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1.
During the last two decades many researchers in mathematics and science education have studied students’ conceptions and ways of reasoning in mathematics and science. Most of this research is content‐specific. It was found that students hold alternative ideas that are not always compatible with those accepted in science. It was suggested that in the process of learning science or mathematics, students should restructure their specific conceptions to make them conform to currently accepted scientific ideas. In our work in mathematics and science education it became apparent that some of the alternative conceptions in science and mathematics are based on the same intuitive rules. We have so far identified two such rules: “More of A, more of B”, and “Subdivision processes can always be repeated”. The first rule is reflected in subjects’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.) in all tasks related to intensive quantities (density, temperature, concentration, etc.) and in all tasks related to infinite quantities. The second rule is observed in students’, preservice and inservice teachers’ responses to tasks related to successive division of material and geometrical objects and in seriation tasks. In this paper, we describe and discuss these rules and their relevance to science and mathematics education. 相似文献
2.
Conclusion The purpose of this paper is not to denigrate pencil-and-paper tests of intellectual capabilities. The Understanding in Science
Test, if it were not for its reliability problems, may be a useful test of intellectual processing. It appears not to be a
successful analogue to clinically-administered Piagetian tasks.
The same may be said of the other written or group tests of this nature. If they are reliable, they may provide useful measures
of intellectual ability. Our research, though, suggests that, for junior high school students and younger, they may not possess
high concurrent validity with Piagetian tasks. 相似文献
3.
In the last twenty years researchers have studied students’ mathematical and scientific conceptions and reasoning. Most of this research is content‐specific. It has been found that students often hold ideas that are not in line with accepted scientific notions. In our joint work in mathematics and science education it became apparent that many of these alternative conceptions hail from the same intuitive rules. We have so far identified two such rules: ‘The more of A, the more of B’ and, ‘Everything can be divided by two’. The first rule is reflected in students’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.), in all tasks related to intensive quantities (density, temperature, concentration, etc.), and in tasks related to infinite quantities. The second rule is observed in responses related to successive division of material and geometrical objects, and in successive dilution tasks. In this paper we describe and discuss the first rule and its relevance to science and mathematics education. In a second paper (Tirosh and Stavy, in press) we shall describe and discuss the second rule. 相似文献
4.
In the last twenty years, researchers have studied students’ mathematical and scientific conceptions and reasoning. Most of this research is content‐specific. It has been found that students often hold ideas that are not in line with accepted scientific notions. In our joint work in mathematics and science education, it became apparent that many of these alternative conceptions hail from a small number of intuitive rules. We have so far identified two such rules: ‘The more of A, the more of B’, and, ‘Everything can be divided by two’. The first rule is reflected in students’ responses to many tasks, including all classical Piagetian conservation tasks (conservation of number, area, weight, volume, matter, etc.), all tasks related to intensive quantities (density, temperature, concentration, etc.), and tasks related to infinite quantities. The second rule is observed in responses related to successive division of material and geometrical objects, and in seriation tasks. In this paper we describe and discuss the second rule and its relevance to science and mathematics education. In a previous paper (Stavy and Tirosh 1995, in press) we described and discussed the first rule. 相似文献
5.
A review of the literature suggests a relationship between life-long development of formal reasoning schema and performance in professional education careers. The study investigated implications of cognitive development of preservice teachers as it relates to their classroom teaching performance. Ninety-one seniors involved in a field-oriented teacher education program were given classroom responsibilities which included teaching a science unit. Formal thinking abilities were assessed using two types of developmental level tasks, performance on traditional type Piagetian tasks and recognition of formal thought approaches in solving educational tasks. Professional behaviors were assessed using observational ratings of classroom instructional and planning activities. Subjects assessed as formal operational, 30% of sample, using Piagetian performance tasks, had significantly higher facility in performing model classroom teaching behaviors than transitional or concrete subjects. Higher recognition ability of formal thought approaches to teaching was not related to facility in performing classroom teaching when compared to performance on Piagetian tasks. The relationship held up in seven of eight broad teaching behavior categories observed in classroom instruction. The results supported a general portrait of teaching behavior specifically related to teachers of differing cognitive functional levels. Implications for professional training programs are discussed. 相似文献
6.
ZHANG Chun-li 《课程.教材.教法》2008,(10)
发展性评价体系中一个重要的工作就是开发多样化的评价工具和方法。在课题研究中我们重点开展了如下七个方面的评价工具的开发与实践:日常观察,等级和分项测试,成长记录袋,表现性任务,通过浓缩孩子成长特点的评价,二次评价,通过家长、学校合作,取得了较好的效果。 相似文献
7.
