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1.
This study investigated the effects of two context variables, ratio type and problem setting, on the performance of seventh-grade students on a qualitative and numerical proportional reasoning test. Six forms of the qualitative and numerical tests were designed, each form using a single context (one of two settings for each of three ratio types). Different ratio types appear to have a stronger impact on the difficulty of the qualitative and numerical proportional reasoning problems than small differences in problem setting. However, the familiarity of problem setting did show an increasingly large effect on qualitative reasoning as the difficulty of ratio type increased. We also investigated the nature of the relationships between rational number skills, qualitative reasoning about ratios, and numerical proportional reasoning. Qualitative reasoning appears to be sufficient, but not necessary for numerical proportional reasoning. The evidence for the requisite nature of rational number skills for proportional reasoning was equivocal. The implications of these findings for science education are discussed. 相似文献
2.
Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teachers,
2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005) claimed that the development of proportional reasoning relies on various kinds of understanding and thinking processes. The
critical components suggested were individuals’ understanding of the rational number subconstructs, unitizing, quantities
and covariance, relative thinking, measurement and “reasoning up and down”. In this study, we empirically tested a theoretical
model based on the one suggested by Lamon (Teaching fractions and ratios for understanding. Essential content knowledge and
instructional strategies for teachers, 2nd edn. Lawrence Erlbaum Associates, Mahwah, 2005), as well as an extended model which included an additional component of solving missing value proportional problems. Data
were collected from 238 prospective kindergarten teachers. To a great extent, the data provided support for the extended model.
These findings allow us to make some first speculations regarding the knowledge that prospective kindergarten teachers possess
in regard to proportional reasoning and the types of processes that might be emphasized during their education. 相似文献
3.
National standards for teaching mathematics in primary schools in the Netherlands leave little room for formal fractions.
However,a newly developed programme in fractions aims at learning formal fractions. The starting point in the development
of this curriculum is the students’ acquisition of `numeracy infractions’. In this case study we describe the growth in reasoning
ability with fractions of one student in this newly developed programme of 30 lessons during one whole school year. In the
study we found indications that the programme and its teaching stimulated the progress of an average performer in mathematics.
Moreover we found arguments as to what extent formal operations with fractions suits as an educational goal.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
4.
As part of individual interviews incorporating whole number and rational number tasks, 323 grade 6 children in Victoria, Australia
were asked to nominate the larger of two fractions for eight pairs, giving reasons for their choice. All tasks were expected
to be undertaken mentally. The relative difficulty of the pairs was found to be close to that predicted, with the exception
of fractions with the same numerators and different denominators, which proved surprisingly difficult. Students who demonstrated
the greatest success were likely to use benchmark (transitive) and residual thinking. It is hypothesised that the methods
of these successful students could form the basis of instructional approaches which may yield the kind of connected understanding
promoted in various curriculum documents and required for the development of proportional reasoning in later years. 相似文献
5.
《British Educational Research Journal》2004,30(3):359-377
Sociocultural researchers have claimed that students' learning of science is a discursive process, with scientific concepts and ways of reasoning being learned through engagement in practical enquiry and social interaction as well as individualized activity. It is also often claimed that interacting with partners while carrying out scientific investigations is beneficial to students' learning and the development of their understanding. The research we describe investigated the validity of these claims and explored their educational implications. An experimental teaching programme was designed to enable children in British primary schools to talk and reason together and to apply these skills in their study of science. The results obtained indicate that (a) children can be enabled to use talk more effectively as a tool for reasoning and (b) talk‐based activities can have a useful function in scaffolding the development of reasoning and scientific understanding. The implications of the findings for educational policy and practice are discussed. 相似文献
6.
Masoud Kabiri Mahmood Ghazi-Tabatabaei Abbas Bazargan Mohsen Shokoohi-Yekta Kamal Kharrazi 《教育实用测度》2017,30(1):27-38
Numerous diagnostic studies have been conducted on large-scale assessments to illustrate the students’ mastery profile in the areas of math and reading; however, for science a limited number of investigations are reported. This study investigated Iranian eighth graders’ competency mastery of science and examined the utility of the General Diagnostic Model (GDM) to produce diagnostic information using TIMSS 2011 data. Eight diagnostic attributes were extracted, using documentary analysis of the major large-scale assessment frameworks, including basic science knowledge, using models, reasoning, using science, representing data, explaining of phenomena, predicting, and scientific inquiry. These attributes were then assigned to each item in order to construct the Q matrix, through focus group discussions, survey of head science teachers, think-aloud verbal protocol, and analysis of written answers. Results show the utility of GDM to generate rich diagnostic information for a national large-scale assessment. Moreover, the findings indicated that students performed relatively well in using science, but performed weakly in reasoning, explaining of phenomena, and scientific inquiry, which all required complex skills and higher-order thinking abilities. 相似文献
7.
