教师变量对小学生数学学习成绩影响的多水平分析

32名小学数学教师与这些教师所教班级的1691名学生参与了本研究。两个测量工具评价了教师的数学学科知识与学科教学知识,对教师的55节数学课进行了录像,并按照学习任务的认知水平与课堂对话的特点进行了编码,同时测查了学生的期末数学学习成绩。多水平分析结果表明:教师的学科教学知识、课堂学习任务的认知水平、课堂对话中教师提问问题的类型与对话的权威来源对学生的数学成绩具有显著的预测作用;而教师的学科知识对学生数学成绩的影响未达到显著性水平。     

Thinking aloud together: A teacher’s semiotic mediation of a whole-class conversation about percents

How does classroom interaction support students’ apprenticeship into the ways of speaking, writing, and diagramming that constitute the practice of mathematics? We address this problem through an interpretative analysis of a whole-group conversation about alternative ways of solving a problem involving percent discounts that occurred in a sixth grade classroom. This research study draws upon Dewey’s theory of inquiry, Vygotsky’s cultural–historical psychology, Freudenthal’s realistic mathematics education, and Halliday’s systemic functional linguistics (SFL). From Freudenthal, we borrow the notions of mathematizing and guided reinvention—the former notion offers a view of mathematics as an activity of structuring subject matter and the latter one provides insights into the processes whereby mathematizing is learned and taught in the classroom. We glean from Dewey his view of reflective thinking as inquiry and the role that conversations may serve therein. We rely upon Vygotsky’s notions of a verbal thinking plane and a social phase of learning in order to reconsider the function of whole-class interaction in apprenticing students into mathematizing. Finally, SFL provides us with tools for explaining the choices of grammar and vocabulary students and teachers make as they realize meanings in whole-group conversations. Treating the selected whole-class conversation as a text, we focus our analysis on how this text came to mean what it did. Our central questions are as follows: What meanings were realized in the whole-class conversation by teacher and students and how were these meanings realized? How did the teacher’s lexico-grammatical choices guide the students’ choices? In addressing these questions, we advance an interpretation of the conversation as paradigmatic of students and teacher thinking aloud together about percents.     

Fostering a “head start” in math: observing teachers in early childhood mathematics engagement

ABSTRACT

Studies show that early engagement with mathematics leads to increased math achievement later in life. Yet, early childhood teachers do not regard mathematics as critical to young learners’ development and lack confidence with helping children learn mathematics. Early childhood teacher comfort and engagement with mathematics is a critical element to promoting intentional math instruction. Research was conducted to examine the effects of an innovative professional development program for Head Start preschool teachers with the goal of increasing pedagogical content knowledge and confidence in teaching mathematics. The findings in this article focus on classroom observations that concentrated on teacher engagement with mathematics.     

Connecting Biology and Mathematics: First Prepare the Teachers

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers.     

Mathematics‐teachers’ Knowledge Bases: implications for teacher education

Understanding the knowledge bases of mathematics teachers is an important task in working towards the construction of adequate models for: (i) teacher education and development, and (ii) teacher operations in the classroom. To date, little systematic attention has been focused on this task. The primary aim of this study is to obtain a view from the field of mathematics teacher knowledge with respect to content knowledge in mathematics, content‐specific pedagogical knowledge in mathematics and curriculum knowledge relevant to teaching tasks. This study has used data obtained from a survey of primary teachers and secondary mathematics teachers. Analysis of the results has indicated that less than half of the teachers in the study believed that they were sufficiently prepared in mathematics content, and that almost two‐thirds of the teachers in the sample believed that their level of knowledge in contemporary teaching methodologies in mathematics is not sufficient for their role as school teachers. Key differences emerge between the primary and secondary sectors and also within the secondary sector. Implications for preservice and in‐service mathematics teacher education are drawn.     

A Mathematics Teachers’ Perspective and its Relationship to Practice

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.     

Vicious Cycles of Identifying and Mathematizing: A Case Study of the Development of Mathematical Failure

This study uses a new communicational lens that conceptualizes the activity of learning mathematics as interplay between mathematizing and identifying in order to study how the emotional, social, and cognitive aspects of learning mathematics interact with one another. The proposed framework is used to analyze the case of Idit, a girl who started out as a high achiever in 7th-grade math and ended up failing that same subject in 9th grade, complaining of severe “mathematics anxiety.” This article traces the narratives endorsed by Idit’s parents and teacher, which form the background for the development of her ritual participation in mathematical discourse. Next it attempts to link Idit’s ritual participation in a course I taught with her eventual failure in mathematics. The mechanism behind this failure is conceptualized as a vicious cycle that thrives on the basis of a ritualistic discourse motivated mainly by grades and other instrumental motives for learning mathematics. The analysis of this case gives rise to a model of how mathematical identities of failure may develop hand in hand with the failure to learn new mathematical skills.     

Using an Undergraduate Geometry Course to Challenge Pre-service Teachers' Notions of Discourse

This investigation uses classroom discoursein an undergraduate mathematics course tochallenge pre-service secondary mathematicsteachers' notions about mathematical discourse,what it might resemble in the classroom, andhow its various forms can be cultivated byclassroom teachers. The research setting was arequired geometry course taught by the author.Eleven pre-service mathematics teachers intheir junior or senior year of an undergraduate program participated. Results indicated participants made a transition toward an image of discourse as an active process by which students use the collective knowledge of their peers to build mathematical understanding and developed in their ability to participate in such discourse.This awareness, along with participants'analyses of their own habits of discourse asclassroom teachers, prompted shifts in theirprojected image of the role of discourse intheir future practices of teaching. Resultssuggested further that the undergraduatemathematics classroom (as opposed to themethods classroom) offers a powerful and uniqueforum in which pre-service secondary teacherscan practice, articulate, and collectivelyreflect on reform-minded ways of teaching.     

