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1、河北师范大学本科生毕业论文（设计）翻译文章 为了培养出合格的印尼人，即具备解决问题能力的人，数学在教育环境中起着非常重要的作用。因此，为了让学生能够有解决问题的能力，从小学到中学教育的各个层面都授有数学课程。根据KTSP中所论述的，数学学习目标之一就是让学生有解决问题的能力。其中包括理解问题的能力，设计一个数学模型，解决这个模型和阐述所得到的解决办法。 数学（尤其是解决问题时）的重要性不能被大多数学生优化，一些调查可见，绝大多数学生解决数学问题的能力仍然低下。此外，很多学生认为数学是一项艰难而繁琐的学科。作者指出缺乏数学问题解决能力和这些假设的出现，是毫无准备的学生遵循特定学习活动的结果，这些
2、活动忽略了学生本身数学能力的差异性。 这篇文章意在调查数学能力和数学创造力之间是否存在关系以及检测这种关系的结构。另外，为了更加确定这两个结构之间的关系，我们将跟踪几组拥有不同数学能力的学生以及调查这些学生在数学能力检测的表现和数学创造力之间的关系。359个小学数学能力和数学创造力的检测的数据已被收集。数学能力被认为是一个多维的机构，包括数量能力（数字感觉，预代数推理）， 因果能力（因果关系检验），空间能力（折纸，视野和空间旋转的能力），定性的能力（相似性和差异的处理方程）和电感/演绎能力。数学的创造力被定义为一个特定领域的特征，它使个人在数学领域表现的更加流畅，灵活和独创。数据分析表明数学能
3、力和数学创造力之间有积极的相互作用。此外，验证性因素分析表明，数学创造力是数学能力的一个下属结构。此外，潜类分析表明，运用数学能力的不同可以吧学生分为三种不同类别。这些数学能力不同的学生也反映着三种具有不同数学创造力的学生。 数学创造力现在被认为是所有学生应该掌握的必要技能（mann 2005）.实际上，在特定领域知识的创造运用（Sternberg 1999），采用普通数学算法的独创解决方法(Shriki 2010)，以及寻找多种解决数学问题答案的能力 (Sriraman 2005)都被认为是学好数学的重要因素。 在这点，数学创造力与特定领域的深层知识紧密相连(Mann 2005).但是，数学
4、创造力和数学能力之间的关系依然值得深思。那么两个相关的问题出现了:数学能力和数学创造力之间有相互关系吗？数学能力是数学创造力的前提吗？数据表明，相关的研究呈现出截然不同的答案。 因此，这篇文章的目的是调查以及澄清数学能力和数学创造力之间的关系。这篇论文的结构如下：首先，呈现理论背景以及数学关系和数学创造力的关系；其次，讲述研究方法；接着呈现表示数学能力和数学创造力关系的替代方案的结构；然后讲述替代模式对比所呈现的结果；最后，讨论这个研究的结论和局限性。 科学和数学研究表明，对于本质上相似的问题，学生们会产生互不兼容的解决办法。例如，当同一个问题处于不同的语境中时，他们会给与不相宜的反应。这一观
5、察结果提出了对理论教育和实际教育中至关重要的问题。一个核心问题是，各种各样的因素是怎样影响学生们对于某个特定问题的选择呢？更具体地说，这些因素是如何与这个问题相联系的呢？例如：它的结构、它的数据、图形方面，以及所涉及的领域是怎样影响学生的解决方法的呢？与求解者相关的因素（如：年龄、年级、教导）对他或她解决某一特定问题产生什么样的影响？ 通过给学生展示一系列本质相似的问题，再调查每个问题的具体特征和学生反应的关系，这些问题通常会得到解决。一个不太常规的方法是考察学生对于外表相似、本质不同，需要不同解决办法的问题的反应。 两种本质不同的问题被选作这一研究课题：有关潜在无限性的数学问题和有关颗粒性物
6、质的科学问题。这两个问题在形象上和空间上相近，但由于分别来自一个完全不同的理论结构，它们需要不同的应对方法。主要目标是：（a）来检测学生会错误的对两种问题产生相同的或应对措施，还是对每个问题给与不同的解答办法；（b）来检测学生的应对办法随着常规的、学校的教导而改变；（c）来评定学生充分评估每个问题的效果。 来自以色列沙龙区的两百名中学生参加了这一调研。调查者随机挑选了来自同一所学校的七、八、十、十二年级的50名学生。十年级和十二年级的学生的主修学科是数学。 根据国家教学课程设置，所有被调查的学生都学习数学和科学。在七年级时，他们没有受到任何关于几何和无限性上的教导。在调查期间，他们进行了一章关
7、于物质颗粒性质的学习。八年级的学生也没有受到任何关于几何和无限性上的教导。在那一年，他们学习了关于元素、化合物和周期表的科学知识。十年级学生学习了基本欧几里德几何（未定义和定义的术语，公理，公设，定义，定理和样张）。在这些年，他们并没有进行任何关于科学物质结构的额外的学习。十二年级的学生在十一和十二年级时学习了积分的入门课程，他们处理了无穷级数，限制和积分。在这些年级，他们也对科学进行了围观的学习（化学计量，原子、酸、碱的结构，氧化和还原）。 几位教师分别教导学生，这些老师不止在一个年级任教。所有教师都至少有数学或科学的学士学位，中学教师证书，并且至少有三年教学经验。 Thematics ha
8、s an important role in educational settings in order to achieve complete Indonesian human,the human who is able to resolve the problems encountered. Therefore mathematics lessons are given at every level of education from primary to secondary education,with the aim that every student can have the ab
9、ility to solve the problems. As stated in one of the goals of learning mathematics based Kurikulum Tingkat Satuan Pendidikan(KTSP) is that students should have the ability to solve problems which includes the ability to understand the problem,devised a mathematical model,solve the model and interpre
10、t the obtained solution(see 1). The important role of mathematics (especially in problem solving) cannot be optimized by majority students;it is visible from some researches that say the ability of mathematical problem solving of most students is still low. In addition,there are many students who th
11、ink that mathematics is a difficult and tedious subject. The author observes that the lack of mathematics problem solving capabilities and the emergence of these assumptions as a result of unpreparedness students to follow a particular learning activity regardless of the presence of heterogeneity of
12、 students mathematical abilities. This study aims to investigate whether there is a relationship between mathematical ability and mathe-matical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the rela-tionship between the two constructs, we will trace
13、 groups of students that differ across mathematical ability and investigate the relationships amongst these students per-formance on a mathematical ability test and the compo-nents of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical c
14、reativity test, to 359 elementary school students. Mathematical ability was considered as a multi-dimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal abil-ity (examination of causeeffect relations), spatial ability (paper folding, perspective and
15、spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexi-bility and originality in the doma
16、in of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed
17、that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of stu-dents varying in mathematical creativity. Mathematical creativity has recently come to be considered as an es
18、sential skill that may and should be enhanced in all students (Mann 2005). Indeed, the creative application of knowledge in specific circumstances (Sternberg 1999), proposing original solutions by employing common mathematical algorithms (Shriki 2010), as well as the ability to find numerous and dis
