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1.
Helena Johansson 《International Journal of Science and Mathematics Education》2016,14(6):1133-1152
This paper focuses on one aspect of mathematical competence, namely mathematical reasoning, and how this competency influences students’ knowing of physics. This influence was studied by analysing the mathematical reasoning requirements upper secondary students meet when solving tasks in national physics tests. National tests are constructed to mirror the goals stated in the curricula, and these goals are similar across national borders. The framework used for characterising the mathematical reasoning required to solve the tasks in the national physics tests distinguishes between imitative and creative mathematical reasoning. The analysis process consisted of structured comparisons between representative student solutions and the students’ educational history. Of the 209 analysed tasks, 3/4 required mathematical reasoning in order to be solved. Creative mathematical reasoning, which, in particular, involves reasoning based on intrinsic properties, was required for 1/3 of the tasks. The results in this paper give strong evidence that creative mathematical reasoning is required to achieve higher grades on the tests. It is also confirmed that mathematical reasoning is an important and integral part of the physics curricula; and, it is suggested that the ability to use creative mathematical reasoning is necessary to fully master the curricula. 相似文献
2.
Dolev Sarit Even Ruhama 《International Journal of Science and Mathematics Education》2013,13(2):309-327
This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem. Two different units of analysis were used to analyze two central topics in the seventh grade curriculum as follows: (1) equation solving in algebra and (2) triangle properties in geometry. The findings indicate that all six textbooks had considerably larger percentages of geometric tasks than algebraic tasks, which required students to justify or explain their mathematical work. Moreover, considerable differences were found among the six textbooks regarding the percentages of tasks that required students to justify and explain in both topics, but more so with the algebraic topic. Analysis of whether the textbook tasks required students to justify a mathematical claim that is stated by the textbook or a mathematical claim that the students themselves generated also revealed substantial differences among the textbooks. These findings are discussed, as well as the research methods used, in light of relevant literature.
相似文献3.
Baptista Geilsa Costa Santos Santos Rodrigo da Silva Cobern William W. 《International Journal of Science and Mathematics Education》2015,13(2):309-329
This study analyzes six seventh grade Israeli mathematics textbooks, examining (1) the extent to which students are required to justify and explain their mathematical work, and (2) whether students are asked to justify a mathematical claim that is stated by the textbook or a mathematical claim that they themselves generated when solving a problem. Two different units of analysis were used to analyze two central topics in the seventh grade curriculum as follows: (1) equation solving in algebra and (2) triangle properties in geometry. The findings indicate that all six textbooks had considerably larger percentages of geometric tasks than algebraic tasks, which required students to justify or explain their mathematical work. Moreover, considerable differences were found among the six textbooks regarding the percentages of tasks that required students to justify and explain in both topics, but more so with the algebraic topic. Analysis of whether the textbook tasks required students to justify a mathematical claim that is stated by the textbook or a mathematical claim that the students themselves generated also revealed substantial differences among the textbooks. These findings are discussed, as well as the research methods used, in light of relevant literature. 相似文献
4.
Tami S. Martin Sharon M. Soucy McCrone Michelle L. Wallace Bower Jaguthsing Dindyal 《Educational Studies in Mathematics》2005,60(1):95-124
Proof and reasoning are fundamental aspects of mathematics. Yet, how to help students develop the skills they need to engage
in this type of higher-order thinking remains elusive. In order to contribute to the dialogue on this subject, we share results
from a classroom-based interpretive study of teaching and learning proof in geometry. The goal of this research was to identify
factors that may be related to the development of proof understanding. In this paper, we identify and interpret students'
actions, teacher's actions, and social aspects that are evident in a classroom in which students discuss mathematical conjectures,
justification processes and student-generated proofs. We conclude that pedagogical choices made by the teacher, as manifested
in the teacher's actions, are key to the type of classroom environment that is established and, hence, to students' opportunities
to hone their proof and reasoning skills. More specifically, the teacher's choice to pose open-ended tasks (tasks which are
not limited to one specific solution or solution strategy), engage in dialogue that places responsibility for reasoning on
the students, analyze student arguments, and coach students as they reason, creates an environment in which participating
students make conjectures, provide justifications, and build chains of reasoning. In this environment, students who actively
participate in the classroom discourse are supported as they engage in proof development activities. By examining connections
between teacher and student actions within a social context, we offer a first step in linking teachers' practice to students'
understanding of proof. 相似文献
5.
