共查询到20条相似文献，搜索用时 125 毫秒
1.
Blatto-Vallee G Kelly RR Gaustad MG Porter J Fonzi J 《Journal of deaf studies and deaf education》2007,12(4):432-448
This research examined the use of visual-spatial representation by deaf and hearing students while solving mathematical problems. The connection between spatial skills and success in mathematics performance has long been established in the literature. This study examined the distinction between visual-spatial "schematic" representations that encode the spatial relations described in a problem versus visual-spatial "pictorial" representations that encode only the visual appearance of the objects described in a problem. A total of 305 hearing (n = 156) and deaf (n = 149) participants from middle school, high school, and college participated in this study. At all educational levels, the hearing students performed significantly better in solving the mathematical problems compared to their deaf peers. Although the deaf baccalaureate students exhibited the highest performance of all the deaf participants, they only performed as well as the hearing middle school students who were the lowest scoring hearing group. Deaf students remained flat in their performance on the mathematical problem-solving task from middle school through the college associate degree level. The analysis of the students' problem representations showed that the hearing participants utilized visual-spatial schematic representation to a greater extent than did the deaf participants. However, the use of visual-spatial schematic representations was a stronger positive predictor of mathematical problem-solving performance for the deaf students. When deaf students' problem representation focused simply on the visual-spatial pictorial or iconic aspects of the mathematical problems, there was a negative predictive relationship with their problem-solving performance. On two measures of visual-spatial abilities, the hearing students in high school and college performed significantly better than their deaf peers. 相似文献
2.
Iliada Elia Areti Panaoura Anastasia Eracleous Athanasios Gagatsis 《International Journal of Science and Mathematics Education》2007,5(3):533-556
The present study explores pupils’ constructed definitions of the concept of function in relation to their abilities in dealing
with tasks of functions involving different forms of representations and problem solving tasks. A major concern is also to
examine the interrelations between these three ways of thinking about or dealing with the concept of function. The sample
of the study consisted of secondary school pupils in Cyprus. A test was developed which involved seven items: one item requested
pupils to provide a definition of what function is and the other six items were developed in order to investigate pupils’
ability to transfer information from one representation to another and to solve problems on function. Findings revealed pupils’
difficulties in giving a proper definition for the concept of function and resolving problems on functions involving conversions
between diverse modes of representation. Several inconsistencies among pupils’ constructed definitions, their competence to
use different representations of functions and their problem solving ability, were also uncovered, indicating lack of flexibility
between different ways of approaching functions. 相似文献
3.
4.
Despina A. Stylianou 《Educational Studies in Mathematics》2011,76(3):265-280
Representation is viewed as central to mathematical problem solving. Yet, it is becoming obvious that students are having
difficulty negotiating the various forms and functions of representations. This article examines the functions that representation
has in students’ mathematical problem solving and how that compares to its function in the problem solving of experts and
broadly in mathematics. Overall, this work highlights the close connections between the work of experts and students, showing
how students use representations in ways that are inherently similar to those of experts. Both experts and students use representations
as tools towards the understanding, exploration, recording, and monitoring of problem solving. In social contexts, experts
and students use representations for the presentation of their work but also the negotiation and co-construction of shared
understandings. However, this research also highlights where students’ work departs from experts’ representational practices,
hence, providing some directions for pedagogy and further work. 相似文献
5.
6.
Cognitive development of any concept is related with affective development. The present study investigates students’ beliefs about the use of different types of representation in understanding the concept of fractions and their self‐efficacy beliefs about their ability to transfer information between different types of representation, in relation to their performance on understanding the concept. Data were collected from 1701 students in Grade Five to Grade Eight. Results revealed that multiple‐representation flexibility, ability on solving problems with various modes of representation, beliefs about the use of representations and self‐efficacy beliefs about using them constructed an integrated model with strong interrelations in the different educational levels. Confirmatory factor analysis affirmed the existence of differential effects of multiple‐representation flexibility and problem‐solving ability in respect to cognitive performance and the existence of general beliefs and self‐efficacy beliefs about the use and the role of representations. Results suggested the invariance of this structure across primary (Grades Five and Six) and secondary education (Grades Seven and Eight). However, there are interesting differences concerning the interrelations among those cognitive and affective factors between primary and secondary education. 相似文献
7.
Despina A. Stylianou 《Journal of Mathematics Teacher Education》2010,13(4):325-343
Current reform efforts call for an emphasis on the use of representation in the mathematics classroom across levels and topics.