“To See is to Know”: the Pedagogy of the Colonial Exhibition,Semarang, 1914

In this paper, which focuses on a western discourse of race within the pedagogical context, I want to draw some parallels between the “object” and the image in the late nineteenth and early twentieth century classroom and the exhibit of the contemporary museum and exhibition. I suggest that the classroom, museum and exhibition were fundamentally similar pedagogical sites in which the object and the image illustrated similar pedagogical subtexts and were located in architectural environments which were similarly complicit in delimiting the range of meaning which spectators/readers were being encouraged to extract. I emphasise this parallel by focusing on visual representations of “the Other” in the school text and exhibition in both the meteropolian and colonial context. The paper concludes that a discourse of race and cultural contestation pervaded European educational institutions in the nineteenth and early twentieth century in both the metropole and the colonial periphery.

     

Teaching to discuss controversial public issues in fragile times: Approaches of Israeli civics teacher educators

Civics teachers play a critical role in maintaining classroom environments that encourage discussions of controversial public issues. Thus, preparing new teachers to consider the role of such discussions is crucial. Building on theories of teacher knowledge development, this study explores how Israeli civics teacher-educators conceptualize discussions as part of their courses. The findings present four approaches that include: discussion as a pedagogical practice; discussion as a means for reflection; discussion as a way to bring the curriculum to life; and discussion as a vehicle that represents disciplinary content. Based on these findings, the role of discussion as an educational goal, not just a secondary means, will be argued.     

Pedagogies of practice and opportunities to learn about classroom mathematics discussions

In this paper, we argue that to prepare pre-service teachers for doing complex work of teaching like leading classroom mathematics discussions requires an implementation of different pedagogies of teacher education in deliberate ways. In supporting our argument, we use two frameworks: one curricular and one pedagogical. The curricular framework is based on the work of Hammerness et al. (Preparing teachers for a changing world. What teachers should learn and be able to do. San Francisco, Jossey-Bass Educational Series, pp 358–388, 2005) outlining four main goals of teacher learning: a vision of practice, knowledge of students and content, dispositions for using this knowledge, and a repertoire of practices and tools. The pedagogical framework is based on the work of Grossman et al. (Teach Teach Theory Pract 15(2):273–289, 2009a; Teach Coll Record 111(9):2055–2100, 2009b) outlining three pedagogies of practice: representations, decompositions, and approximations of practice. We use the curricular framework to examine the opportunities for teacher learning that were afforded by these three different pedagogies of practice in a unit on leading classroom mathematics discussion in a secondary mathematics methods course. We use evidence from our analysis to show how the coordination of those pedagogies of practice is better than any one of them in addressing important goals for teacher learning about classroom discussions.     

Mathematics engagement in an Australian lower secondary school

The importance of actively engaging in mathematics discourse in order to learn mathematics is well recognized. In this paper, I use Basil Bernstein’s concepts of pedagogic discourse to document and analyse academic learning time of students in Years 8 and 9 at a suburban lower secondary school: in particular, for what proportion of class time students reported being academically engaged, their explanations for this engagement and how they felt about the discourse. It was found that many students had disengaged from mathematical endeavour as a result of the failure of the instructional discourse either to engage students or to serve the purpose of developing discipline-specific content knowledge. The reasons for this relate to the overemphasis on mundane mathematics resulting in some students lacking the cognitive tools to engage with the concepts and having neither the intrinsic nor instrumental motivation to persist with secondary school esoteric mathematics. The implications for mathematics curriculum development are discussed.     

Opportunities for learning given to prospective mathematics teachers: between ritual and explorative instruction

The mathematics education field, including prospective teacher education program, has seen a continuous effort to change teaching practices to be more cognitively demanding, conceptually oriented and student centred. Our goal in this study was to examine how certain underlying assumptions about mathematical learning, as reflected in a skilled instructor’s discourse, align with opportunities to learn. The data included a set of fully transcribed 11 lessons from an introductory algebra course. The method of analysis was built upon the communicational (commognitive) framework and included discerning between the instructor’s mathematizing and identifying talk. This framework was extended to quantify the instructor’s identifying talk over the whole set of lessons. Our findings showed that at the surface level, the instruction in the class seemed to align with “explorative” goals. On a deeper level, however, it was more aligned with “ritual” goals that are concerned with producing narratives about people, not about mathematics.     

The Impact of Sustained, Standards-Based Professional Learning on Second and Third Grade Teachers’ Content and Pedagogical Knowledge in Integrated Mathematics

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.     

Connecting with the horizon: developing teachers’ appreciation of mathematical structure

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.     

Troubling teacher identity: preparing mathematics teachers to teach for diversity

This paper reports on an action research project designed to explore the complexities of pre‐service mathematics teacher resistance to social justice issues. Research on equity and mathematics education has indicated that such resistance seems particularly strong for mathematics teachers. Twelve pre‐service mathematics teachers participated in a course‐based research project to explore this issue. Participants completed a classroom discourse analysis and a self‐study narrative as part of their secondary mathematics methods course. The findings suggest that attention to issues of identity construction within school mathematics can be successfully embedded in methods courses in order to better prepare mathematics teachers to teach for diversity.