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1.
This study explored the training of prospective and practicing mathematics teachers in alternative assessment and its impact on their attitudes toward alternative assessment methods and their beliefs about the nature of mathematics. Data were collected from 51 prospective teachers and 50 practicing teachers who took a course on alternative assessment in mathematics. Findings indicated a significant change in the correlation between the positivist and constructivist dimensions of their beliefs about the nature of mathematics following the course. No significant differences were found between the prospective and practicing teachers’ beliefs either before or after the course nor in their attitudes toward alternative assessment after the course. Before the course, however, the two groups differed significantly in their attitudes toward alternative assessment. Findings also revealed significant changes in attitudes toward alternative assessment and beliefs about the nature of mathematics following participation in the course. These changes in attitudes and beliefs were accompanied by a shift in the nature of the assessment tasks written by the participants. Participants who demonstrated more positive attitudes and constructivist beliefs tended to write more conceptual problems and less procedural exercises. Implications for mathematics teacher training and professional development in alternative assessment are discussed.  相似文献   

2.
This paper describes a study of observed relationships between the design of a preservice elementary mathematics methods course with accompanying field practicum and changes in the extent to which participating prospective teachers identified themselves with the mathematics reform movement after becoming practicing teachers. The curriculum of the course with its embedded field practicum experiences was designed to support prospective teachers in interweaving methods coursework and pedagogical instruction with classroom practice. University and elementary school structures were interwoven by conducting weekly mathematics methods course sessions at a school site followed immediately by related practicum experiences in classrooms in the school. The interweaving of conceptualizations about mathematics teaching and learning was facilitated as the methods instructor provided professional development for classroom teachers simultaneously with the methods course, encouraging the teachers to create “reform-friendly” classroom environments. Survey data from 68 prospective teachers involved in the project were analyzed to identify and describe relationships between course/practicum experiences and the degree to which they as practicing teachers, 1–3 years following the course/practicum, identified with a reform mathematics perspective, as well as to examine factors influencing those relationships.  相似文献   

3.
As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children’s competencies related to children’s mathematical thinking, and children’s community, cultural, and linguistic funds of knowledge or what we refer to as children’s multiple mathematical knowledge bases. Teachers’ noticing supports students’ learning in deep and meaningful ways. Researchers designed and enacted a video analysis activity with prospective teachers in their mathematics methods course. The activity served as a decomposition of practice in order to support prospective teachers in engaging in an approximation of the practice of noticing. Our findings showed that prospective teachers evidenced noticing of mathematics teaching and learning as early as the mathematics methods course. We also found that the prompts and structure of the activity supported prospective teachers by increasing their depth of noticing and their foci in noticing, moving from attending primarily to teacher moves (and merely describing what they saw) to becoming aware of significant interactions (and interpreting effects of these interactions on learning). Implications for teacher educators interested in designing and enacting activities to support noticing are discussed.  相似文献   

4.
数学教师专业是数学专业和教育专业的有机统一;科学设置对数学教师的专门教育内容;建立科学的对数学教师的终身教育机制;数学教师专业化是一个动态的发展过程.  相似文献   

5.
One of the key courses in the mathematics teacher education program in Israel is arithmetic, which engages in contents which these pre-service mathematics teachers (PMTs) will later teach at school. Teaching arithmetic involves knowledge about the essence of the concept of “number” and the development thereof, calculation methods and strategies. properties of operations on different sets of numbers, as well as the properties of the numbers themselves. Hence, the question arises: how to educate PMTs in order to supplement their mathematical knowledge with the required components? The present study explored the development of arithmetic thinking among pre-service teachers intending to teach mathematics at elementary school. This was done by matching the van Hiele theory of the development of geometric thinking to arithmetic. Analysis of findings obtained both in the present study and in many studies of geometry teaching indicates that this approach to considering the learners’ level of thinking development might lead to meaningful learning in arithmetic course for PMTs.  相似文献   

6.
This article analyzes the experiences of prospective secondary mathematics teachers during a teaching methods course, offered prior to their student teaching, but involving actual teaching and reflexive analysis of this teaching. The study focuses on the pedagogical difficulties that arose during their teaching, in which prospective teachers lacked pedagogical content knowledge and skills. It also analyzes the experience of the course itself, which was aimed at scaffolding the work of prospective teachers on developing their pedagogical content knowledge and skills.  相似文献   

7.
The goal of this study is to develop the professional noticing abilities of prospective elementary school teachers in the context of the Stages of Early Arithmetic Learning. In their mathematics methods course, ninety-four prospective elementary school teachers from three institutions participated in a researcher-developed five-session module that progressively nests the three interrelated components of professional noticing—attending, interpreting, and deciding. The module embeds video excerpts of diagnostic interviews of children doing mathematics (representations of practice) to prepare the prospective teachers for similar work. The module culminates with prospective teachers implementing similar diagnostic interviews (approximations of practice) to gain experience in the three component skills of professional noticing. A pre- and post-assessment was administered to measure prospective teachers’ change in the three components. A Wilcoxon signed ranks test was conducted and found the prospective elementary school teachers demonstrated significant growth in all three components. Selected prospective elementary school teacher responses on the pre- and post-assessment are provided to illustrate sample growth in the prospective teachers’ abilities to professionally notice. These results, the first in an ongoing study, indicate the potential that prospective teachers can develop professional noticing skills through this module. Continued data collection and analysis from the ongoing study by these authors and future, longer-term emphasis on professional noticing for prospective teachers should be studied.  相似文献   