The aim of the study was to examine teachers’ conceptions of representation as a process in doing mathematics, and their perspectives
on the role of representations in the teaching and learning of mathematics at the middle-school level. Interviews with middle
school mathematics teachers suggest that teachers use representations in varied ways in their own mathematical work and have
developed working definitions of the term primarily as a product in problem solving. However, teachers’ conception of representation
as a process and a mathematical practice appears to be less developed, and, as a result, representations may have a peripheral
role in their instruction as well. Further, the data suggested that representation is viewed as a topic of study rather than
as a general process, and as a goal for the learning of only a minority of the students—the high-performing ones. Implications
for mathematics teacher education, prospective and practicing, are discussed. 相似文献
8.
Damien C. Cormier Theodore J. Christ Laura D. Offrey Katherine Pratt 《Exceptionality》2016,24(4):225-240
The purpose of this study is to evaluate the relationship of mathematics calculation rate (curriculum-based measurement of mathematics; CBM-M), reading rate (curriculum-based measurement of reading; CBM-R), and mathematics application and problem solving skills (mathematics screener) among students at four levels of proficiency on a statewide test. It was hypothesized that CBM-M provides insufficient information to make good screening decisions and that other measures with content more similar to that of large-scale tests of mathematics would function to improve screening. One hundred and seventy students in third grade from a rural elementary school in the Midwestern United States participated. Structural equation modeling was used to evaluate direct, mediator, and latent growth models. In general, CBM-R mediated the relationship between the mathematics ability screener and passing the state assessment, while CBM-M did not have any significant paths within these models. Results are discussed in terms of the utility of CBM-M and CBM-R procedures in screening for success on state test performance in mathematics. 相似文献
9.
Timothy J. Nokes Robert G. M. Hausmann Kurt VanLehn Sophia Gershman 《Instructional Science》2011,39(5):645-666
Cognitive science principles should have implications for the design of effective learning environments. The self-explanation
principle was chosen for the current work because it has developed significantly over the last 20 years. Early formulations
hypothesized that self-explanation facilitated inference generation to supply missing information about a concept or target
skill, whereas later work hypothesized that self-explanation facilitated mental-model revision (Chi, Handbook of research
on conceptual change, 2000). To better understand the complex relationship between prior knowledge, cognitive processing, and changes to a learner’s
representation, two classes of self-explanation prompts (gap-filling and mental-model revision) were tested in the domain
of physics problem solving. Prompts designed to focus the learner on gap-filling led to greater learning and a reduction in
the amount of tutoring assistance required to solve physics problems. The results are interpreted as support for the instructional
fit hypothesis—the idea that the efficacy of instruction is contingent on the match between the cognitive processing that the instruction
elicits, how those processes modify the underlying knowledge representations for the task, and the utility of those representations
for the task or problem. 相似文献
10.
The purpose of this study was to characterize high school chemistry students' ability to make translations between three representations of the structure of matter, and to determine the degree to which the students' ability to make these translations is related to reasoning ability, spatial reasoning ability, gender, and specific knowledge of the representations. Translation between formula, electron configuration, and ball-and-stick model representations of matter were chosen for study because of their promise for adding to knowledge of students' conceptual ecology, and because they may be of practical use for teaching and evaluation in chemistry classrooms. Representations have the characteristic that they embed selected details of the relevant concept or principle, but permit other details to fade. As one example, the chemical formula for water, H2O, explicitly conveys the identity of the constituent elements and their ratio, but does not explicitly convey the bond angle or whether the bonds are single or double. On the other hand, the ball-and-stick model of water explicitly conveys the bond angle and bond orders, but does not emphasize the ratio of the elements. Translation between representations is an information processing task, requiring understanding of the underlying concept to the extent that the individual can interpret the information provided by the initial representation and infer the details required to construct the target representation. In this study, the use of the translations of representations as an indicator of understanding of chemical concepts is developed in terms of (a) its relationship to four variables associated with achievement in chemistry, (b) specific representation error types, and (c) its utility in revealing details of students' conceptions and concept formation. Translation of representation performance was measured by administering, audio recording, transcribing, and scoring individual, task-based, think-aloud interviews. The associated interview schedule was entitled Translation of Representations—Structure of Matter [TORSOM]. Reasoning ability was measured by the Group Assessment of Logical Thinking—short form (GALT-s), spatial reasoning ability by the spatial reasoning subtest of the Differential Abilities Test (SRDAT), and prior knowledge of the representations by a test developed by the first researcher (Knowledge of Representations—Structure of Matter). When each of the hypothetical correlates were regressed on TORSOM individually, results indicated the KORSOM and GALT-s but not gender or SRDAT were statistically significant (alpha = .05). The two-predictor model accounts for 28% of the variance in the TORSOM scores. Representation error types are described and exemplified. 相似文献
11.