Seventy-one college general biology students were taught a unit in Mendelian genetics by the traditional lecture method. Emphasis was placed on meiotic formation of gametes, the Law of Segregation, and the Law of Independent Assortment. The Punnett-square model was used for all practice problems. Eight weeks later, a content-validated retention test was given to evaluate the students' retention of problem-solving skills. The test required students to use proportional reasoning (identifying ratios from the Punnett squares), combinatorial reasoning (identifying combinations of gametes from parental genotypes), and probabilistic reasoning (estimating gamete or offspring probabilities). Each of the 71 students was also given three Piagetian interview tasks to evaluate intellectual development in the areas of reasoning under question. The balance-beam task, the electronic switch-box task, and colored squares and diamonds were used to test for proportional reasoning, combinatorial reasoning, and probabilistic reasoning, respectively. Pearson correlations and factor analysis failed to show direct relationships among Piagetian tasks for the three kinds of reasoning and their corresponding occurrence in genetics problems. Some correlations were higher between different reasoning types than between similar types. Analysis of variance showed significant differences for all three reasoning types among concrete-operational, transitional, and formal-operational students with the retention test. Post-hoc analysis of ANOVAs indicated that formal-operational students had significantly more success in the three reasoning areas than transitional students, and transitional students had significantly more success than concrete-operational students. 相似文献
6.
Mansoor Niaz 《科学教学研究杂志》1989,26(3):221-235
It has been suggested that proportional reasoning tasks contain field effects. Field-dependent students are considered to be highly influenced by the structure of the perceptual field and lack an articulated conceptual framework. To test the hypothesis that there is a significant correlation between field independence and proportional reasoning tasks, a sample of science students were tested to determine performance in proportional reasoning and degree of field independence. It was found that even students who are normally capable of proportional reasoning can be misled by the presence of field effects. A significant correlation (r = 0.50; p = 0.001) was found between the test of field independence and the nine items of proportional reasoning. Educational implications are drawn. 相似文献
7.
《Learning and Instruction》2003,13(4):367-380
Informal reasoning fallacies are arguments that are psychologically pervasive but logically incorrect. The aim of this study was to test the hypothesis that students’ ability to identify the fallacies is associated with a process of text comprehension, specifically with a sub-process of inference during text comprehension. One hundred and eighty four high school students from three grade levels of an urban heterogeneous high school in Israel participated in the study. The students were asked to complete informal reasoning fallacies and text comprehension tasks. It was found that performance in the text comprehension tasks significantly predicted students’ ability to identify the fallacies. 相似文献
8.
Ibrahim Bayazit 《International Journal of Science and Mathematics Education》2013,11(3):651-682
This study examines new Turkish elementary school mathematics textbooks to provide perspectives on the quality of the tasks related to the proportion concept and the ways they are presented. Tasks were analysed for several dimensions with a particular focus on their level of cognitive demands (LCD). Tasks were distinguished in two groups in terms of LCD: lower-level demand and higher-level demand. The findings revealed that 75 % of the tasks were related to higher-level demand in that they requested a certain level of interpretation, required connecting knowledge and procedures related to each other, demanded responses with some explanation and reinforced students’ non-algorithmic thinking. Only 25 % of the tasks were related to a lower-level demand, and these tasks could be resolved by recalling and implementing rules, procedures and factual knowledge without reflecting upon the meaning behind them. Most of the tasks were presented in multiple representations and framed in non-mathematical contexts. All these task characteristics indicate that the new elementary school textbooks have the capacity to promote students’ proportional reasoning. The findings also inform the international community about crucial aspects of the curriculum reforms in Turkey and provide suggestions for teachers and textbook writers concerning the quality of the tasks and their selection and implementation in the classrooms. 相似文献
9.
