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1.
Michal Tabach Rina Hershkowitz Baruch Schwarz 《Educational Studies in Mathematics》2006,63(3):235-258
Studies of knowledge constructing often focus on the analysis of a single episode, without considering enough the history
of the learners, or the future learners' trajectories with regard to the concepts learned. This paper presents an example
of knowledge constructing within the context of peer learning. We show how the design of the task and the tools available
to the students afford the constructing of conceptual knowledge (the phenomenon of exponential growth and variation, as it
is expressed in its numerical and graphical representations). We trace the constructing of knowledge through a series of dyadic
sessions for a few months in a classroom environment. We show that knowledge is constructed cumulatively, each activity allowing
for the consolidating of previous constructs. This pattern indicates the nature of the processes involved: knowledge constructing
and consolidating are dialectical processes, developing over time, when new constructs stem from old ones already consolidated,
which gain consolidation through the new construction, creating a new abstract entity. We also discuss the potential of the
tool the students used (a spreadsheet program) to such processes of learning mathematics. 相似文献
2.
Einat Heyd-Metzuyanim Michal Tabach Talli Nachlieli 《Journal of Mathematics Teacher Education》2016,19(6):547-574
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. 相似文献
3.
Dina Tirosh Pessia Tsamir Esther Levenson Michal Tabach Ruthi Barkai 《Educational Studies in Mathematics》2013,83(2):309-322
This article reports on young children’s self-efficacy beliefs and their corresponding performance of mathematical and nonmathematical tasks typically encountered in kindergarten. Participants included 132 kindergarten children aged 5–6 years old. Among the participants, 69 children were identified by the social welfare department as being abused and/or neglected. Individual interviews were conducted where children were asked to assess their self-efficacy regarding sorting tasks, mathematics tasks, and reciting the alphabet. Children were then requested to perform each of the tasks. Results revealed that no significant differences were found between the abused and neglected children and their peers regarding their self-efficacy beliefs and performances for any of the tasks. For some of the tasks, children were able to correctly assess their performance, while for other tasks, children overestimated their performance. Possible reasons for these outcomes are discussed. 相似文献
4.
Collaborative work in small groups is often a suitable context for yielding substantial individual learning outcomes. Indeed, small-group collaboration has recently become an educational goal rather than a means. Yet, this goal is difficult to attain, and students must be taught how to learn together. In this paper, we focus on how to prepare teachers to become facilitators of small-group collaboration. The current case study monitors a group of six prospective teachers and their instructor during a one-semester course. The instructor was a skilled mathematics teacher with strong beliefs about what is entailed in establishing a mini-culture of learning to learn together and about how to facilitate student group work in problem-solving situations. We describe the learning path followed by the instructor, including the digital environment. The findings show that by the end of the course, the students became more competent facilitators of learning to learn together. 相似文献
5.
Michal Tabach Ruthi Barkai Pessia Tsamir Dina Tirosh Tommy Dreyfus Esther Levenson 《International Journal of Science and Mathematics Education》2010,8(6):1071-1090
According to reform documents, teachers are expected to teach proofs and proving in school mathematics. Research results indicate
that high school students prefer verbal proofs to other formats. We found it interesting and important to examine the position
of secondary school teachers with regard to verbal proofs. Fifty high school teachers were asked to prove various elementary
number theory statements, to write correct and incorrect proofs that students may use, and to evaluate given justifications
to statements from elementary number theory. While all the participants provided correct proofs to the statements, our findings
indicate that teachers are not aware of students’ preference for verbal justifications. Also, about half of the teachers rejected
correct verbal justifications. They claimed that these justifications lacked generality and are mere examples. 相似文献
6.
Journal of Mathematics Teacher Education - 相似文献
7.
Educational Studies in Mathematics - 相似文献
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9.
Pessia Tsamir Dina Tirosh Michal Tabach Esther Levenson 《Educational Studies in Mathematics》2010,73(3):217-231
Engaging students with multiple solution problems is considered good practice. Solutions to problems consist of the outcomes
of the problem as well as the methods employed to reach these outcomes. In this study we analyze the results obtained from
two groups of kindergarten children who engaged in one task, the Create an Equal Number Task. This task had five possible
outcomes and five different methods which may be employed in reaching these outcomes. Children, whose teachers had attended
the program Starting Right: Mathematics in Kindergartens, found more outcomes and employed more methods than children whose
teachers did not attend this program. Results suggest that the habit of mind of searching for more than one outcome and employing
more than one method may be promoted in kindergarten. 相似文献
10.
Michal Tabach Esther Levenson Ruthi Barkai Pessia Tsamir Dina Tirosh Tommy Dreyfus 《Journal of Mathematics Teacher Education》2011,14(6):465-481
In light of recent reform recommendations, teachers are expected to turn proofs and proving into an ongoing component of their
classroom practice. Two questions emerging from this requirement are: Is the mathematical knowledge of high school teachers
sufficient to prove various kinds of statements? Does teachers’ knowledge allow them to determine the validity of an argument
made by their students? The results of this study, in which 50 secondary school teachers participated, point to a positive
answer to the first question in the framework of elementary number theory (ENT). However, the picture is more complex with
respect to the second one. Results indicated that some teachers may over-value the generality of symbolic mode of representation
and under-value the generality of verbal ones. Possibly, the verbal representation of an argument is less transparent and
more difficult to understand. 相似文献