8.
This is an intervention study that explored the effect of using video lesson analysis methodology (VLAM) on the ability of prospective middle/high school mathematics teachers to analyze mathematics teaching. The sample of the study consisted of 26 female prospective mathematics teachers enrolled in a methods course at the United Arab Emirates University. The participants were divided equally into two groups, experimental and control. The experimental group was involved in video lesson analysis where they analyzed ten video lessons throughout the semester. The group members interacted via discussion forums through Blackboard technology. Both groups wrote analyses of two video lessons, one before the intervention program and another at the end of it. It was found that the intervention remarkably improved the ability to analyze mathematics teaching of the experimental group while little improvement occurred to the control group. Implications for teacher education programs are discussed.  相似文献   

9.
Irrational Numbers: The Gap between Formal and Intuitive Knowledge   总被引：1，自引：0，他引：1  
This report focuses on prospective secondary mathematics teachers’ understanding of irrational numbers. Various dimensions of participants’ knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the real number line, and operations amongst the elements of the two sets. The results indicate that there are inconsistencies between participants’ intuitions and their formal and algorithmic knowledge. Explanations used by the vast majority of participants relied primarily on considering the infinite non-repeating decimal representations of irrationals, which provided a limited access to issues mentioned above.  相似文献   

10.
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   

11.
Nine prospective secondary mathematics teachers were interviewed about their teaching internship experience. The results of these interviews revealed that 7 of the 9 participants professed to value reform-oriented teaching and conceptual understanding in mathematics, yet all were paired with cooperating teachers who seemed to value traditional instruction and procedural understanding in mathematics. We explored the reasons that some of these student interns had positive experiences with their cooperating teachers and university supervisors while others had negative experiences. We found that the participants valued (a) critical feedback that was constructive and contained concrete recommendations for improvement, (b) freedom to use their own teaching methods, and (c) a friendly and supportive relationship with their mentors. The differing teaching philosophies of student teachers and their cooperating teachers contributed to negative experiences only when student teachers were not allowed freedom in their teaching methods.  相似文献   

12.
Teacher preparation programs face a significant challenge in determining how to design learning experiences that develop the combination of knowledge, practices, and dispositions needed for effective classroom teaching. Time constraints and the theory–practice divide are two well-documented concerns. We introduce the conceptual framework and design elements of a video-enhanced mathematics methods course that targets these concerns. The course centers on systematic reflection and analysis of practice intended to foster career-long learning. We then examine the impact of this course on several facets of learning-from-teaching competencies, including teacher knowledge, beliefs, and practices. Sixty-two preservice teachers enrolled in a one-year post-bachelor elementary teacher preparation program were randomly assigned to attend this course or a more typical mathematics methods course. Findings suggest that teacher preparation experiences centered on systematic reflection and analysis create opportunities to develop certain aspects of learning-from-teaching competencies that remain otherwise underdeveloped. Implications for the design of teacher preparation include the integration in mathematics methods courses of cycles of analysis through video-enhanced discussions; collaborative planning, implementation, and reflection on teaching; and live observation and co-constructed interpretations and considerations of next steps.  相似文献   

13.
Based on findings from a semester-long study, this article examines the development of Samoan prospective teachers’ mathematical understandings and mathematics attitudes when investigating authentic contexts and applying working mathematically processes, mental computations and problem-solving strategies to find solutions of problems. The prospective teachers had enrolled for the second time (having failed their first attempt), in the first-year mathematics methods course of a 2-year Diploma of Education (Primary) programme. The group also included those enrolled in the Diploma of Education (Early Childhood and Special Needs) programmes, who recognizing their own limited understanding of mathematics would ordinarily shy away from opportunities for improvement. Given the negative mathematical and learning experiences, this group was ideal to engage in innovative and creative approaches that would make mathematics learning more meaningful and contextual in a Samoan environment. Only data from the attitudinal questionnaires and interviews are presented in this article. Main findings have implications for teaching and learning mathematics.  相似文献   

14.
Prospective elementary teachers must understand fraction division deeply in order to meaningfully teach this topic to their future students. This paper explores the nature of the subject content knowledge of fraction division possessed by a group of Taiwanese prospective elementary teachers at the beginning of their mathematics methods course. The findings provide preliminary evidence that many prospective Taiwanese elementary teachers have developed the knowledge package of fraction division as described by Ma (Knowing and teaching elementary mathematics: Teachers?? understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates, Mahwah, 1999). The nature of various strategies used by these teachers provides further illustration of a secure common content knowledge that can serve as a benchmark for the development of mathematics courses for prospective teachers. However, the findings also show that the tasks of representing fraction division, through either word problems or pictorial diagrams, are challenging even for those highly proficient in elementary and middle school mathematics. The broader implications of this research for the international community are discussed, and recommendations for elementary teacher education programs are presented.  相似文献   