Anton E. Lawson Christine B. McElrath Margaret S. Burton Bart D. James Roy P. Doyle Stephen L. Woodward Lawrence Kellerman Jan D. Snyder 《科学教学研究杂志》1991,28(10):953-970
This study tested the constructivist hypothesis that the acquisition of domain-specific conceptual knowledge (declarative knowledge) requires use of general procedural knowledge. More specifically, it was hypothesized that use of a general pattern of hypothetico-deductive reasoning is necessary for the acquisition of novel domain-specific concepts. To test this hypothesis 314 high school biology and chemistry students were first tested to determine whether or not they were skilled in the use of hypothetico-deductive reasoning. Based on this test, students were classified as reflective, transitional, or intuitive thinkers. All students were then presented with a series of four concept-acquisition tasks. It was predicted that reflective (hypothetico-deductive) thinkers would acquire the concepts while intuitive (empirico-inductive) thinkers would not. Transitional thinkers were expected to be partially successful. These predictions were confirmed as skill in hypothetico-deductive reasoning (developmental level), but not age, was highly correlated with performance on the concept acquisition tasks (X2 = 71.14, p < 0.00001). This result was interpreted to be supportive of the constructivist hypothesis. 相似文献
10.
Grammatical knowledge is an important part of L1 language education. Nevertheless, teachers find it challenging to convey an in-depth understanding of grammar to their students. Previous research suggests that understanding might be stimulated by focusing on grammatical reasoning. The current mixed-methods study explores the grammatical reasoning of 108 Dutch L1 student teachers’ in odd one out tasks, showing that student teachers struggle with such reasoning tasks. A multilevel regression analysis indicates that their level of grammatical understanding as measured by a Test of Grammatical Understanding (TGU) and the elaborateness of student teachers’ argumentation significantly predict the quality of their grammatical reasoning. Student teachers’ performances were also compared to 14 year old pre-university students’ performances (N = 120). Contrary to what was hypothesized, senior student teachers did not manage to outperform junior student teachers, nor did student teachers outperform pre-university students. The paper discusses plausible reasons for these findings and explores how teacher education might need to shift focus to better develop student teachers’ grammatical reasoning skills. 相似文献
11.
This study compared the relationships of self‐efficacy and reasoning ability to achievement in introductory college biology. Based on the hypothesis that developing formal and postformal reasoning ability is a primary factor influencing self‐efficacy, a significant positive correlation was predicted between reasoning ability and degree of self‐efficacy to complete biological tasks. Further, reasoning ability was predicted to be more highly correlated with course achievement than self‐efficacy. The study involved pre‐ and posttesting 459 introductory biology students. Both self‐efficacy and reasoning ability increased during the semester. As predicted, self‐efficacy and reasoning ability were positively correlated. Depending on the nature of the achievement measure, reasoning ability accounted for some 15 to 30 times more variance in achievement than self‐efficacy. Also, as predicted, reasoning ability was a strong predictor of self‐efficacy, but self‐efficacy was not a strong predictor of reasoning ability. Self‐efficacy estimates and achievement were higher for the concrete tasks than for the formal tasks and higher for the formal tasks than for the postformal tasks. In general, students tended to overestimate their abilities to carry out the concrete, formal, and postformal tasks. Results support the study's working hypothesis that intellectual development continues for some students during the college years, that a postformal level of intellectual development exists, and that reasoning ability is a primary factor influencing both self‐efficacy and achievement. Student overestimation of their abilities may contribute to complacency, lack of effort, and to less than optimal achievement. Consequently, it may be advantageous early in the semester to provide students with particularly challenging tasks that “shock” them out of their complacency and perhaps increase their effort, their reasoning skills, and their achievement. © 2006 Wiley Periodicals, Inc. J Res Sci Teach 44: 706–724, 2007 相似文献
12.
