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1.
Jinfa Cai Ning WangJohn C. Moyer Chuang WangBikai Nie 《International Journal of Educational Research》2011,50(2):117-136
In this article, we present the results from a longitudinal examination of the impact of a Standards-based or reform mathematics curriculum (called CMP) and traditional mathematics curricula (called non-CMP) on students’ learning of algebra using various outcome measures. Findings include the following: (1) students did not sacrifice basic mathematical skills if they are taught using a Standards-based or reform mathematics curriculum like CMP; (2) African American students experienced greater gain in symbol manipulation when they used a traditional curriculum; (3) the use of either the CMP or a non-CMP curriculum improved the mathematics achievement of all students, including students of color; (4) the use of CMP contributed to significantly higher problem-solving growth for all ethnic groups; and (5) a high level of conceptual emphasis in a classroom improved the students’ ability to represent problem situations. (However, the level of conceptual emphasis bears no relation to students’ problem solving or symbol manipulation skills.) 相似文献
2.
Christine Pauli Kurt ReusserUrs Grob 《International Journal of Educational Research》2007,46(5):294-305
In mathematics instruction, can a teacher implement surface features of instruction that foster self-regulated learning as well as achieve quality at the deeper level of instruction, that is, focus on higher-order thinking, problem-solving, and mathematical modeling? An educational reform effort in Switzerland, which is based on constructivist and sociocultural theories of mathematics learning, targets both these dimensions: self-regulated learning and conceptual understanding. We examined the realization of the two dimensions in classroom instruction in a video-based study of 79 eighth-grade math classes using three kinds of data: videotapes of mathematics lessons, student and teacher questionnaires, and achievement tests. As to the surface level of instruction, teachers reported how frequently they provided opportunities for self-regulated learning. With regard to the deeper level of instruction, teachers reported how frequently they provided opportunities for independent problem solving. In addition, we examined the extent to which teachers’ pedagogical beliefs reflected a constructivist orientation. The results showed that teachers implemented the two dimensions relatively independently of one another. Teachers’ constructivist-oriented beliefs influenced only opportunities provided for independent problem solving and did not affect opportunities for self-regulated learning. Opportunities for self-regulated learning had a positive effect on students’ learning experience. Professional development should encourage teachers to take greater account of both surface-level and deeper-level (quality) features of instruction. 相似文献
3.
Early childhood preservice teachers participated in a qualitative multiple case study to explore and examine the effectiveness of reform-based constructivist methods used in a mathematics methods course to change their mathematics anxiety, mathematics self-efficacy, and mathematics teachers’ efficacy beliefs. Findings indicated that instructor’s use of a variety of reform-based strategies to teach and model concepts were effective in reducing their mathematics anxiety and improving their mathematics self-efficacy and mathematics teaching efficacy beliefs. Based on these findings, it is recommended that mathematics methods course instructors use reform-based constructivist methods in their courses as outlined by the NCTM’s (2014) principles. Teacher educators must also consider carefully their attitudes and disposition toward mathematics along with the type of classroom and learning environment they establish in mathematics methods courses. They must emphasize conceptual understanding during mathematics methods courses, understand the connection between preservice teachers’ mathematics anxiety and mathematics efficacy beliefs, and integrate field experiences as well as peer teaching opportunities into mathematics methods courses. 相似文献
4.
There is an acknowledged gap between the theory presented in university preparation programmes and the reality of classroom practice that has resulted in many secondary mathematics pre-service teachers failing to implement university-endorsed teaching strategies. Using responses to a questionnaire and interviews, this qualitative study examined the factors that support or inhibit secondary mathematics pre-service teachers’ implementation of problem-solving tasks during professional experience. The results showed that even though the majority of pre-service teachers reported having beliefs compatible with using problem-solving tasks, the secondary students’ ability, preparation time, and the cooperating teacher were key factors that inhibited pre-service teachers’ implementation of problem-solving tasks. It is recommended that pre-service teachers regularly visit classrooms to observe the evolving implementation of problem-solving approaches. Furthermore, cooperating teachers should be required to attend professional development before the professional experience so they understand the goals of the university preparation programme and have the requisite skills and knowledge to support the implementation of problem-solving tasks in learning mathematics. 相似文献
5.
