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1.
International comparative studies such as the Trend in International Mathematics and Science Study (TIMSS) and the OECD Programme
for International Student Assessment (PISA) indicate that Korean students have consistently performed well. In addition, a
recent study titled Mathematics Teaching in the 21st Century (MT21) compared prospective teachers’ knowledge and beliefs about teaching and learning in six participant countries, reporting
that Korean prospective secondary mathematics teachers were better prepared than those in other countries. In this context,
this study has examined the curricula for mathematics teacher education and teacher employment tests in order to investigate
the social expectation for teacher professionalization in Korea, particularly focusing on teacher knowledge. The analysis
shows that while elementary mathematics teacher education emphasizes pedagogical knowledge, the secondary mathematics education
curricula are highly content knowledge oriented. However, the secondary mathematics teacher education includes various aspects
of pedagogical content knowledge in its curricula and teacher employment test. This research also identifies the discourse
concerning mathematics instruction for diversity and equity and the emphasis of reflective practice as the significant development
of the current Korean teacher education. 相似文献
2.
Ji-Won Son 《ZDM》2012,44(2):161-174
The overall level of conceptual understanding and mathematical proficiency of students has been a matter of increasing national
interest in South Korea. Recently, a new edition of mathematics textbooks aligned with the amendment of the 7th national mathematics
curriculum has become available for all elementary grade levels. To characterize the current reform efforts in South Korea,
this study examined the quality of the mathematical problems in the current version of the Korean reform textbooks (KM 2)
compared with the previous version (KM 1) and one representative US reform curriculum text (EM). Webb’s (Research monograph No. 18: Alignment of science and mathematics standards and assessments in four states. National Institute for Science Education, Madison, 1999) depth of knowledge framework and Son and Senk’s (Educ Stud Math 74(2):117–142, 2010) cognitive expectation feature were employed to examine the kind and level of students’ opportunities to learn along with
the type of word problems presented in the three sets of materials. Analysis revealed that the KM 2 provided better opportunities
for students to learn fraction addition and subtraction than the KM 1 in terms of the depth and breadth of cognitive complexity.
However, there was little difference in addressing and developing the meaning of fraction addition and subtraction through
word problems. Moreover, compared with the US reform curriculum materials, the KM 2 provided more problems requiring lower
depth of knowledge levels than the US counterpart. Implications of these findings for curriculum developers, textbook and
learning materials developers, teachers and future researchers are discussed. 相似文献
3.
ABSTRACTThis research is a secondary analysis with Korean students’ data collected in the TIMSS 2015 to describe the moderation effects of instructional practices on the relationships between students’ emotional dispositions toward mathematics and mathematics achievement. From the TIMSS 2015 database, we collected mathematics achievement scores, a student-level contextual scale for students’ emotional disposition, and teacher-level contextual scales representing teachers’ instructional practices. We applied hierarchical linear modelling to construct multilevel models. The findings showed that the achievement gap between emotional dispositions – like and dislike – became smaller when teachers more frequently implemented certain instructional practices like asking students to complete challenging exercises, decide their own problem-solving procedures, and express their ideas in class. Students who disliked mathematics were likely to have higher scores as their teachers implemented each of those practices more frequently. Findings provide important implications to teachers regarding: It is important to encourage students to reason through instructional practices like asking them to decide their own problem-solving procedures and to solve challenging problems. 相似文献
4.
Lance Nielsen 《Acta Appl Math》2010,110(1):409-429
In this paper we develop a method of forming functions of noncommuting operators (or disentangling) using functions that are
not necessarily analytic at the origin in ℂ
n
. The method of disentangling follows Feynman’s heuristic rules from in (Feynman in Phys. Rev. 84:18–128, 1951) a mathematically rigorous fashion, generalizing the work of Jefferies and Johnson and the present author in (Jefferies and
Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001). In fact, the work in (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) allow only functions analytic in a polydisk centered at the origin in ℂ
n
while the method introduced in this paper enable functions that are not analytic at the origin to be used. It is shown that
the disentangling formalism introduced here reduces to that of (Jefferies and Johnson in Russ. J. Math. 8:153–181, 2001) and (Jefferies et al. in J. Korean Math. Soc. 38:193–226, 2001) under the appropriate assumptions. A basic commutativity theorem is also established. 相似文献
5.