随着学制的缩短,非物理类理工学科《普通物理》课程亟待改革,改革的主要任务是编写一套适用于我校的非物理类《普通物理》教材,研制一套与教材配套的多媒体光盘,编写一套与教材配套的试题库,总结出一套旨在培养学生创新精神的课堂教学模式。 相似文献
13.
Perner (1991) has claimed that the linguistic structures and reasoning tasks mastered by 4-year-olds share a requirement to handle metarepresentation. In contrast, de Villiers (2000) has argued that they share a requirement to handle misrepresentation. In the current study, a correlation is observed between success on false belief tasks and the acquisition of relative clause sentences. This correlation is not predicted by de Villiers's account because such sentences do not require the handling of misrepresentation, but it is consistent with Perner's account because such sentences do require the handling of metarepresentation. It is proposed that only an account that integrates the accounts of both de Villiers and Perner can explain extant data on language and cognition in 4-year-olds. 相似文献
14.
Wim Van Dooren Dirk De Bock Dave Weyers Lieven Verschaffel 《Educational Studies in Mathematics》2004,56(2-3):179-207
In the international community of mathematics and science educators the intuitive rules theory developed by the Israeli researchers Tirosh and Stavy receives much attention. According to this theory, students' responses to a variety of mathematical and scientific tasks can be explained in terms of their application of some common intuitive rules. Two major intuitive rules are manifested in comparison tasks: ‘More A—more B’ and ‘Same A—same B’. In this paper, we address two important questions for which the existing literature on intuitive rules does not provide a convincing research-based answer: (1) are the reasoning processes of students who respond in line with a given intuitive rule actually affected by that rule or by essentially other misconceptions (leading to the same answer), and (2) are individual students consistent in their choice of one of the intuitive rules when confronted with different, conceptually unrelated tasks? A test consisting of five comparison problems from different mathematical subdomains was administered collectively to 172 Flemish students from Grades 10 to 12. An analysis of students' written calculations and justifications suggested that the students were considerably less affected by the intuitive rules than their multiple-choice answers actually suggested. Instead, essentially different misconceptions and errors were found. With respect to the issue of individual consistency, we found that students who made many errors did not answer systematically in line with one of the two intuitive rules. 相似文献
15.
Keith Jones 《Educational Studies in Mathematics》2000,44(1-3):55-85
A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In geometry, forms of software usually known as dynamicgeometry environments may be useful as they can enable students tointeract with geometrical theory. Yet the meanings that students gain ofdeductive reasoning through experience with such software is likely to beshaped, not only by the tasks they tackle and their interactions with theirteacher and with other students, but also by features of the softwareenvironment. In order to try to illuminate this latter phenomenon, and todetermine the longer-term influence of using such software, this paperreports on data from a longitudinal study of 12-year-old students'interpretations of geometrical objects and relationships when using dynamicgeometry software. The focus of the paper is the progressivemathematisation of the student's sense of the software, examining theirinterpretations and using the explanations that students give of thegeometrical properties of various quadrilaterals that they construct as oneindicator of this. The research suggests that the students' explanations canevolve from imprecise, `everyday' expressions, through reasoning that isovertly mediated by the software environment, to mathematicalexplanations of the geometric situation that transcend the particular toolbeing used. This latter stage, it is suggested, should help to provide afoundation on which to build further notions of deductive reasoning inmathematics.This revised version was published online in September 2005 with corrections to the Cover Date. 相似文献
16.