《Studying Teacher Education》2013,9(2):169-181
The authors describe a journey of self-study during which one author shifted from traditional, teacher-driven approaches to a more problem-based inquiry approach to teaching mathematics. He videotaped a series of lessons taught to sixth-grade students over a semester and analyzed his teaching during discussions with his mentor at the university. The shared analysis helped him learn to involve his students more directly in their own learning. A major lesson learned was that understanding the potential value of a problem-solving approach to teaching mathematics does not guarantee corresponding changes in the classroom. Two vital elements of lesson development emerged as focal points for self-study. After first learning how to prepare worthwhile mathematical tasks, the teacher also learned the importance of implementing effective questioning strategies to help students think more deeply about the mathematics they were learning. 相似文献
6.
The perspective of situated learning offers a theoretical framework for understanding the dialectical relations between the social and the individual dimensions of classroom microculture. The purpose of this article is to show how sociomathematical norms constructed during whole-class discussions provide a reference for the elaboration of mathematical practices and for the interactive regulation of learning. Qualitative data regarding the transition from additive to multiplicative problem solving were collected in two third-grade classrooms during an entire school year. The sociomathematical norms constructed in the two classrooms were identified and compared. An in-depth analysis focusing on two interactive episodes in one classroom showed the forms of regulation of learning that emerged in relation to the norm of “effectiveness”. Both episodes demonstrated how the processes of regulation resulting from teacher–student interactions incorporated and orchestrated regulations resulting from peer interactions and thereby contributed to the progression of the students’ problem-solving procedures. 相似文献
7.
This study compared how selected mathematics textbooks from Mainland China and the United States at the lower secondary grade level represent various types of problems for classroom teaching and learning. The examination of problems was carried out based on the classifications of problem types established in the study, including routine problems versus non-routine problems, open-ended problems versus close-ended problems, traditional problems versus non-traditional problems, and application problems versus non-application problems, among others. Both the similarities and differences in the representation of problems in the selected textbooks were analyzed. The results were used to explore the possible influences of those textbooks on students’ different performances in mathematics, as revealed in cross-national comparisons. Discussions about how to improve the representation of problems in mathematics textbooks were provided at the end of the study. 相似文献
8.
“Accepting Emotional Complexity”: A Socio-Constructivist Perspective on the Role of Emotions in the Mathematics Classroom 总被引：1，自引：0，他引：1
Peter Op ’t Eynde Erik De Corte Lieven Verschaffel 《Educational Studies in Mathematics》2006,63(2):193-207
A socio-constructivist account of learning and emotions stresses the situatedness of every learning activity and points to the close interactions between cognitive, conative and affective factors in students’ learning and problem solving. Emotions are perceived as being constituted by the dynamic interplay of cognitive, physiological, and motivational processes in a specific context. Understanding the role of emotions in the mathematics classroom then implies understanding the nature of these situated processes and the way they relate to students’ problem-solving behaviour. We will present data from a multiple-case study of 16 students out of 4 different junior high classes that aimed to investigate students’ emotional processes when solving a mathematical problem in their classrooms. After identifying the different emotions and analyzing their relations to motivational and cognitive processes, the relation with students’ mathematics-related beliefs will be examined. We will specifically use Frank’s case to illustrate how the use of a thoughtful combination of a variety of different research instruments enabled us to gather insightful data on the role of emotions in mathematical problem solving. 相似文献
9.
《Teaching and Teacher Education》2005,21(4):439-456
Seven elementary teachers participated in a project designed to help them learn to teach mathematics according to reform recommendations. Teachers were provided opportunities to learn through both private reflection and public inquiry about their teaching and children's learning. The teachers’ instruction, reflection, and beliefs were studied. All of the teachers adopted some reform-based procedures including having children report problem-solving strategies. However, only three of them developed more complex practice in which children were involved in inquiry into one another's strategies. The groups had different beliefs about the autonomy of children to construct mathematics and their own autonomy to make instructional decisions. 相似文献
10.