Lawson's test of formal reasoning was used in the Israeli educational context in order to investigate the relationship between students' achievement in science and in mathematics, to compare the performance of boys and girls, and to compare the performance of Israeli and U.S. populations. It was found that, in general, boys outperform girls; there is only a small correlation between achievement in science and math and Lawson test; and that the Israeli population achieved significantly higher than the U.S. population on the Piagetian skills measured by the test: It was concluded that the future use of Lawson's test by the high school teacher is doubtful. 相似文献
8.
Frederick P. Deluca 《科学教学研究杂志》1981,18(1):51-59
The purpose of this study was to reexamine Piagetian stages by way of the application of cluster analysis and to seek information concerning the occurrence of stages and the influence of different tasks and gender on cluster patterns. Six Piagetian tasks were administered to 182 males and 176 females ages 9 through 18 years old. Analysis and interpretation of the data suggested the following conclusions: (1) Piagetian stages exist as a general sequence through which intellectual development progresses; however, the males in the study conformed more to Piagetian stages than did the females; (2) deviation from Piagetian stages was influenced by gender and the type of task; (3) lack of synchronization of substages across several tasks suggested that Piagetian tasks were more situation-specific than indicated by Piaget, and it also helped to explain why strong, correlations among tasks at a given level have been difficult to obtain; (4) for the males, the greatest discontinuity occurred between substages IIIA and IIIB, not between IIB and IIIA as stated by Piaget; and (5) the group of 13-year-old females tended to cluster with the 17- and 18-year-old female groups, but it was not known why. 相似文献
9.
Reuven Babai 《International Journal of Science and Mathematics Education》2010,8(2):203-221
According to the intuitive rules theory, students are affected by a small number of intuitive rules when solving a wide variety
of science and mathematics tasks. The current study considers the relationship between students’ Piagetian cognitive levels
and their tendency to answer in line with intuitive rules when solving comparison tasks. The findings indicate that the tendency
to answer according to the intuitive rules varies with cognitive level. Surprisingly, a higher rate of incorrect responses
according to the rule same A–same B was found for the higher cognitive level. Further findings and implications for science and mathematics education are discussed. 相似文献
10.
The current study investigated the development of children's performance on tasks that have been suggested to underlie early mathematics skills, including measures of cardinality, ordinality, and intelligence. Eighty‐seven children were tested in their first (T1) and second (T2) school year (at ages 5 and 6). Children's performance on all tasks demonstrated good reliability and significantly improved with age. Correlational analyses revealed that performance on some mathematics‐related tasks were nonsignificantly correlated between T1 and T2 (number line and number comparison), showing that these skills are relatively unstable. Detailed analyses also indicated that the way children solve these tasks show qualitative changes over time. By contrast, children's performance on measures of intelligence and nonnumerical ordering abilities were strongly correlated between T1 and T2. Additionally, ordering skills also showed moderate to strong correlations with counting procedures both cross‐sectionally and longitudinally. These results suggest that, initially, mathematics skills strongly rely on nonmathematical abilities. 相似文献
11.
Dr. habil. Timo Ehmke Dr. Barbara Drechsel Jun.-Prof. Dr. Claus H. Carstensen 《Zeitschrift für Erziehungswissenschaft》2008,11(3):368-387
This study analyses the effects which repeating a class has on ninth grade students’ development of mathematical competency. The following research questions were addressed: How many students repeat grades in the different types of schools? How do students who repeat a grade differ from those who do not in their performance and background characteristics? How much extra mathematics do students repeating a grade learn in one school year? What are the differences between various types of school? Can students with poor mathematics grades in particular profit from repeating a grade? The sample is a sub-sample of the PISA-I-Plus study and comprises N = 360 ninth grade students. The total sample of PISA-I-Plus is representative for all ninth/tenth grade students from the different school types in Germany. The data survey was carried out in the ninth grade and then repeated after the students had repeated a year. The results document differences in the amount of grade repeat quotas between types of school. Furthermore, compared to students not repeating, those repeating a grade had lower mathematics (d = 1.02) and german (d = 1.14) grades, a lower level of mathematical literacy (d = 0.51), and lower test results with regard to basic cognitive abilities (d = 0.32). In terms of the development of mathematical literacy, the students repeating a grade could improve by an average of 23 points (d = 0.27) on the PISA mathematics scale. However, the results identify 38 percent of students repeating a grade who do not make any significant improvement in mathematics or even get worse. A differentiation according to school types shows that students repeating a grade in integrated comprehensive secondary schools and in schools with several educational levels in particular do not, on average, show any noteworthy improvement in their mathematical literacy. The analysis of the school grades received in mathematics shows that students whose mathematics grades are unsatisfactory do not benefit more from repeating a grade than students whose mathematics performance has been rated as being “satisfactory” or better. The article concludes with a discussion of the possible consequences of changing the way in which repetitions of grades are dealt with. 相似文献
12.
