voice in triggering teachers’ pedagogical change and the adjustments in ‘teachering’ and ‘studenting’ required by such curricula are considered.  相似文献   

    18.
    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.  相似文献   

    19.
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    20.
    This article reports on a national survey of higher education institutions in the United States to answer the question, “Who teaches mathematics content courses for prospective elementary teachers, and what are these instructors’ academic and teaching backgrounds?” We surveyed 1,926 institutions, and a faculty member from each of 825 institutions (42.8?%) participated in the survey. The survey results demonstrate that the majority of institutions are not meeting the recommendations of the Conference Board of the Mathematical Sciences (The mathematical education of teachers. American Mathematical Society, Providence, RI, 2001), the National Council of Teachers of Mathematics (Professional standards for teaching mathematics. National Council of Teachers of Mathematics, Reston, VA, 2005), and the National Council on Teacher Quality (Greenberg and Walsh 2008) for prospective elementary teachers to take at least nine credits of mathematics content designed specifically for them. Additionally, most instructors for these courses do not have elementary teaching experience and have likely not had opportunities to think deeply about the important ideas in elementary mathematics, and most institutions do not provide training and/or support for these instructors.  相似文献   

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