This article shows how Yup’ik cosmology, epistemology, and everyday practice have implications for the teaching of school
mathematics. Math in a Cultural Context (MCC) has a long–term collaborative relationship with Yup’ik elders and experienced
Yup’ik teachers. Because of this long–term ethnographically–oriented relationship, the authors – both insiders and an outsider
– have been able to understand the mathematical implications of everyday Yup’ik practice. As the article demonstrates, body
proportional measuring and symmetry/splitting are two generative solution strategies used by Yup’ik elders in solving everyday
problems. We argue that proportional measuring coupled with symmetry/splitting can provide school mathematics with an alternative
pathway to the teaching of some aspects of geometry and rational number reasoning. 相似文献
8.
Many children and adults have difficulty gaining a comprehensive understanding of rational numbers. Although fractions are taught before decimals and percentages in many countries, including the USA, a number of researchers have argued that decimals are easier to learn than fractions and therefore teaching them first might mitigate children’s difficulty with rational numbers in general. We evaluate this proposal by discussing evidence regarding whether decimals are in fact easier to understand than fractions and whether teaching decimals before fractions leads to superior learning. Our review indicates that decimals are not generally easier to understand than fractions, though they are easier on some tasks. Learners have similar difficulty in understanding fraction and decimal magnitudes, arithmetic, and density, as well as with converting from either notation to the other. There was too little research on knowledge of percentages to include them in the comparisons or to establish the ideal order of instruction of the three types of rational numbers. Although existing research is insufficient to determine the best sequence for teaching the three rational number formats, we recommend several types of research that could help in addressing the issue in the future. 相似文献
9.
The array representation and primary children’s understanding and reasoning in multiplication 总被引：1，自引：0，他引：1
Patrick Barmby Tony Harries Steve Higgins Jennifer Suggate 《Educational Studies in Mathematics》2009,70(3):217-241
We examine whether the array representation can support children’s understanding and reasoning in multiplication. To begin,
we define what we mean by understanding and reasoning. We adopt a ‘representational-reasoning’ model of understanding, where
understanding is seen as connections being made between mental representations of concepts, with reasoning linking together
the different parts of the understanding. We examine in detail the implications of this model, drawing upon the wider literature
on assessing understanding, multiple representations, self explanations and key developmental understandings. Having also
established theoretically why the array representation might support children’s understanding and reasoning, we describe the
results of a study which looked at children using the array for multiplication calculations. Children worked in pairs on laptop
computers, using Flash Macromedia programs with the array representation to carry out multiplication calculations. In using
this approach, we were able to record all the actions carried out by children on the computer, using a recording program called
Camtasia. The analysis of the obtained audiovisual data identified ways in which the array representation helped children,
and also problems that children had with using the array. Based on these results, implications for using the array in the
classroom are considered. 相似文献
10.
Since the 1990s, researchers have increasingly drawn attention to the multiplicity of representations used in science. This
issue of RISE advances this line of research by placing such representations at the centre of science teaching and learning. The authors
show that representations do not simply transmit scientific information; they are integral to reasoning about scientific phenomena.
This focus on thinking with representations mediates between well-resolved representations and formal reasoning of disciplinary
science, and the capacity-limited, perceptually-driven nature of human cognition. The teaching practices described here build
on three key principles: Each representation is interpreted through others; natural language is a sign system that is used
to interpret a variety of other kinds of representations; and this chain of signs or representations is ultimately grounded
in bodily experiences of perception and action. In these papers, the researchers provide examples and analysis of teachers
scaffolding students in using representations to construct new knowledge, and in constructing new representations to express
and develop their knowledge. The result is a new delineation of the power and the challenges of teaching science with multiple
representations. 相似文献
11.