15.
This paper reports a study of preservice teachers who investigated their own teaching during a field-based component of a mathematics education methods course. The course was designed to engage the preservice teachers in both mathematical and pedagogical inquiry. Analysis of video recordings of course discussions, audiotaped interviews with preservice teachers, audiotaped discussions of instructor's planning meetings, and copies of the instructor's and preservice teachers' journals identified two critical incidents that depict students' resistance to the course directions. Analysis of these critical incidents suggests that prospective teachers' interactions with their students can become the mirror through which we can investigate their interactions with us, as teacher educators, and with our course activities. In this way we might reframe the problem of resistance to one of listening—listening to the students, to each other, and to ourselves.  相似文献   

16.
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17.
Abstract

This article describes reflections of two mathematicians and a mathematics teacher educator who collaborated on the development and implementation of courses (probability and statistics connections, number concept connections, and middle school mathematics methods) for middle school mathematics preservice teachers. The instructors of the courses, two in mathematics and one in mathematics education, worked together to more explicitly link course materials, assignments, and the pedagogical approaches. Collectively, the courses were designed to address the five components of preservice teachers’ mathematical knowledge for teaching (PT-MKT), and to model effective teaching practices. Using their collective experiences co-planning and implementing these course adjustments were made in the subsequent year. The instructors were pleased by their implementation and student outcomes in all three courses.

We describe how each component of the PT-MKT framework was approached in these courses and discuss challenges experienced by the instructors, who were part of a larger effort to develop and implement a middle school teacher preparation program. The information shared is based on data collected as part of a program evaluation effort, and is bolstered by the instructors’ recollection of events. Overall, the instructors enhanced the curricula and their instructional practices and found that the attention placed on developing PT-MKT support the mathematical development of middle school mathematics preservice teachers.  相似文献   

18.
Mathematical habits of prospective teachers affect problem comprehension and success and expose their beliefs about mathematics. Prospective elementary teachers (PSTs) (n = 121) engaged in a problem solving activity each week in class. Data were collected from PSTs enrolled in an undergraduate elementary mathematics methods course at a Southeastern State University over multiple semesters (six semesters, seven classes). PSTs’ solution methods for one intentionally misleading mathematics problem were analyzed using a convergent parallel mixed methods content analysis. Two-thirds of PSTs misunderstood the problem scenario and directly translated numbers from the problem text. PSTs who answered correctly used a problem model strategy to comprehend the scenario and were more likely to use multiple models, draw a diagram, and draw a diagram before using another model. However, a large number of PSTs who answered incorrectly also used multiple models and drew diagrams. Self-correction was not common (8 of 121), because their equations did not provide feedback or support comprehension. Three kinds of imprecision also affected problem comprehension and were evident in both correct and incorrect solutions. Intentionally misleading problems helped PSTs see consequences of their mathematical habits and highlighted the importance of sense making and precision when creating problem models.  相似文献   

19.
We report on interview results from a classroom teaching experiment in a Number and Operations course for prospective elementary teachers. Improving the number sense of this population is an important goal for mathematics teacher education, and researchers have found this goal to be difficult to accomplish. In earlier work, we devised a local instruction theory for the development of number sense, which focused on whole-number mental computation. In this study, the local instruction theory was applied to the rational-number domain, with the help of a framework for reasoning about fraction magnitude, and it guided instruction in the content course. We interviewed seven participants pre- and post-instruction, and we found that their reasoning on fraction comparison tasks improved. The participants made more correct comparisons, reasoned more flexibly, and came to favor less conventional and more sophisticated strategies. These improvements in number sense parallel those that we found previously in mental computation. In addition to the overall results, we highlight two cases of improvement that illustrate ways in which prospective elementary teachers’ reasoning about fraction magnitude can change.  相似文献   

20.
This study aimed to determine the effect of a computer-assisted instruction method using GeoGebra on achievement of prospective secondary mathematics teachers in the definite integral topic and to determine their opinions about this method. The study group consisted of 35 prospective secondary mathematics teachers studying in the mathematics education program at a state university in Turkey. The study was carried out using an embedded design, and the Definite Integral Knowledge Test and an opinion form were used for data collection. Upon analyzing the data, the computer-assisted instruction method using GeoGebra was found to positively contribute to the success of teaching the definite integral topic. Prospective teachers stated that this method should be used in math courses as it creates a fun and interesting environment with dynamic learning elements, provides visualization and opportunities to learn mathematics through practice and exercises, enables thorough understanding and explication of skills, and makes way for conceptual learning instead of memorizing. Furthermore, this study was found to facilitate conceptual learning of the relationship between the lower sum, upper sum and Riemann sum.  相似文献   

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