Peter Sullivan Judith Mousley Robyn Zevenbergen 《International Journal of Science and Mathematics Education》2006,4(1):117-143
The basic unit of school based mathematics teaching is the lesson. This article is a contribution to understanding teacher actions that facilitate successful lessons, defined as those that engage all students, especially those who may sometimes feel alienated from mathematics and schooling, in productive and successful mathematical thinking and learning. An underlying assumption is that lessons can seek to build a sense in the students that their experience has elements in common with the rest of the class and that this can be done through attention to particular aspects of the mathematical and socio-mathematical goals. We examine three teacher actions that address the mathematical goals: using open-ended tasks, preparing prompts to support students experiencing difficulty, and posing extension tasks to students who finish the set tasks quickly; as well as actions that address the socio-mathematical goals by making classroom processes explicit. To illustrate and elaborate these actions, we describe a particular lesson taught to a heterogeneous upper primary (age 11–12) class. 相似文献
11.
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
12.
The purpose of this case study was to investigate the values demonstrated by an elementary school teacher in her mathematics teaching and what values her students perceived. This research adopted the valuing theory (Raths, Harmin & Simon, 1987) and used classroom observations and interviews to document the teacher’s mathematics pedagogical values and a questionnaire, interviews, and instructional artifacts to document the students’ perceptions of these values. The results of this research identified two educational values and three mathematics pedagogical values that were influenced by the teacher’s personal beliefs about Buddhism, Confucianism, and curriculum. Her goals for education were to reinstate the students’ original enlightenment and the students’ respect for ethics and experts when dealing with people and life; and her values about mathematics learning were that it depends on individual efforts and personal understanding, her central purposes for teaching were to make students understand the mathematics content and to cultivate their problem-solving methods, and her purposes for evaluation were to understand students’ learning and to encourage students to correct their errors. The students’ awareness of these goals and values did not parallel the teacher’s personal priorities. The implications of teachers’ pedagogical values on teacher professional development and curriculum reform are discussed. 相似文献
13.
Undoubtedly the acquisition of mathematical skills for problem solving is critically important in today’s sophisticated technological world. There is growing evidence that meta-cognition application is an important component of academic success in general and impacts on mathematical achievement in particular. Teachers’ application of meta-cognition therefore directs and reflects their teaching-practice behaviour which influences their learners’ learning with understanding in problem-solving. The purpose of the study reported on in this article was to explore teachers’ available meta-cognitive skills in class with the intention of supporting learners’ development of mathematics in problem-solving in some selected rural primary schools in the Eastern Cape, South Africa. The participants were three teachers purposefully selected from three primary schools. Interviews were conducted with the three teachers and three lessons were observed. The interviews, as an extension of observation, focused on the teachers’ knowledge or understanding of available meta-cognitive skills and how they used these skills in helping their learners’ development of mathematics problem-solving. The findings included a detailed exploration of the teachers’ acquisition and use of specific metacognitive skills, either consciously or unconsciously, during teaching and learning processes in order to develop their mathematics learners’ meta-cognitive skills as well as in solving mathematical problems. The results of the observation showed that there was evidence of teachers applying meta-cognitive skills unconsciously in assisting their learners in problemsolving in class. The interviews confirmed this evidence of available meta-cognitive skills which the teachers usually applied in assisting their learners in problem-solving in class. Recommendations have been made regarding teachers’ methods of teaching to improve the development of such skills in the lives of their mathematics learners through problemsolving. 相似文献
14.
The aim of this study was to investigate how participation and reification of ideas about mathematics teaching are constituted
in on-line discussions when prospective primary mathematics teachers analysed video-cases about mathematics teaching. Prospective
teachers enrolled in a mathematics methodology course participated for 4 weeks in two virtual learning environments that integrated
the analysis of video-clips, on-line discussions and writing essays about key aspects of mathematics teaching. Three aspects
were considered relevant to explain the prospective teachers’ learning: the way in which the theoretical information was used
to frame and to interpret the events from mathematics teaching; the characteristics of engagement with others participating
in the on-line discussions and the role played by prospective teachers’ beliefs. Possible reasons for the importance of these
features include the specific questions posed in on-line discussions and the use of video-clips of mathematics teaching. These
findings are considered useful in designing virtual learning environments and the kinds of tasks through which the understanding
of mathematics teaching and learning-to-notice skills can be developed. 相似文献
15.