《Contemporary educational psychology》1998,23(2):132-148
The results of two evaluation studies with respect to a programme for enhancing inductive reasoning ability of third grade students are presented. The programme is a classroom version of the German programme ‘Denktraining für Kinder 1’ (Cognitive training for children; Klauer, 1989). In the first formative evaluation study, two experimental groups with 30 students in total and one control group with 9 students were involved. Observations during the lessons, and teachers' reports showed that teachers were able to implement the programme. Both experimental groups significantly outperformed the control group on a posttest immediately after the programme and on a follow-up test 3 1/2 months later. Further analyses of the data revealed tentative evidence of the superiority of a direct teaching method. In the second summative evaluation study, the same programme was applied to a larger sample (experimental groups: n = 99 in total; and control groups: n = 232 in total) of third grade students. On the basis of Study 1, the programme instructions were slightly changed. The experimental groups scored significantly higher on a posttest three months after completion of the programme. 相似文献
12.
Judith Sowder Barbara Armstrong Susan Lamon Martin Simon Larry Sowder Alba Thompson 《Journal of Mathematics Teacher Education》1998,1(2):127-155
The middle-grades mathematics related to multiplicative structures has undergone careful scrutiny over the past decade. Researchers
have identified the types of reasonings involved; the difficulties students have with the concepts and why these difficulties
might occur; and the interconnections within this content area. On the basis of this research we make four recommendations
for the preparation and professional development of teachers. The recommendations deal with different but related forms of
reasoning: quantitative reasoning, multiplicative reasoning, proportional reasoning, and reasoning with rational numbers.
Problematic issues that follow from the recommendations are discussed.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
13.
Ros Somerville Kate Ayre Daniel Tunbridge Katy Cole Richard Stollery Mary Sanders 《Educational Psychology in Practice》2015,31(3):265-278
This study evaluates the efficacy of a mathematics intervention devised by Essex Educational Psychology Service (EPS), UK. The intervention was designed to develop understanding and skills across four key domains within arithmetical development, by applying the principles of errorless learning, distributed practice and teaching to mastery. A quasi-experimental design was used to investigate the success of the intervention in raising the level of arithmetical skills of lower achieving pupils up to National Curriculum Level 2. The results indicated that children engaging with the intervention made significantly more progress than children not engaging with the intervention, with ratio gains of 2.51 in arithmetical skills. In addition, gains were made in mathematical reasoning. 相似文献
14.
This research describes an intensive study undertaken to determine children's representational strategies for relational numbers
(e.g. proportions, ratios, fractions). Relational numbers have three quantities associated with them: a whole and two parts.
Given these three quantities, children can form a representation based on a part-whole relationship or on a part-part relationship.
Fifteen children (6th, 7th, and 8th graders) solved fifteen probability problems which varied information content and quantitative
relationships between the quantities expressed in the problems. A quantitative and qualitative analysis revealed that children
prefer a part-part representation to solve problems with relational quantities. 相似文献
15.
以英汉对比语言学为理论指导,从以下三个方面对胡允桓先生和贾宗谊先生的《红字》译本进行对比研究:一是英汉词汇差异;二是英汉句法差异;三是英汉文化差异。通过对上述三方面系统地比较研究,笔者认为贾的译著在“信、达、雅”各方面均优于胡的译著。最后,对这两个中文译本做出综合性评价,并建议将英汉语对比研究成果应用于整个英语教学实践,帮助学生排除汉语负迁移的干扰,提高外语教学质量。 相似文献
16.
Dirk De Bock Wim Van Dooren Dirk Janssens Lieven Verschaffel 《Educational Studies in Mathematics》2002,50(3):311-334
Several recent ascertaining studies revealed a deep-rooted and almost irresistible tendency among 12–16-year old students
to improperly apply the linear or proportional model in word problems involving lengths, areas and volumes of similar plane
figures and solids. While these previous studies showed to what extent students' improper use of linear reasoning is affected
by different characteristics of the task, it remained largely unclear what aspects of their knowledge base are responsible
for the occurrence and strength of this phenomenon and how these aspects relate to other more general misconceptions and buggy
rules identified in the literature. This paper reports an in-depth investigation by means of individual semi-standardised
interviews aimed at analysing the thinking process underlying students' improper linear reasoning and how this process is
affected by their mathematical conceptions, beliefs and habits. During these interviews,students' solution processes were
revealed through a number of well-specified questions by the interviewer with respect to one single non-linear application
problem, as well as through their reactions to subsequent kinds of cognitive conflict. The interviews provided a lot of information
about the actual process of problem solving from students falling into the ‘linearity trap’ and the mechanism behind it. Although
some students seem to really ‘believe’ that quantities are always linked proportionally, their improper use of linearity often
results from superficial and intuitive reasoning, influenced by specific mathematical conceptions, habits and beliefs leading
to a deficient modelling process.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
17.
