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1.
Helen M. Doerr 《Educational Studies in Mathematics》2006,62(1):3-24
Recent research suggests that the examination of students' work may lead to changes in teaching practice that are more effective in terms of students' mathematical learning. However, the link between the examination of students' work and the teachers' actions in the classroom is largely unexamined, particularly at the secondary level. In this paper, I present the results of a study in which teachers had extensive opportunities to examine the development of students' conceptual models of exponential growth in the context of their own classrooms. I describe two related aspects of the practice of one teacher: (a) how she listened to students' alternative solution strategies and (b) how she responded to these strategies in her practice. The results of the analysis suggest that as the teacher listened to her students, she developed a sophisticated schema for understanding the diversity of student thinking. The actions of the teacher supported extensive student engagement with the task and led the students to revise and refine their own mathematical thinking. This latter action reflects a significant shift in classroom practice from the role of the teacher as evaluator of student ideas to the role of students as self-evaluators of their emerging ideas. 相似文献
2.
This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students’ mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program. These skills (attending, interpreting, and responding) are defined as teachers’ professional noticing of students’ thinking. Results indicate that seniors respond to students’ thinking in significantly different ways from juniors and sophomores. Converging the data highlighted inconsistencies in how participants’ were making sense of students’ mathematical thinking, as well as in participants’ self-identified strengths and weaknesses. 相似文献
3.
通过对174名小学数学专家教师和307名小学数学普通教师的教师专业知识进行测查,研究者发现,总的来说,我国的小学数学教师在数学史、数学思想等方面的知识较差;小学数学教师的PCK总体水平较低,具体地说,教师缺乏“有关学习者”的知识,大部分小学数学教师缺乏探究的意识和解决开放性问题的能力;专家教师和普通教师在教师专业知识的几个大维度上有显著的差异。基于这个研究结果,研究者提出在小学数学教师培训课程中应该补充数学文化思想史方面的内容,鼓励教师参与学生数学学习方面的研究,提升教师的探究意识和问题解决能力,并形成优势互补、分层设计的教师培训课程模式。 相似文献
4.
In the past decade, there has been an increased emphasis on the preparation of teachers who can effectively engage students
in meaningful mathematics with technology tools. This study presents a closer look at how three prospective teachers interpreted
and developed in their role of facilitating students’ mathematical problem solving with a technology tool. A cycle of planning–experience–reflection
was repeated twice during an undergraduate course to allow the prospective teachers to change their strategies when working
with two different groups of students. Case study methods were used to identify and analyze critical events that occurred
throughout the different phases of the study and how these events may have influenced the prospective teachers’ work with
students. Looking across the cases, several themes emerged. The prospective teachers (1) used their problem solving approaches
to influence their pedagogical decisions; (2) desired to ask questions that would guide students in their solution strategies;
(3) recognized their own struggle in facilitating students’ problem solving and focused on improving their interactions with
students; (4) assumed the role of an explainer for some portion of their work with students; (5) used technological representations
to promote students’ mathematical thinking or focus their attention; and (6) used the technology tools in ways consistent
with the nature of their interactions and perceived role with students. The implications inform the development of an expanded
learning trajectory for what we might expect as prospective teachers develop an understanding of how to teach mathematics
in technology-rich environments. 相似文献
5.
Ailish Hannigan Olivia Gill Aisling M. Leavy 《Journal of Mathematics Teacher Education》2013,16(6):427-449
The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of statistics and are willing to give more relevance to the teaching of statistics; however, many mathematics teachers do not consider themselves well prepared to teach statistics. The aims of this study were to investigate the conceptual understanding of statistics of prospective secondary mathematics teachers; the nature of their attitudes towards statistics and if there was a relationship between attitude towards statistics and conceptual understanding of statistics. Conceptual understanding was measured using a standard assessment instrument (comprehensive assessment of outcomes in a first statistics course) which allows comparison across other disciplines. Despite being very mathematically able and confident, the prospective mathematics teachers in this study do no better in the assessment than students from other (mostly non-quantitative) disciplines. This, perhaps, gives further evidence that statistical thinking is different from mathematical thinking and that a strong background in mathematics does not necessarily translate to statistical thinking. Conceptual knowledge was poor in some fundamental areas of statistics such as being able to properly describe the distribution of a quantitative variable and data production. The attitudes of these teachers towards statistics were measured using a widely used instrument (survey of attitudes towards statistics). The results indicate generally positive attitudes but an acknowledgement that statistics is not a subject quickly learned by everyone and requires discipline to learn. No strong correlation was found between attitudes and conceptual knowledge. It is recommended that in order to improve teacher knowledge, teacher education programmes must include tailored modules in statistics and highlight the differences between mathematical and statistical thinking. 相似文献
6.