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
12.
Kok-Sing Tang 《International Journal of Science Education》2016,38(13):2069-2095
The purpose of this study is to examines the relationship between the communicative approach of classroom talk and the modes of representations used by science teachers. Based on video data from two physics classrooms in Singapore, a recurring pattern in the relationship was observed as the teaching sequence of a lesson unfolded. It was found that as the mode of representation shifted from enactive (action based) to iconic (image based) to symbolic (language based), there was a concurrent and coordinated shift in the classroom communicative approach from interactive–dialogic to interactive–authoritative to non-interactive–authoritative. Specifically, the shift from enactive to iconic to symbolic representations occurred mainly within the interactive–dialogic approach while the shift towards the interactive–authoritative and non-interactive–authoritative approaches occurred when symbolic modes of representation were used. This concurrent and coordinated shift has implications on how we conceive the use of representations in conjunction with the co-occurring classroom discourse, both theoretically and pedagogically. 相似文献
13.
The present study aims to investigate the effects of a design experiment developed for third-grade students in the field of mathematics word problems. The main focus of the program was developing students?? knowledge about word problem solving strategies with an emphasis on the role of visual representations in mathematical modeling. The experiment involved five experimental and six control classes (N?=?106 and 138, respectively) of third-grade students. The experiment comprised 20 lessons with 73 word problems, providing a systematic overview of the basic word problem types. Teachers of the experimental classes received a booklet containing lesson plans and overhead transparencies with different types of visual representations attached to the word problems. Students themselves were invited to make drawings for each task, and group work and teacher-led discussion shaped their beliefs about the role of visual representations in word problem solving. The effect sizes of the experiment were calculated from the results of two tests: an arithmetic skill and a word problem test, and the unbiased estimates for Cohen??s d proved to be 0.20 and 0.62. There were significant changes also in experimental group students?? beliefs about mathematics. The experiment pointed to the possibility, feasibility, and importance of learning about visual representations in mathematical word problem solving as early as in grade?3 (around age 9?C10). 相似文献
14.
在教学教学中培养学生的反思意识,不仅是正确、迅速解决问题的需要和保征,而且也是优化思维品质,提高思维能力的有效途径.本文介绍了笔者在概念教学、解题教学中对此进行的探索. 相似文献
15.
Representing the Electromagnetic Field: How Maxwell��s Mathematics Empowered Faraday��s Field Theory
Ryan D. Tweney 《Science & Education》2011,20(7-8):687-700
James Clerk Maxwell ??translated?? Michael Faraday??s experimentally-based field theory into the mathematical representation now known as ??Maxwell??s Equations.?? Working with a variety of mathematical representations and physical models Maxwell extended the reach of Faraday??s theory and brought it into consistency with other results in the physics of electricity and magnetism. Examination of Maxwell??s procedures opens many issues about the role of mathematical representation in physics and the learning background required for its success. Specifically, Maxwell??s training in ??Cambridge University?? mathematical physics emphasized the use of analogous equations across fields of physics and the repeated solving of extremely difficult problems in physics. Such training develops an array of overlearned mathematical representations supported by highly sophisticated cognitive mechanisms for the retrieval of relevant information from long term memory. For Maxwell, mathematics constituted a new form of representation in physics, enhancing the formal derivational and calculational role of mathematics and opening a cognitive means for the conduct of ??experiments in the mind?? and for sophisticated representations of theory. 相似文献
16.
学习高等数学的目的在于应用数学思想方法解决实际问题,将数学建模思想渗透到高等数学教学中,可提高学生应用数学知识和方法解决实际问题的能力。因此,要把数学建模思想贯穿在教学的始终,使数学建模意识成为学生思考问题的方法和习惯。在高等数学教学中渗透数学建模思想,可以通过概念教学、定理教学、解题教学等方面来进行,使学生浸润在数学美的享受之中。 相似文献
17.
Dominic Voyer 《International Journal of Science and Mathematics Education》2011,9(5):1073-1092
Many factors influence a student’s performance in word (or textbook) problem solving in class. Among them is the comprehension
process the pupils construct during their attempt to solve the problem. The comprehension process may include some less formal
representations, based on pupils’ real-world knowledge, which support the construction of a ‘situation model’. In this study,
we examine some factors related to the pupil or to the word problem itself, which may influence the comprehension process,
and we assess the effects of the situation model on pupils’ problem solving performance. The sample is composed of 750 pupils
of grade 6 elementary school. They were selected from 35 classes in 17 Francophone schools located in the province of Quebec,
Canada. For this study, 3 arithmetic problems were developed. Each problem was written in 4 different versions, to allow the
manipulation of the type of information included in the problem statement. Each pupil was asked to solve 3 problems of the
same version and to complete a task that allowed us to evaluate the construction of a situation model. Our results show that
pupils with weaker arithmetic skills construct different representations, based on the information presented in the problem.