Remmers (Adv. Math. 36:283–296, 1980) uses group diagrams in the Euclidean plane to demonstrate how equality in a semigroup S “mirrors” that inside the group G sharing the same presentation with S, when S satisfies Adyan’s condition—no cycles in the left/right graphs of the semigroup’s presentation. Goldstein and Teymouri (Semigroup
Forum 47:299–304, 1993) introduce a conjugacy equivalence relation for semigroups S. By closely examining the geometry of annular group diagrams in the plane, they show how their equivalence relation mirrors
conjugacy inside G, for S satisfying Adyan’s. In this article we introduce two cancellative commutative congruences. Following their leads, we examine
the geometry of group diagrams on closed surfaces of higher genera to demonstrate how these congruences mirror equality inside
two naturally associated Abelian quotient groups G/[G,G] and G/G
2, respectively. In these instances we can drop Adyan’s condition. 相似文献
6.
The article starts focusing egalitarianism in a Norwegian curricular context in general and in mathematics education from
primary schools to teacher education in particular. It progresses by locating and problematizing some major ideologies in
mathematics education such as rationalism, activism, competitivism and ‘autodidactism’ on one hand and egalitarianism on the
other. Some results from TIMSS, where Norway differs significantly from other countries, are touched upon and contrasted with
episodes from qualitative studies. It is asked, from a general didaktic point of view, whether egalitarian values in mathematics
education should be seen as strength or weekness, and the other way round, whether mathematical education contributes to or
counterworks egalitarianism in society. 相似文献
7.
Buchholz’s Ω
μ+1-rules provide a major tool for the proof-theoretic analysis of arithmetical inductive definitions. The aim of this paper
is to put this approach into the new context of modal fixed point logic. We introduce a deductive system based on an Ω-rule
tailored for modal fixed point logic and develop the basic techniques for establishing soundness and completeness of the corresponding
system. In the concluding section we prove a cut elimination and collapsing result similar to that of Buchholz (Iterated inductive
definitions and subsystems of analysis: recent proof theoretic studies. Lecture notes in mathematics, vol. 897, pp. 189–233,
Springer, Berlin, 1981). 相似文献
8.
Ring semigroups whose subsemigroups form a chain 总被引:1,自引:1,他引:0
Greg Oman 《Semigroup Forum》2009,78(2):374-377
A multiplicative semigroup S is called a ring semigroup if an addition may be defined on S so that (S,+,⋅) is a ring. Such semigroups have been well-studied in the literature (see Bell in Words, Languages and Combinatorics,
pp. 24–31, World Scientific, Singapore, 1994; Jones in Semigroup Forum 47(1):1–6, 1993; Jones and Ligh in Semigroup Forum 17(2):163–173, 1979). In this note, we use Mihăilescu’s Theorem (formerly Catalan’s Conjecture) to characterize the ring semigroups whose subsemigroups
containing 0 form a chain with respect to set inclusion. 相似文献
9.
This paper draws on data from the international TEDS-M study, organized by the IEA, and utilizes a conceptual framework describing
the Taiwanese perspective of mathematics and mathematics teaching competences (MTCs) with regard to investigating the uniqueness
and patterns of Taiwanese future primary teacher performance in the international context. The framework includes content-oriented
and thought-oriented categories of mathematics competence. The latter category contains subcategories adopted and revised
from (3rd Mediterranean conference on mathematical education. Hellenic Mathematical Society, Athens, 2003) the competence approach by Niss. Hsieh’s (Research on the development of the professional ability for teaching mathematics
in the secondary school level (3/3). Taiwan: National Science Council, 2009) model is also adopted and revised to serve as an analytical framework, including four categories relating to MTCs, representations,
language, and misconceptions or error procedures. This paper shows that in thought-oriented mathematics competences Taiwan
and Singapore share a unique pattern of higher percent correct in competences related to formalization, abstraction, and operations
in mathematics than in those related to the way of thinking, modelling and reasoning in and with mathematics. The paper also
addresses weak teaching competences claimed in domestic studies, which conflict with the TEDS-M results. Namely, in contrary
to the international trend, Taiwanese future primary teachers are weak at judging mathematics competences required by students
to learn mathematical concepts or solve problems, and superior at diagnosing and dealing with student misconceptions and error
procedures. 相似文献
10.