19、tinctively different answers in mathematical tasks (Sriraman 2005), are considered to be important elements for success in mathematics. In this view, mathematical creativity is closely related to deep knowledge in the specific domain (Mann 2005). However, the relationship between mathematical creati
20、vity and mathematical ability is still ambiguous. Two relative questions arise: Is there a correlation between mathemati-cal creativity and mathematical ability? Are mathematical abilities prerequisites of mathematical creativity or vice versa? To date, related research has led to conflicting result
21、s. Therefore, the aim of this paper is to investigate and clarify the relationship between mathematical crea-tivity and mathematical ability. The paper is organized as follows. First, the theoretical background is presented, addressing the relationship of ability and creativity in mathematics. Then,
22、 the method-ology is presented. Afterwards the structures of the alter-native models regarding the relationship of mathematical ability and mathematical creativity are presented, followed by the results yielded by the comparison of the alternative models and the comparison among the groups of studen
23、ts.Finally, the conclusions and limitations of the study are discussed. Research in science and mathematics education has indicated that students sometimes produce mutually incompatible solutions to essentially similar problems.For instance,they provide uncongenial responses to the same problem when
24、 it is given in two different contexts(Clough & Driver,1986;Hiebert & Lefevre,1986). This observation raises issues which are of great theoretical and practical importance to education. A central issue is, how do various factors affect the students choice of response to a given problem? More specifi
25、cally,how do factors related to the problem, i.e.lts structure, the numerical data,the figural aspects, and the content domain in which it is embedded, affect the solution? What effects do factors related to the solver,i.e.age,grade level,and instruction, have on his or her solution to a given probl
26、em? These issues are usually approached by presenting students with a variety of essentially similar problems and investigating the relationship between the specific features of each of these problems and studentsresponses (Silver,1986;Stavy,1990).A less conventional way is examining studentsrespons
27、es to problems which are externally similar though essentially different and require different solutions. Two essentially different problems, a mathematical problem related to potential infinity and a scientific problem related to the particulate nature of matter,were chosen for this study.These two
28、 problems are figurally and spatially similar but since each stems form an entirely different theoretical framework, they require different responses. The main aims were: (a) to determine if students tend to erroneously produce the same response to both problems or rather give different ,adequate re
29、sponse to each of them;(b)to investigate whether studentsresponses change with formal, school-based instructions; and (c) to assess the effects of exposing students to the adequate interpretations each of these problems. Two-hundred upper middle-class students from the Sharon area in Israel particip
30、ated in this study, Fifty students were randomly selected from the seventh,eighth,tenth,and twelfth grade levels in the same school. The tenth-and twelfth-grade students studied mathematics as their major subject. All participating students studied mathematics and science according to the national c
31、urriculum. The topics that the subjects studied are as follows: In the seventh grade they did not receive any instruction in mathematics concerning geometry or infinite processes. At the time of the research, they had finished studying a chapter on the particulate nature of matter. The eighth-grade
32、students also had not received any instruction concerning geometry or infinite processes. In that year, they had received formal instruction in science related to elements, compounds,and the periodic table. The tenth-grade students had studied basic Euclidean geometry (i.e. Undefined and defined ter
33、ms,axioms,postulates,definitions,theorems,and proofs) in the ninth and tenth grades. During these years, they did not receive any additional instruction in science concerning the structure of matter. The twelfth-grade students had studied,in the eleventh and twelfth grades,an introductory course in
34、calculus in which they dealt with infinite series, ;limits,and integrals. They also studied,in these grades,science on a minor level(stoichiometry, the structure of the atom,acids and bases,oxidation and reduction,etc.). The students were taught by several teachers,all of whom had taught in more than one grade level. All teachers had at least a bachelors degree in either mathematics or science,a teacher certificate for secondary school,and at least three years of teaching experience.