Drawing on socio-cultural theory, we understand the norms regulating the practices within the mathematics classroom as resulting
from the social representations of the socially dominant groups and of the school culture related to what constitutes learning
mathematics. Immigrant studients, having their own personal histories as members of particular social groups, and having been
in school traditions other than the one predominant in the host society, have their own images of what mathematics in school
is about. Individuals interacting in the classroom are all re-interpreting the different episodes from the perspective of
the social representations of the larger groups with which they identify themselves. In multiethnic classrooms different re-interpretations
of the same norms clash. The lack of negotiation gives rise to obstacles to immigrant students’ participation in the mathematical
conversations and, therefore, interferes with the students’ learning process. 相似文献
16.
?se Hansson 《Educational Studies in Mathematics》2012,81(1):103-125
In the multilingual mathematics classroom, the assignment for teachers to scaffold students by means of instruction and guidance in order to facilitate language progress and learning for all is often emphasized. In Sweden, where mathematics education is characterized by a low level of teacher responsibility for students’ performance, this responsibility is in part passed on to students. However, research investigating the complexity of relations between mathematics teaching and learning in multilingual classrooms, as well as effect studies of mathematics teaching, often take the existence of teachers’ responsibility for offering specific content activities for granted. This study investigates the relations between different aspects of responsibility in mathematics teaching and students’ performance in the multilingual mathematics classroom. The relationship between different group compositions and how the responsibility is expressed is also investigated. Multilevel structural equation models using TIMSS 2003 data identified a substantial positive influence on mathematics achievement of teachers taking responsibility for students’ learning processes by organizing and offering a learning environment where the teacher actively and openly supports the students in their mathematics learning, and where the students also are active and learn mathematics themselves. A correlation was also revealed between group composition, in terms of students’ social and linguistic background, and how mathematics teaching was performed. This relationship indicates pedagogical segregation in Swedish mathematics education by teachers taking less responsibility for students’ learning processes in classes with a high proportion of students born abroad or a high proportion of students with low socio-economic status. 相似文献
17.
Engaging students in a challenging (cognitively demanding) task and launching a mathematics lesson with a task before instruction are two characteristics of a reform-oriented approach to mathematics instruction often considered together. The authors systematically contrasted teaching with challenging tasks using a task-first lesson structure with that of a discussion-first lesson structure to three composite classes of first- and second-grade students (n = 73). Subsequent assessments of mathematical performance revealed that the discussion-first lesson structure was somewhat more efficacious in improving fluency performance but both structures similarly improved problem-solving performance. The findings suggest there is more than one way of incorporating challenging tasks into mathematics lessons to produce sizeable learning gains. 相似文献
18.
教师的教学效能感(the sense of teaching efficacy),是指教师对自己在教学活动中可否有能力去完成好教学活动的判断。教学效果具体体现在对教材、备课、课堂教学等问题上,其程度的高低,直接决定了教师的教育教学工作的成败,提高教学效果感,要从教育预见能力、传导能力及教育过程的控制能力三个方面努力。 相似文献
19.
20.
A popular explanation for low student achievement in many developing countries’ primary schools is that students have relatively little opportunity to learn (OTL) the skills needed for academic success. However logical this explanation may be, surprisingly little empirical evidence has been presented to support it. In this paper we address this gap by estimating the effect of OTL on students’ academic performance using rich data we gathered on the teaching process in a large number of South African and Botswana Grade 6 classrooms. We use an innovative classroom fixed effects approach to estimate the impact of OTL on students’ mathematics achievement gains. We found statistically significant but very different results for our South Africa and Botswana samples. The discussion of those results in the context of differences in the two school systems gives us insights into the importance and limits of OTL as an explainer of student learning in low achievement schools. 相似文献