《International Journal of Educational Research》2002,37(2):195-210
Historically, content preparation and pedagogical preparation of teachers in California have been separated. Recently, in integrating these areas, many mathematics methodology instructors have incorporated children's thinking into their courses, which are generally offered late in students’ undergraduate studies. We have implemented and studied a model for integrating mathematical content and children's mathematical thinking earlier, so that prospective elementary school teachers (PSTs) engage with children's mathematical thinking while enrolled in their first mathematics course. PSTs’ work with children in the Children's Mathematical Thinking Experience (CMTE) may enhance their mathematical learning. Preliminary study results indicate that the sophistication of CMTE students’ beliefs about mathematics, teaching, and learning increased more than the sophistication of beliefs held by students enrolled in a reform-oriented early field experience and that experiences considering children's mathematical thinking provided PSTs with increased motivation for learning mathematics. 相似文献
7.
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
8.
Connected and culturally embedded beliefs: Chinese and US teachers talk about how their students best learn mathematics 总被引：1，自引：0，他引：1
Christopher A. Correa Michelle Perry Linda M. Sims Kevin F. Miller Ge Fang 《Teaching and Teacher Education》2008
This study compares US and Chinese elementary mathematics teachers' beliefs about how students learn mathematics. Interviews with teachers in each country revealed that Chinese and US teachers have distinct ways of thinking about how mathematics should be taught and how students learn. Many Chinese teachers talked about developing students’ interest in mathematics and relating the content of mathematics lessons to real-life situations. The US teachers talked about students' learning styles and using hands-on approaches to learning mathematics. Furthermore, these beliefs may be widespread and persistent within each country because the set of ideas among teachers appear to be internally consistent. Implications for teacher change and the study of teachers' beliefs are discussed. 相似文献
9.
Amy E. Ryken 《Journal of Mathematics Teacher Education》2009,12(5):347-364
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
10.
Julie Amador 《International Journal of Science and Mathematics Education》2016,14(1):217-241
The focus on professional noticing in mathematics education has recently gained increased interest as researchers work to understand how and what is noticed and how this translates into practice. Much of this work has focused on the professional noticing practices of inservice teachers and preservice teachers, with less attention focused on those educating teachers. This research explores how novice mathematics teacher educators professionally notice as they engage in teaching experiments and create models of student’s mathematical thinking. Findings indicate the novice teacher educators are including some evaluative comments in their professional noticing practices but lack in-depth interpretive analysis about student thinking and rarely make connections between student’s thinking and the broader principles of teaching and learning. These findings provide evidence for the importance of supporting teacher educators with developing their abilities to professionally notice. 相似文献
11.
Andrew M. Tyminski V. Serbay Zambak Corey Drake Tonia J. Land 《Journal of Mathematics Teacher Education》2014,17(5):463-487
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
12.
结合数学与经济学之间的联系,将经济问题转化为数学问题,用数学方法对经济学问题进行分析.从课程目标、学习重点来说,经济数学教学与高等数学的教学有很大的区别.从经济数学教学的课程体系、方式、方法等方面对如何激发学生学习经济数学的兴趣,培养学生的数学思维,从而提高他们的数学应用能力进行一定的探讨. 相似文献
13.