Ilana Waisman Mark Leikin Shelley Shaul Roza Leikin 《International Journal of Science and Mathematics Education》2014,12(3):669-696
In this study, we examine the impact and the interplay of general giftedness (G) and excellence in mathematics (EM) on high school students’ mathematical performance associated with translations from graphical to symbolic representations of functions, as reflected in cortical electrical activity (by means of ERP—event-related potentials—methodology). We report on findings of comparative data analysis based on 75 right-handed male high school students (16?–?18 years old) divided into four research groups designed by a combination of EM and G factors. Effects of EM factor appeared at the behavioral and electrophysiological levels. The fifth group of participants included 9 students with extraordinary mathematical abilities (S-MG: super mathematically gifted). We found that in EM participants, the G factor has no impact on the performance associated with translation between representations of the functions. The highest overall electrical activity is found in excelling in mathematics students who are not identified as generally gifted (NG-EM students). This increased electrical activity can be an indicator of increased cognitive load in this group of students. We identified accumulative and unique characteristics of S-MG at the behavioral and electrophysiological levels. We explain the findings by the nature of the tasks used in the study. We argue that a combination of the ERP techniques along with more traditional educational research methods enables obtaining reliable measures on the mental processing involved in learning mathematics and mathematical problem solving. 相似文献
13.
Jacques Grégoire Catherine van Nieuwenhoven 《European Journal of Psychology of Education - EJPE》1995,10(1):61-75
For about ten years, new research data have led us to enlarge the Piagetian model of the learning of the concept of number. Research investigations of counting have especially emphasized the importance of some abilities related to the construction of the concept of number. We think these researches should more greatly influence the practice of assessment. But valid tests should be available for psychologists and teachers to appraise the child development of the mastery of counting. For this purpose, we developed a set of tasks on the base of a critical analysis of Gelman and Gallistel counting principles. In a first step of our research, we used these tasks in a large sample of children from the French-speaking community of Belgium. This sample was composed of pupils from the third year of the nursery school (N=439) and from the first year of the primary school (N=103). Some of our results are quite different from those of previous investigations. We observe that many 5-year-old children are far from mastering and to coordinating the counting principles. A significant percent of pupils in the first year of the primary school are in the same situation. The implications of these difficulties for the beginning of the learning of arithmetic are emphasized. 相似文献
14.
Three years after the end of a two-year intervention program intended to promote formal operational thinking, the achievement of students initially 11 years of age was tested by their results in British National examinations, taken at age 16. Although the intervention was set within the context of science learning, the effects were found in science, mathematics, and English. In contrast to results reported earlier for the older cohort aged 12 years initially, where the boys showed greater achievement than girls in science and mathematics, here the effect was limited to girls. In comparison with control classes the effect sizes were science, 0.67σ mathematics, 0.72σ, and English, 0.69σ. Although half of the students showed increased achievement in science, which was consistent with the Piagetian model used in the intervention, the achievement of some in science, mathematics, and English was not associated with gains on Piagetian tests above those of control students. These results were attributed to aspects of the intervention methodology intended to enhance metacognition. The distinction between intervention and instruction was discussed in relation to normative data on Piagetian development in adolescents. 相似文献
15.
Many studies have found a strong relationship between the mathematics students study in school and their performance on an academic or school mathematics assessment but not on an assessment of mathematics literacy (ML). With many countries, like the USA, placing emphasis on finishing secondary education being mathematically literate and prepared for college or career, this raises the question about the relationship between the mathematics studied in school and any ML students may have. The Programme for International Student Assessment (PISA) ML assessment is embedded in real-world contexts that provide an important window on how ready students are to tackle the situations and problems that await them whether they intend to pursue further education beyond high school or intend to go directly into the labour force. In this paper, we draw upon the PISA 2012 data to investigate the extent to which the cumulative exposure to rigorous mathematics content, such as that embedded in college- and career-ready standards, is associated with ML as assessed in PISA. Results reveal that both exposure to rigorous school mathematics and experiencing the instruction of this mathematics through real-world applications are significantly related to all the real-world contextualized PISA ML scores. 相似文献
16.
