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1.
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
2.
Esther Levenson Pessia Tsamir Dina Tirosh 《Journal of Mathematics Teacher Education》2010,13(4):345-369
This article focuses on elementary school teachers’ preferences for mathematically based (MB) and practically based (PB) explanations.
Using the context of even and odd numbers, it explores the types of explanations teachers generate on their own as well as
the types of explanations they prefer after reviewing various explanations. It also investigates the basis for these preferences.
Results show that teacher-generated explanations include more MB explanations than PB explanations. However, many still choose
to use mostly PB explanations in their classrooms, believing that these explanations will be most convincing to their students.
The implications for teacher education are discussed. 相似文献
3.
Esther Levenson Dina Tirosh Pessia Tsamir 《International Journal of Science and Mathematics Education》2006,4(2):319-344
This paper is an initial investigation of teachers’ and students’ preferences for mathematically-based (MB) and practically-based (PB) explanations and the relationship between those preferences and sociomathematical norms. The study focuses on one fifth grade teacher and two of her students and discusses three issues. The first issue concerns students’ abilities to understand and accept MB explanations. The second issue concerns the choices teachers make regarding the types of explanations they introduce to their classes and the basis for these choices. The third issue concerns the place of the individuals’ preferences within the sociomathematical norms of the class. The findings indicate that elementary school students are capable of understanding MB explanations and some might even prefer them. We also found that although a teacher might personally prefer MB explanations, this preference may be set aside for didactical considerations. Finally, we discuss the complex relationship between individual preferences for MB and PB explanations and sociomathematical norms. 相似文献
4.
This paper describes university students’ grasp of inflection points. The participants were asked what inflection points are, to mark inflection points on graphs, to judge the validity of related statements, and to find inflection points by investigating (1) a function, (2) the derivative, and (3) the graph of the derivative. We found four erroneous images of inflection points: (1) f ′ (x)?=?0 as a necessary condition, (2) f ′ (x)?≠?0 as a necessary condition, (3) f ″ (x)?=?0 as a sufficient condition, and (4) the location of “a peak point, where the graph bends” as an inflection point. We use the lenses of Fischbein, Tall, and Vinner and Duval’s frameworks to analyze students’ errors that were rooted in mathematical and in real-life contexts. 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.
In this paper we examine the possibility of differentiating between two types of nonexamples. The first type, intuitive nonexamples, consists of nonexamples which are intuitively accepted as such. That is, children immediately identify them as nonexamples.
The second type, non-intuitive nonexamples, consists of nonexamples that bear a significant similarity to valid examples of the concept, and consequently are more often
mistakenly identified as examples. We describe and discuss these notions and present a study regarding kindergarten children’s
grasp of nonexamples of triangles.
相似文献
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7.
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
8.
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
9.
10.
Pessia Tsamir 《Educational Studies in Mathematics》2001,48(2-3):289-307
This paper demonstrates how research-based knowledge about students’ incompatible answers to different representations of
the same task could be used in mathematics instruction. The `It's the Same Task' research-based activity is described; this
activity encourages students to reflect on their thinking about infinite quantities and to avoid contradictions by using only
one criterion, one-to-one correspondence, for comparing infinite quantities. This activity led the vast majority of participants
to the realization that producing contradictory reactions to the same mathematical task is problematic and to avoid this contradiction
by using the one-to-one correspondence as the unique criterion for the comparison-of-infinite-sets tasks.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献