Sources of Self-efficacy in a Science Methods Course for Primary Teacher Education Students 总被引：1，自引：0，他引：1
D. H. Palmer 《Research in Science Education》2006,36(4):337-353
Self-efficacy has been shown to be an issue of concern for primary teacher education students – many of them have low self-efficacy and this can negatively affect their future teaching of science. Previous research has identified four factors that may contribute towards self-efficacy: enactive mastery experiences, vicarious experiences, verbal persuasion and physiological/affective states. It could also be argued that there are additional sources of self-efficacy that apply to primary teacher education students, namely cognitive content mastery, cognitive pedagogical mastery and simulated modelling. The main purpose of the present paper was to investigate the relative importance of the various sources of self-efficacy in a primary science methods course. Data on changes in self-efficacy and sources of self-efficacy were collected throughout the course using formal and informal surveys. It was found that the main source of self-efficacy was cognitive pedagogical mastery. 相似文献
18.
The reasoning patterns used by a sample of Western Australian secondary school students aged 13‐16 were investigated with regard to the following reasoning modes: proportional reasoning, controlling variables, probabilistic reasoning, correlational reasoning, and combinatorial reasoning. There was a wide range in students’ reasoning abilities at all year levels. Large percentages of students did not use formal operational reasoning patterns when they attempted to solve problems assessing their ability to use each of the five reasoning modes. Commonly used, but incorrect reasoning patterns were identified for each reasoning mode. The students’ ability to use formal reasoning patterns was found to be an important factor in determining student achievement in lower secondary science, in their selection of year 11 science subjects, and their achievement in these subjects. The results of the study indicate that it is important for teachers to be aware of the reasoning patterns of their students and the cognitive demands of course content, so that they can optimally match the content and their teaching strategies with the abilities of their students. Further research is needed to establish the nature of instruction which might best facilitate cognitive growth. 相似文献
19.
Parmjit Singh 《Educational Studies in Mathematics》2000,43(3):271-292
The purpose of this study was to construct an understanding of two grade six students' proportional reasoning schemes. The
data from the clinical interviews gives insight as to the importance of multiplicative thinking in proportional reasoning.
Two mental operations, unitizing and iterating play an important role in student's use of multiplicative thinking in proportion
tasks. Unitizing a composite unit and iterating it to its referent point enables one to preserve the invariance of a ratio.
Proportions involved the coordination of two number sequences, keeping the ratio unit invariant under the iteration. In the
iteration process, one needed to explicitly conceptualize the iteration action of the composite ratio unit to make sense of
ratio problems and to have sufficient understanding of the meaning of multiplication and division and its relevance in the
iteration process. One needed to have constructed multiplicative structures and iteration schemes in order to reason proportionally.
This revised version was published online in July 2006 with corrections to the Cover Date. 相似文献
20.
Although Likert-type rating scales are used in a great number of early childhood studies, knowledge of how the number of response options affects the psychometric properties of scales used with children is limited. The purpose of this study is to contribute to this knowledge. Data were collected from second grade students and third grade students. Accordingly, 1,092 second- and third-graders completed a 2-point, 3-point, and 4-point version of the School Attachment Scale for Children and Adolescents. Participants came from 11 schools, different in terms of socioeconomic status. The children received the versions approximately three weeks apart. Results revealed that as the number of response options increased, the means tended to decrease and the distribution to be normal. For the 2-point version, most items were below the cut-off point in terms of discrimination indexes. Compared to the 2-point version, there was a significant increase in discrimination indexes for the 3- and 4-point versions, and the items’ discrimination indexes were high. It was concluded that the reliability coefficient increased with an increasing number of response options for all subdimensions of the scale. When the validity estimations of the three subdimensions were examined for the three versions of the scale, it was found that the 3- and 4-point versions were appropriate for the validity and that the validity of the 2-point version was weak. It was observed that using 2-point Likert-type scales with children negatively affected the psychometric properties and that these properties improved with an increased number of response options. 相似文献