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1.
Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children’s mathematical thinking, as well as their cultural, linguistic, and community-based knowledge. This article presents a conjectured learning trajectory for prospective teachers’ (PSTs’) development related to integrating children’s multiple mathematical knowledge bases (i.e., the understandings and experiences that have the potential to shape and support children’s mathematics learning—including children’s mathematical thinking, and children’s cultural, home, and community-based knowledge), in mathematics instruction. Data were collected from 200 PSTs enrolled in mathematics methods courses at six United States universities. Data sources included beginning and end-of-semester surveys, interviews, and PSTs’ written work. Our conjectured learning trajectory can serve as a tool for mathematics teacher educators and researchers as they focus on PSTs’ development of equitable mathematics instruction.  相似文献   

2.
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   

3.
This 3 year longitudinal study reports the feasibility of an Improving Teacher Quality: No Child Left Behind project for impacting teachers’ content and pedagogical knowledge in mathematics in nine Title I elementary schools in the southeastern United States. Data were collected for 3 years to determine the impact of standards and research-based teacher training on these aspects of teacher quality. Content knowledge for the scope of this research study refers to the knowledge that teachers have about subject matter. Teacher quality is directly related to teachers’ “highly qualified” status, as defined by the No Child Left Behind mandate. According to this mandate, every classroom should have a teacher qualified to teach in his subject area and be able to “raise the percentage of students who are proficient in reading and math, and in narrowing the test-score gap between advantaged and disadvantaged students.” Participants were six second grade and seven third grade teachers of mathematics from nine schools within one failing school district. The implementation of standards-based methods in the nine Title I Schools increased teacher quality in elementary school mathematics. In fact, qualitative and quantitative data revealed significant gains in teachers’ mathematics content and pedagogical knowledge at both grade levels.  相似文献   

4.
This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers’ pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete understanding of content and pedagogical content knowledge related to exponential functions. The teachers’ understanding of how to translate from table to closed-form and recursive equations grew as a result of their use of the Mathematics: Modeling Our World textbook, while the Discovering Algebra textbook appeared to be more beneficial in terms of pedagogical content knowledge. Teachers read from the student lessons in both textbooks, but read differently from the sections of both textbooks intended for the teacher. They focused more on the purpose of the Mathematics: Modeling Our World lesson and more on the places where students might experience difficulties in the margins of the Discovering Algebra lesson. The teachers’ learning was influenced by their own personal characteristics (e.g., previous textbook experiences) as well as textbook qualities (e.g., organization).  相似文献   

5.
Connecting students’ cultural and community mathematical practices to school mathematics is a critical issue in mathematics education. The goal of the study was to identify how teachers incorporate children’s cultural and out-of-school mathematics in instruction. Four related practices were identified, and three drew on children’s cultural or out-of-school experiences: (a) using these experiences as contexts for problems, (b) linking these experiences to school mathematics, and (c) identifying embedded mathematical practices prominent in these experiences. A fourth category, teacher initiated situated settings, focused on shared experiences using the classroom as a site of culture. Findings suggest that these practices represent varying levels of complexity and that use of this framework might support teachers in better relating students’ cultural and out-of-school experiences to mathematics.  相似文献   

6.
In the current shifts in mathematics classrooms, teachers are challenged to use effective pedagogy to develop inquiry communities in which all participants are offered opportunities to engage in the reasoning discourse of proficient mathematical practices. The challenge for teachers is to know how to implement these pedagogical changes. This article outlines how a teacher and researcher worked together in a collaborative partnership using a purposely designed communication and participation framework as a tool to scaffold development of collective reasoning in the inquiry community. The findings illustrate the interconnections between the teacher’s beliefs, past experiences, and current, and future expectations for her diverse students. Explanations are provided of how different, often conflicting, voices emerged including one that drew on the teacher’s cultural knowledge. This provided many learning opportunities for the researcher as the teacher developed her students’ voices in culturally appropriate ways.  相似文献   

7.
This research explored science teachers’ pedagogical discontentment and described its role in teachers’ consideration of new teaching practices. Pedagogical discontentment is an expression of the degree to which one is discontented because one’s teaching practices do not achieve one’s teaching goals. Through a series of structured interviews conducted with 18 practicing science teachers of various grade levels, content areas, routes of preparation, and amount of experience, areas of commonality in the teachers’ pedagogical discontentment were identified. The common areas of pedagogical discontentment include the ability to teach all students science, science content knowledge, balancing depth versus breath of instruction, implementing inquiry instruction, and assessing science learning. We draw implications for using this construct to craft more effective professional development.  相似文献   