Keith Jones 《Educational Studies in Mathematics》2000,44(1-2):55-85
A key issue for mathematics education is howchildren can be supported in shifting from `because it looks right' or`because it works in these cases' to convincing arguments which work ingeneral. In geometry, forms of software usually known as dynamicgeometry environments may be useful as they can enable students tointeract with geometrical theory. Yet the meanings that students gain ofdeductive reasoning through experience with such software is likely to beshaped, not only by the tasks they tackle and their interactions with theirteacher and with other students, but also by features of the softwareenvironment. In order to try to illuminate this latter phenomenon, and todetermine the longer-term influence of using such software, this paperreports on data from a longitudinal study of 12-year-old students'interpretations of geometrical objects and relationships when using dynamicgeometry software. The focus of the paper is the progressivemathematisation of the student's sense of the software, examining theirinterpretations and using the explanations that students give of thegeometrical properties of various quadrilaterals that they construct as oneindicator of this. The research suggests that the students' explanations canevolve from imprecise, `everyday' expressions, through reasoning that isovertly mediated by the software environment, to mathematicalexplanations of the geometric situation that transcend the particular toolbeing used. This latter stage, it is suggested, should help to provide afoundation on which to build further notions of deductive reasoning inmathematics. 相似文献
17.
Recognising critical reasoning and problem-solving as one of the key skills for twenty-first century citizenship, various types of problem contexts have been practiced in science classrooms to enhance students’ understandings and use of evidence-based thinking and justification. Good problems need to allow students to adapt and evaluate the effectiveness of their knowledge, reasoning and problem-solving strategies. When students are engaged in complex and open-ended problem tasks, it is assumed their reasoning and problem-solving paths become complex with creativity and evidence in order to justify their conclusion and solutions. This study investigated the levels of reasoning evident in student discourse when engaging in different types of problem-solving tasks and the role of teacher interactions on students’ reasoning. Fifteen students and a classroom teacher in a Grade 5–6 classroom participated in this study. Through case analyses, the study findings suggest that (a) there was no clear co-relation between certain structures of problem tasks and the level of reasoning in students’ problem-solving discourse, (b) students exhibited more data-based reasoning than evidence-based and rule-based justification in experiment-based problem-solving tasks, and (c) teacher intervention supported higher levels of student reasoning. Pedagogical reflections on the difficulties of constructing effective problem-solving tasks and the need for developing teacher scaffolding strategies are discussed. 相似文献
18.
刘玉金 《山东教育学院学报》2014,(4):50-54
本文运用问卷调查法对《体育与健康》课程进行深入调查、了解和论证,结果显示：大学体育课程和中学体育课程内容有相同之嫌,在某种程度上达不到锻炼学生身体的效果和目的。建议为了更好的促进学生身体的发展,应改进教材内容,提高学生对体育练习的兴趣和积极性。 相似文献
19.
《教育实用测度》2013,26(2):181-200
This study investigates the usefulness of small-scale interview studies as a means to explore the validity of science achievement tests in several formats. Interviews and observations were conducted with 41 high school students taking multiple-choice and constructed-response science items, and with 49 fifth- and sixth-grade students completing hands-on science tasks. The procedure provided support for interpretations of subscales of achievement, identified some of the reasoning processes and sources of knowledge that students applied to the tasks, and revealed ways in which the strategies applied by successful and unsuccessful students differed. The importance of conducting small-scale, qualitative interview studies as part of the test validation process is discussed. 相似文献
20.
George Kospentaris Panagiotis Spyrou Dionyssios Lappas 《Educational Studies in Mathematics》2011,77(1):105-127
The aim of this study is to investigate the strategies employed by advanced high school and university students working on
six tasks concerning comparison and conservation of area. Special care has been taken in the test design so that the problems
could be dealt with using a variety of solution methods. Written responses and in-depth interviews with 21 12th graders and
university students of mathematics provided the empirical data. The results show that the majority of the participants either
did not prefer or had difficulties employing adequately formal reasoning. Visualization factors seem to exert considerable
influence. Moreover, many students confuse congruence with area equivalence. 相似文献