Can the use of background music improve the behaviour and academic performance of children with emotional and behavioural difficulties? 总被引：1，自引：0，他引：1
《British Journal of Special Education》1998,25(2):88-91
Historically, there have been many claims regarding the beneficial effects of music on behaviour and development, but there has been little empirical work to verify them. Our present research studied the effects of providing background music in the classroom on the behaviour and performance in mathematical tasks of ten children attending a school for children with emotional and behavioural difficulties, who exhibited a high frequency of disruptive behaviour. There was a significant improvement in behaviour and mathematics performance for all the children. The effects were particularly marked for those whose problems were related to constant stimulus-seeking and over-activity. Improvements were also observed in improved co-operation and a reduction in aggression during the lessons immediately following the study. 相似文献
17.
In this study we investigate a strategy for engaging high school mathematics teachers in an initial examination of their teaching in a way that is non-threatening and at the same time effectively supports the development
of teachers’ pedagogical content knowledge [Shulman (1986). Educational Researcher, 15(2), 4–14]. Based on the work undertaken by the QUASAR project with middle school mathematics teachers, we engaged a group
of seven high school mathematics teachers in learning about the Levels of Cognitive Demand, a set of criteria that can be
used to examine mathematical tasks critically. Using qualitative methods of data collection and analysis, we sought to understand
how focusing the teachers on critically examining mathematical tasks influenced their thinking about the nature of mathematical
tasks as well as their choice of tasks to use in their classrooms. Our research indicates that the teachers showed growth
in the ways that they consider tasks, and that some of the teachers changed their patterns of task choice. Further, this study
provides a new research instrument for measuring teachers’ growth in pedagogical content knowledge.
An earlier version of this paper was presented at the American Educational Research Association Annual Meeting, New Orleans,
LA, April 2002. 相似文献
18.
W J Friedman 《Child development》1977,48(4):1593-1599
Developmental psychological approaches to the study of time have fallen into 3 categories: studies of time perception; studies of logical, reconstructive abilities; and studies of the understanding of conventional time systems. The present work examines problems spanning the latter 2 categories--the development of children's understanding of temporal cycles and the relationship between cyclic concepts and cognitive development. 62 children, ranging in age from 4 to 10 years, were administered Piagetian tests of classification and seriation and a variety of specially designed cyclic tasks. Results show major progress in the representation of cyclic order and recurrence during the age period examined. For a variety of particular cycles, order responses were shown before continuity responses. The ability to produce a correct order is related to seriation performance but not classification performance when the variance attributable to age is partialed out. Continuity responses appear to be unrelated to performance on either of the Piagetian tasks tested when age is controlled. 相似文献
19.
Aleksandar Baucal Francesco Arcidiacono Nevena Budjevac 《European Journal of Psychology of Education - EJPE》2013,28(2):475-495
The aim of this paper is to highlight and discuss advantages and constraints of different methods applied within the field of children's thinking studies, through the test of the repeated question hypothesis validity, using the conservation of liquid task. In our perspective, the Piagetian interview is an ecologically valid context for externalization and modification of children's thinking. We used an experimental procedure organized in standard and modified tasks, involving primary school children in Serbia. The results of quantitative and qualitative analyses show that the repeated question is not the unique cause of children's misleading in demonstrating to understand conservation. Other dimensions explain why children change their answers when they are tested by the two tasks we used, which offers an insight into the influence of research procedures on children's answers. 相似文献
20.
当前很多初中生都认为数学是初中学科中最难学的,无论是学习效果还是学习成绩都不太理想。对此,学校和家庭要联合起来,寻找可能阻碍初中数学授课成效的相关原因。笔者在总结以往的课堂经验和教学效果的过程中,发现在课堂上应用数形结合的教学思想时,教学效果是最佳的。将数形结合与初中数学教材知识点相结合,能够降低知识点的难度。对此,笔者经过研究分析,简述了在初中数学课堂中使用数形结合法的好处,并根据初中数学中的重难点,对数形结合法在数学教学中的科学应用展开了论述。 相似文献