8.
A professional learning program for teachers of junior secondary mathematics regarding the content and pedagogy of senior secondary mathematics is the context for this study of teachers’ mathematical and pedagogical knowledge. The analysis of teachers’ reflections on their learning explored teachers’ understanding of mathematical connections and their appreciation of mathematical structure. The findings indicate that a professional learning program about senior secondary mathematics can enable practicing teachers to deepen and broaden their knowledge for teaching junior secondary mathematics and develop their practice to support their students’ present and future learning of mathematics. Further research is needed about professional learning approaches and tasks that may enable teachers to imbed and develop awareness of structure in their practice.  相似文献   

9.
In this study we created, implemented, and evaluated the impact of proportional reasoning authentic investigative tasks on the mathematical content and pedagogical knowledge and attitudes of pre-service elementary and middle school mathematics teachers. For this purpose, a special teaching model was developed, implemented, and tested as part of the pre-service mathematics teacher education programs conducted in Israeli teacher colleges. The conclusion of the study is that application of the model, through which the pre-service teachers gain experience of and are exposed to authentic investigative proportional reasoning tasks with incorporation of theory (reading and analyzing relevant research reports) and practice, leads to a significant positive change in the pre-service teachers’ mathematical content and pedagogical knowledge. In addition, improvement occurred in their attitudes and beliefs towards learning and teaching mathematics in general, and ratio and proportion in particular.  相似文献   

10.
This study investigated changes in beginning teachers’ self-perceptions of their pedagogical knowledge and skills after their first year of teaching. Surveys were administered to 322 graduating student teachers at the end of the initial teacher preparation programme and at the end of their first year of teaching to compare if there were any differences in their self-perceptions. The results of the study showed significant increases in beginning teachers’ perceptions of their pedagogical knowledge and skills in three factors: Instructional Support, Accommodating Diversity and Classroom Management. Results established the development of teachers to be an ongoing process that is initiated but not completed in initial teacher preparation. Implications of findings for induction and mentoring of beginning teachers are discussed.  相似文献   

11.
In this paper we try to characterize the pedagogical approaches that mathematics teachers are developing to meet the challenges posed by education reforms. A key aspect is the identification of the perspectives that underlie those pedagogical approaches, using the term perspective to include a broad pedagogical structure composed of multiple conceptions that are related to some aspects of a teacher’s practice. Through the study of the practice of a secondary mathematics teacher, we try to explore how his/her pedagogical approaches on mathematics, mathematics learning, and mathematics teaching are related to the relational architecture that is established in the classroom during the development of an instructional unit of similarity at a secondary school level, and we examine if that relationship can be explained in terms of the underlying perspective. The results of the study have shown the characteristics of that relationship, and the important role that the teacher’s knowledge of the students’ difficulties plays both in making decisions and in developing the teachers’ actions.  相似文献   

12.
Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics. The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications for mathematics teacher education, prospective and practicing, are discussed.  相似文献   

13.
In order to evaluate the effectiveness of an experimental elementary mathematics field experience course, we have designed a new assessment instrument. These video-based prediction assessments engage prospective teachers in a video analysis of a child solving mathematical tasks. The prospective teachers build a model of that child’s mathematics and then use that model to predict how the child will respond to a subsequent task. In this paper, we share data concerning the evolution and effectiveness of the instrument. Results from implementation indicate moderate to high degrees of inter-rater reliability in using the rubric to assess prospective teachers’ models and predictions. They also indicate strong correlation between participation in the experimental course and prospective teachers’ performances on the video-based prediction assessments. Such findings suggest that prediction assessments effectively evaluate the pedagogical content knowledge that we are seeking to foster among the prospective teachers.  相似文献   

14.
Prospective elementary teachers’ (N = 148) motivation to participate in whole-class discussions during mathematics content courses for teachers, as expressed in their own words on an open-ended questionnaire, were studied. Results indicated that prospective teachers were motivated by positive utility values for participating (to achieve a short-term goal of learning mathematics or a long-term goal of becoming a teacher), to demonstrate competence (to achieve performance-approach goals), or to help others (to achieve social goals). Negative utility values for participating were expressed by those who preferred to learn through actively listening. Five motivational profiles, as composed of interactions among motivational values, beliefs, goals and self-reported participation practices, were prevalent in this sample. Self-reported variations among participants’ utility values and participation practices suggested that prospective teachers engaged differentially in opportunities to learn to communicate mathematically. Results provide pedagogical learner knowledge for mathematics teacher educators. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.  相似文献   

