排序方式： 共有24条查询结果，搜索用时 16 毫秒
1.
Our study investigates perspectives of mathematics teacher educators related to the usage of their mathematical knowledge
in teaching “Methods of Teaching Elementary Mathematics” courses. Five mathematics teacher educators, all with experience
in teaching methods courses for prospective elementary school teachers, participated in this study. In a clinical interview
setting, the participants described where and how, in their teaching of elementary methods courses, they had an opportunity
to use their advanced mathematical knowledge and provided examples of such opportunities or situations. We outline five apparently
different viewpoints and then turn to the similar concerns that were expressed by the participants. In conclusion, we connect
the individual perspectives by situating them in the context of unifying themes, both theoretical and practical. 相似文献
2.
Exemplifying definitions: a case of a square 总被引：1，自引：1，他引：0
In this study we utilize the notion of learner-generated examples, suggesting that examples generated by students mirror their
understanding of particular mathematical concepts. In particular, we explore examples generated by a group of prospective
secondary school teachers for a definition of a square. Our framework for analysis includes the categories of accessibility
and correctness, richness, and generality. Results shed light on participants’ understanding of what a mathematical definition
should entail and, moreover, contrast their pedagogical preferences with mathematical considerations. 相似文献
3.
4.
This article is a systematic reflection on a sequence of episodes related to teaching probability. Our central claim is that
reducing problems to a consideration of the sample space, which consists of equiprobable outcomes, may not be in accord with
learners’ initial ways of reasoning. We suggest a “desirable pedagogical approach” in which the solution builds on the set
of outcomes as identified by learners and serves as a bridge towards mathematical convention. To explore prospective high
school mathematics teachers’ ideas related to addressing a potential learner’s mistake and their reactions towards the suggested
approach, we presented them with two tasks. In Task I, participants (n = 30) were asked to suggest a pedagogical remedy to a frequent mistake found in dealing with a standard probability problem,
whereas in Task II, they were asked to solve a probabilistic problem, which they had not encountered previously. We discuss
participants’ mathematical solutions to Task II in reference to their pedagogical approaches to Task I. The presented disparity
serves in extending the convincing power of the suggested pedagogical approach. 相似文献
5.
6.
Rina Zazkis 《Educational Studies in Mathematics》1998,36(1):73-89
Differences in preservice elementary school teachers' perceptions between divisibility by two, or 'evenness' and divisibility by another number have been observed. This led to an inquiry into participants' understanding of the parity of the whole numbers. The results reveal that the equivalence of the number properties of being 'even' and being 'divisible by two' is not taken for granted. Rather, the parity is often perceived as a function of the last digit of the number. The extent of this perception is investigated. Some pedagogical approaches are considered. 相似文献
7.
This report focuses on prospective secondary mathematics teachers’ understanding of irrational numbers. Various dimensions
of participants’ knowledge regarding the relation between the two sets, rational and irrational, are examined. Three issues
are addressed: richness and density of numbers, the fitting of rational and irrational numbers on the real number line, and
operations amongst the elements of the two sets. The results indicate that there are inconsistencies between participants’
intuitions and their formal and algorithmic knowledge. Explanations used by the vast majority of participants relied primarily
on considering the infinite non-repeating decimal representations of irrationals, which provided a limited access to issues
mentioned above. 相似文献
8.
What makes a counterexample exemplary? 总被引：1，自引：1，他引：0
In this paper we describe two episodes of instructional interaction, in which examples are used in order to help students
face their misconceptions. We introduce the notions of pivotal example and bridging example and highlight their role in creating
and resolving a cognitive conflict. We suggest that the convincing power of counterexamples depends on the extent to which
they are in accord with individuals’ example spaces. 相似文献
9.
10.