11.
Gül Kaleli-Yılmaz Alper Hanci 《International Journal of Mathematical Education in Science & Technology》2016,47(5):674-695
The aim of this study is to determine how the TIMSS mathematics success of the 8th grade students differentiates according to the school type, gender, mathematics report mark, parents' education level, cognitive domains and cognitive domains by gender. Relational survey method was used in the study. Six-hundred fifty two 8th grade students studying in the same city in Turkey participated in this study. In this study, a 45 question test that was made up by choosing TIMSS 2011 mathematics questionnaire was used as a data collection tool. Quantitative data analysis methods were used in the data analysis, frequency, percentage, average, standard deviation, independent sample test, one-way analysis of variance and post-hoc tests were applied to data by using SPSS packaged software. At the end of the study, it was determined that the school type, mathematics school mark, parents' education level and cognitive domains influenced the students' TIMSS mathematics success but their gender was a neutral element. Moreover, it was seen that schools which are really successful in national exams are more successful in TIMSS exam; students whose mathematics school marks are 5 and whose parents graduated from university are more successful in TIMSS exams than others. 相似文献
12.
Ljiljana Petrović Dragana Stanojević 《Journal of Mathematical Modelling and Algorithms》2010,9(1):113-128
In this paper we consider different concepts of causality in filtered probability spaces. Especially, we consider a generalization
of a causality relationship “G is a cause of J within H ” which was first given by Mykland (1986) and which is based on Granger’s definition of causality (Granger, Econometrica 37:424–438, 1969). Then we apply this concept on weak solutions of stochastic differential equations with driving semimartingales. We also
show that the given causality concept is closely connected to the concept of extremality of measures and links Granger’s causality
with the concept of adapted distribution. Finally, the concept of causality is applied on solution of martingale problem. 相似文献
13.
A cross‐curricular structured‐probe task‐based clinical interview study with 44 pairs of third year high‐school mathematics students, most of whom were high achieving, was conducted to investigate their approaches to a variety of algebra problems. This paper presents results from three problems that were posed in symbolic form. Two problems are TIMSS items (a linear inequality and an equation involving square roots). The other problem involves square roots. We found that the majority of student pairs used symbol manipulation when solving the problems, and while many students seemed to prefer symbolic over graphical and tabular representations in their first attempt at solving the problems, we found that it was common for student pairs to use more than one strategy throughout the course of their solving. Students' use of graphing calculators to solve the problems is discussed. 相似文献
14.
Tom Meyerovitch 《Inventiones Mathematicae》2011,184(3):567-589
We discuss some numerical invariants of multidimensional shifts of finite type (SFTs) which are associated with the growth
rates of the number of admissible finite configurations. Extending an unpublished example of Tsirelson (A strange two-dimensional
symbolic system, 1992), we show that growth complexities of the form exp (n
α+o(1)) are possible for non-integer α’s. In terminology of de Carvalho (Port. Math. 54(1):19–40, 1997), such subshifts have entropy dimension α. The class of possible α’s are identified in terms of arithmetical classes of real numbers of Weihrauch and Zheng (Math. Log. Q. 47(1):51–65, 2001). 相似文献
15.
J. H. Wang 《Journal of Optimization Theory and Applications》2011,148(1):125-145
The present paper is concerned with the convergence problems of Newton’s method and the uniqueness problems of singular points
for sections on Riemannian manifolds. Suppose that the covariant derivative of the sections satisfies the generalized Lipschitz
condition. The convergence balls of Newton’s method and the uniqueness balls of singular points are estimated. Some applications
to special cases, which include the Kantorovich’s condition and the γ-condition, as well as the Smale’s γ-theory for sections on Riemannian manifolds, are given. In particular, the estimates here are completely independent of the
sectional curvature of the underlying Riemannian manifold and improve significantly the corresponding ones due to Dedieu,
Priouret and Malajovich (IMA J. Numer. Anal. 23:395–419, 2003), as well as the ones in Li and Wang (Sci. China Ser. A. 48(11):1465–1478, 2005). 相似文献
16.