Also, pupils who give greater importance to situational information in a problem have greater success in solving the problem.
The situation model influences pupils’ problem solving performance, but this influence depends on the type of information
included in the problem statement, as well as on the arithmetic skills of each individual pupil. 相似文献
18.
Examining the Effects of Different Multiple Representational Systems in Learning Primary Mathematics
《学习科学杂志》2013,22(1):25-61
Multi-representational learning environments are now commonplace in schools and homes. Research that has evaluated the effectiveness of such environments shows that learners can benefit from multiple representations once they have mastered a number of complex tasks. One of the key tasks for learning with multiple representations is successful translation between representations. In order to explore the factors that influence learners' translation between representations, this article presents 2 experiments with a multi-representational environment where the difficulty of translating between representations was manipulated. Pairs of pictorial, mathematical, or mixed pictorial and mathematical representations were used to teach children in 1 of 3 experimental conditions aspects of computational estimation. In Experiment 1, all children learned to become more accurate estimators. Children in the pictorial and the mathematical conditions improved in their ability to judge the accuracy of their estimates, but children in the mixed condition did not. Experiment 2 explored if the mixed condition's difficulties with translation were temporary by requiring additional time to be spent on the system. It was found that children in all the experimental conditions improved in their judgments of estimation accuracy. It is argued that the mixed condition's failure to improve in Experiment 1 was due to the difficulties they experienced in translating information between disparate types of representation. Their success in Experiment 2 was explained not by learning to translate between representations, but through the adoption of a single representation that contained all the necessary information. This strategy was only effective because of the way that information was distributed across representations. 相似文献
19.
Yi-Hung Lin Mark Wilson Ching-Lin Cheng 《European Journal of Psychology of Education - EJPE》2013,28(4):1141-1161
In teaching, representations are used as ways to illustrate the concepts underlying a specific topic. For example, use symbols (e.g., 1?+?2?=?3) to express the concept of addition. To compare students’ abilities to interpret different representations in mathematics, the symbolic representation (SR) test and the pictorial representation (PR) test were designed, and then administered to 681 sixth graders in Taipei, Taiwan. This study adopts two different modeling perspectives, the testlet perspective and the multi-ability perspective, to analyze this SR and PR test data in the context of item response theory. The main results show that:
- Students scored on average significantly higher on the SR test than the PR test.
- The effects of the item stem testlets could be large, but they are statistically non-significant; however, the influence of the number of items in the testlet should also be considered.
- The nature of the option representations, SR and PR, represents two different mathematics abilities.
- The main factor that influences students’ item responses is students’ abilities to interpret SR and PR, and the testlet effects generated from the shared item stem can be ignored.
- Regarding the parameter estimates of the best-fitting model: (a) the person ability variance estimates show that the ability distributions on the SR and PR dimension may not be the same, (b) the correlation estimate between the SR and PR dimension indicates that these two abilities are moderately correlated, and (c) the item difficulty estimates for different models are similar.
20.
Hélia Jacinto Susana Carreira 《International Journal of Science and Mathematics Education》2017,15(6):1115-1136
This study offers a view on students’ technology-based problem solving activity through the lens of a theoretical model which accounts for the relationship between mathematical and technological knowledge in successful problem solving. This study takes a qualitative approach building on the work of a 13-year-old girl as an exemplary case of the nature of young students’ spontaneous mathematical problem solving with technology. The empirical data comprise digital records of her approaches to two problems from a web-based mathematical competition where she resorted to GeoGebra and an interview where she explains and describes her usual problem solving activity with this tool. Based on a proposed model for describing the processes of mathematical problem solving with technologies (MPST), the main results show that this student’s solving and expressing the solution are held from the early and continuing interplay between mathematical skills and the perception of the affordances of the tool. The analytical model offers a clear picture of the type of actions that lead to the solution of each problem, revealing the student’s ability to deal with mathematics and technology in problem solving. By acknowledging this as a case of a human-with-media in solving mathematical problems, the students’ efficient way of merging technological and mathematical knowledge is portrayed in terms of her techno-mathematical fluency. 相似文献