15.
通过对初中数学青年骨干教师L老师的叙事研究．研究者认为初中数学学科教学知识对学科内容知识量的要求是有限的,但对教师理解内容知识的深刻性有较高要求;实践与反思是形成学科教学知识的关键。L老师学科教学知识的生成途径有其独特的地方,值得其他教师借鉴和学习,可以概括为“二研五专”,即：研究教材、研题磨题、专业阅读、专题研究、专业现场、专题写作、专家引领。  相似文献   

16.
This paper addresses the accumulating knowledge of prospective teachers of secondary school mathematics and their acquired proficiency during the course “Psychological aspects of mathematics education,” in which we discussed theoretical models including the intuitive rules theory. Participants’ performances are examined by means of an extensive report of two episodes, one during the course and one afterwards. These episodes marked different stages in the prospective teachers’ analysis of their own and of students’ solutions, which led me to conclude that exposing prospective teachers to the intuitive rules theory is important, since their familiarity with the theory provided them with a tool to reflect on their own mathematical solutions (subject matter knowledge; SMK), on others’ solutions, and on the tasks (pedagogical content knowledge; PCK).  相似文献   

17.
The relation is studied between teachers’ pedagogical content knowledge of reading and the quality of their subsequent classroom behaviour in teaching fluent reading. A confirmatory factor analysis model with two latent variables is tested and shows adequate goodness-of-fit indices. Contrary to our expectations, the results of structural equation modelling reveal a small but significant γ-value of .29, indicating that only 8% of the variance in teachers’ classroom behaviour in teaching fluent reading is accounted for by teachers’ pedagogical content knowledge of reading. Presumably teacher knowledge is not as stable and conclusive as one might think. More research is needed in determining the factors that work restricting for teachers in putting their knowledge into classroom practice. It is recommended that preservice and in-service teacher training should not be limited to transfer of knowledge, but should also assist teachers in designing and performing effective fluent reading instruction.  相似文献   

18.
This study investigated 481 in-service elementary teachers’ level of mathematical content knowledge, attitudes toward mathematics, beliefs about the effectiveness of inquiry-based instruction, use of inquiry-based instruction and modeled the relationship among these variables. Upper elementary teachers (grades 3–5) were found to have greater content knowledge and more positive attitudes toward mathematics than primary teachers (grades K-2). There was no difference in teachers’ beliefs about effective instruction, but primary level teachers were found to use inquiry-based instruction more frequently than upper elementary teachers. Consistent with Ernest’s [Ernest (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching, 15(1), 13–33] model of mathematics teaching, content knowledge, attitudes, and beliefs were all found to be related to teachers’ instructional practice. Furthermore, beliefs were found to partially mediate the effects of content knowledge and attitudes on instructional practice. Content knowledge was found to be negatively related to beliefs in the effectiveness of inquiry-based instruction and teachers’ use of inquiry-based instruction in their classrooms. However, overall, teachers with more positive attitudes toward mathematics were more likely to believe in the effectiveness of inquiry-based instruction and use it more frequently in their classroom. Teacher beliefs were found to have the strongest effect on teachers’ practice. Implications for the goals and objectives of elementary mathematics methods courses and professional development are discussed.
Jesse L. M. WilkinsEmail:
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19.
Fundamental for mentoring a preservice teacher is the mentor’s articulation of pedagogical knowledge, which in this research draws upon specific practices, viz.: planning, timetabling lessons, preparation, teaching strategies, content knowledge, problem solving, questioning, classroom management, implementation, assessment and viewpoints for teaching. Mentoring is haphazard; consequently, mentors need a pedagogical knowledge framework and a repertoire of pedagogical knowledge strategies to guide a preservice teacher’s development. Yet, what are strategies for mentoring pedagogical knowledge practices? This qualitative research investigates mentoring strategies assigned to pedagogical knowledge from 27 experienced mentor teachers. Findings showed that there were multiple strategies that can be linked to specific pedagogical knowledge practices. For example, mentoring strategies associated with planning for teaching can include co-planning, verbally reflecting on planning with the mentee and showing examples of the mentor teacher’s planning (e.g. teacher’s plans, school plans, district and state plans). This article provides a bank of practical strategies for mentoring pedagogical knowledge practices to assist a preservice teacher’s development.  相似文献   

20.
This article reports on a study that investigated a professional development initiative in Australia to address a decline in reading comprehension scores in the middle and upper years of Primary school. It describes the professional learning journey of a middle primary teacher and his literacy coach over a period of 12 months as they worked to improve the teacher’s knowledge and skills to explicitly teach reading comprehension. A series of classroom observations and interviews at the beginning, middle and end of the school year were analysed for the kinds of reading skills taught and the nature of the instruction. The data suggest that there were significant changes in the teacher’s pedagogical repertoires and practices and an observed improvement in the student’s understandings of different comprehension knowledge, skills and strategies.  相似文献   

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