We are studying in this article an interplay between workers in organizations under the assumption that workers exhibit behavioral
biases: envy, jealousy, or admiration toward the other coworkers’ compensation. We assume workers care about their relative
position, and we study the impact of this assumption on their efforts and on their optimal incentive contracts. We explicitly
solve for the optimal incentive contract of moral hazard a la Holmstrom and Milgrom (Econometrica 55:303–328, 1987). We model team production by agents in which each agent’s effort generates an observable signal and depends on efforts of
other agents. One of the important findings is that an agent’s optimal effort is negatively impacted by the behavioral biases
in other agents’ judgments. We also show envious behavior is destructive for organizations. Consistent with Tirole (Econometrica
69(1):1–35, 2001), our findings suggest that in the presence of agency problems induced by envy or jealousy, the optimal compensation exhibits
high pay-for-performance sensitivity. 相似文献
17.
Kyungmee Park 《ZDM》2012,44(2):121-135
This study identifies the characteristics of mathematics classrooms in Korea. First, conventional Korean mathematics lessons
are analyzed from the perspective of “theory of variation”. Second, an innovative lesson for gifted children is reported in
detail and analyzed from the perspective of “Lakatos’ proofs and refutations”. Third, the classroom characteristics identified
in both the conventional lessons and the innovative lesson are interpreted in terms of the underlying cultural values that
they share with other East Asian countries. The study concludes that although the two faces of Korean mathematics lessons look different, they may flow from the same “heart”—that of the common Confucian heritage culture culture, and in particular
East Asian pragmatism. 相似文献
18.
Klaus Keimel 《Semigroup Forum》2008,77(1):109-142
Already in his PhD Thesis on compact Abelian semigroups under the direction of Karl Heinrich Hofmann the author was lead to
investigate locally compact cones (Keimel in Math. Z. 99:205–428, 1967). This happened in the setting of Hausdorff topologies. The theme of topological cones has been reappearing in the author’s
work in a non-Hausdorff setting motivated by the needs of mathematical models for a denotational semantics of languages combining
probabilistic and nondeterministic choice. This is in the line of common work with Karl Heinrich Hofmann in Continuous Lattices and Domains (Gierz et al. in Encyclopedia of Mathematics and its Applications, vol. 93, 2003).
Domain Theory is based on order theoretical notions from which intrinsic non-Hausdorff topologies are derived. Along these
lines, domain theoretical variants of (sub-) probability measures have been introduced by Jones and Plotkin (Jones, PhD thesis,
1990; Jones and Plotkin in Proceedings of the Fourth Annual Symposium on Logic in Computer Science, pp. 186–195, 1989). Kirch (Master’s thesis, 1993) and Tix (Master’s thesis, 1995) have extended this theory to a domain theoretical version of measures and they have introduced and studied directed complete
partially ordered cones as appropriate structures. Driven by the needs of a semantics for languages combining probability
and nondeterminism, Tix (Theor. Comput. Sci 264:205–218, 1999; PhD thesis, 1999) and later on Plotkin and Keimel (Electron. Notes Theor. Comput. Sci. 129:1–104, 2005) developed basic functional analytic tools for these structures.
In this paper we extend this theory to topological cones the topologies of which are strongly non-Hausdorff. We carefully
introduce these structures and their elementary properties. We prove Hahn-Banach type separation theorems under appropriate
local convexity hypotheses. We finally construct a monad assigning to every topological cone C another topological cone
the elements of which are nonempty compact convex subsets of C. For proving that this construction has good properties needed for the application in semantics we use the functional analytic
tools developed before.
Dedicated to Karl Heinrich Hofmann at the occasion of his 75th birthday.
Thanks to Gordon Plotkin for numerous discussions. Preliminary results have been announced at MFPS XXIII 20. In his Master’s thesis supervised by the author, B. Cohen 6 has worked out some of those results. 相似文献
19.