M. Kathleen Heid Glendon W. Blume Rose Mary Zbiek Barbara S. Edwards 《Educational Studies in Mathematics》1998,37(3):223-249
Understanding students' understanding of mathematical ideas can inform mathematics teaching, and task-based interviews are
one way in which teachers can learn more about their students' understandings. The CIME project was designed to empower mathematics
teachers to use interviews to understand their students' mathematical understandings as well as to prepare teachers to use
technology-intensive curricula. This study examined the influences on three high school mathematics teachers as they learned
to use task-based interviews to understand students' mathematical understandings. The areas of teacher knowledge and conceptions
that influenced the teachers we studied were: teachers' mathematical understandings and knowledge of technology and the perceived
importance of curriculum topics; teachers' views of knowing mathematics; teachers' perceptions of students' characteristics
and needs; and teachers' perceptions of interviewing and the role of questioning in interviews.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
This article explores the personal identities of two prospective elementary teachers as they progressed from mathematics methods coursework into their capstone student teaching semester. Results indicate that both prospective teachers perceived contrasting obligations of effective mathematics teaching in the teacher education and student teaching contexts, yet came to reconcile these differences in different ways. Whereas one prospective teacher was able to oppose the obligations set forth in the student teaching context, the other complied with obligations in both the teacher education and student teaching contexts. Implications for teacher education include differentiated experiences and placements, methods design, and explicit foci on students’ mathematical thinking. 相似文献
15.
Kooloos Chris Oolbekkink-Marchand Helma van Boven Saskia Kaenders Rainer Heckman Gert 《Journal of Mathematics Teacher Education》2022,25(4):453-477
Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.
相似文献16.
Irene Bloom 《Journal of Mathematics Teacher Education》2007,10(4-6):399-403
This paper describes the implementation of extended analysis tasks (EATs) in a required mathematics course for prospective high school mathematics teachers, and investigates the mathematical discovery promoted through engagement with these tasks. Extended analysis tasks are designed to move students beyond the problem context to the underlying mathematical structure of the problem. The results of this study revealed that with careful implementation, these tasks were effective for generating powerful mathematical thinking in preservice mathematics teachers, improving their problem solving, and generally enhancing the habits-of-mind exhibited by successful mathematicians (Carlson & Bloom, 2005). 相似文献
17.
18.
Megan H. Wickstrom 《Equity & Excellence in Education》2015,48(4):589-605
Creating equitable opportunities so all students can learn and succeed mathematically has been a key focus of mathematics education across several decades. Central to student achievement are students’ mathematical identity and their feelings of success during instruction. Researchers (e.g., Boaler & Staples, 2008) have shown that teachers can be particularly powerful in shaping students’ beliefs, feelings of success, and achievement, but few studies have investigated how teachers frame what it means to be successful or “smart” in mathematics. Through the social construct of smartness (Hatt, 2012) and the learning perspectives of incremental and entity theories (Blackwell, Trzesnieski, & Dweck, 2007; Yeager & Dweck, 2012), I examine how one teacher, Mrs. Purl, conceptualized what it meant to be smart in mathematics and how this perception changed slowly, over time, through repeated examination and discussion of individual student's thinking. As Mrs. Purl came to know her students at a personal level, she began to see that her perceptions were not always accurate and warranted reexamination. 相似文献
19.
LOU EDWARD MATTHEWS 《Educational Studies in Mathematics》2003,53(1):61-82
A collective case study guided by reconceptualized critical theory explored the teaching of four elementary teachers as they
incorporated a model of culturally relevant teaching into their mathematics instruction at four predominantly Black schools
in Bermuda. The study examined how teachers sought to (a) foster critical mathematical thinking and critical consciousness,
(b) build on informal mathematical and cultural knowledge; and (c) utilize empowerment orientations toward students' culture
and experience. The teachers embraced culturally relevant teaching but varied in their efforts to incorporate these perspectives
into instruction. Four facets of their teaching are illuminated. These complexities included situations were teaching focused
on sustaining empowered relationships;building on or to students' cultural knowledge; and fostering critical thinking as framed in the model, or personal definitions.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
20.
应用题是数学的重要组成部分,也是教学的重点和难点,学生应用题解题能力可以在一定程度上代表数学知识掌握水平。教师应把教授学生怎样解答应用题作为教学重点,巩固学生的数学基础知识,培养学生的数学思维和逻辑思维能力。文章对数学教学中教师怎样对学生进行应用题教学进行论述。 相似文献