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1.

We use eye tracking as a method to examine how different mathematical representations of the same mathematical object are attended to by students. The results of this study show that there is a meaningful difference in the eye movements between formulas and graphs. This difference can be understood in terms of the cultural and social shaping of human perception, as well as in terms of differences between the symbolic and graphical registers.

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2.
数学术语的隐喻歧义及其人文内涵   总被引：2，自引：0，他引：2  
数学术语指的是指称或限定某类数学对象的字、词或词组。通常是用词语的一般意义隐喻其数学意义。这种隐喻存在着歧义现象,主要包括指称对象的模糊或变异,限定对象的语义转换以及种属关系的误解。这些现象会给相关数学概念的学习造成障碍或误解。同时,这些隐喻现象中蕴涵着人文因素,挖掘这些人文因素并将之用于数学课程与教学,有益于数学与人文的沟通。  相似文献   

3.
国内外的相关研究表明,眼动研究可以通过对数学问题解决过程中的眼动轨迹进行记录以及对注视时间、注视次数等眼动指标的分析,进而了解数学问题解决过程中,大脑的内部加工机制。数学学科能力主要体现为数学问题的解决能力,通过数学学科教育中的眼动研究文献分析发现,眼动研究有助于探寻数学问题解决过程中注意分配及加工策略选择过程。在数学学科教育中针对这些认知加工的特点进行策略教学旨在:培养高效的注意能力、提取关键的表征信息、激发多知识体系的想象力,更好地提高学科教育的有效性。  相似文献   

4.
In this qualitative study of mathematical discourse between elementary teachers, we examined linguistic invention and semantic warrant production as participants made successive attempts to communicate mathematical ideas. Linguistic invention is a creative practice of describing mathematics in terms of personal experience. We introduce semantic warrant production, which emerged as part of our analysis of substantial arguments produced by teachers learning mathematics. Participants engaged in linguistic invention and semantic warrant production to convince themselves and others of the validity of their mathematical inferences about a graph of rate of change versus time. Personal experiences that are taken-as-shared in a learning community can support accurate mathematical inference if connections between conventional language, common experiences, and mathematical representations are made explicit by learners.  相似文献   

5.
This paper presents a strategy for specifying latent variable regressions in the hierarchical modeling framework (LVR-HM). This model takes advantage of the Structural Equation Modeling (SEM) approach in terms of modeling flexibility—regression among latent variables—and of the HM approach in terms of allowing for more general data structures. A fully Bayesian approach via Markov Chain Monte Carlo (MCMC) techniques is applied to the LVR-HM. Through analyzing the data from a longitudinal study of educational achievement, gender difference are explored in the growth of mathematical achievement across grade 7 through grade 10. Allowing for the fact that initial status effect to rates of change may differ for girls and boys, the LVR-HM is specified in a way that rates of change parameters are modeled as a function of initial status parameters and the interaction between initial status and gender.  相似文献   

6.
It is well established that early general language during preschool is critical for children's mathematical abilities. In an attempt to further characterize this association between language and mathematics, an increasing number of studies show that one specific type of language, namely mathematical language or the key linguistic concepts that are required for performing mathematical activities, is even more critical to children's mathematical abilities. The purpose of this systematic review is to summarize the evidence on mathematical language and mathematical abilities. We focus on preschool children as nearly all of the existing work has been done at this age. We first explain how mathematical language has been defined across studies, and report how it has been evaluated in studies in preschool. Next, we present the results of our systematic review. Following the PRISMA guidelines and after a critical appraisal, we ended with a set of 18 papers that were all of sufficient methodological quality. In these studies, mathematical language was defined as terms that are about numbers and operations on numbers (e.g., nine), but also included linguistic terms that do not directly refer to numbers, yet are important to understand mathematical concepts (i.e., quantitative and spatial terms such as fewest and middle, respectively). Some of these studies evaluated children's performance on mathematical language tasks, while others evaluated the mathematical language input provided to the child by their (educational) environment (teachers/parents/interventionists). Mathematical language correlated positively with children's mathematical abilities, concurrently and longitudinally. It also directly affected children's mathematical abilities, as was shown by intervention studies. We discuss potential directions for future research and highlight implications for education, arguing for more support for teachers and parents to improve the use of mathematical language in the classroom and in home settings.  相似文献   

7.
以数学学习兴趣（I）和学习能力（J）两个指标针对高中三个年级的数学学习现状进行调查表明：1）年级因素、性别因素以及年级和性别的交叉因素对数学学习的状况非常明显的影响,年级对学习兴趣和学习能力均有显著的影响,而性别只对学习能力有影响,对学习兴趣无显著影响。2）随着年级的升高,男、女生的数学学习兴趣和学习能力都随之发生显著地变化,男生的学习兴趣和学习能力随着年级的增加而增强,因此高三男生的数学学习兴趣和能力最高;高一年级女生的学习兴趣最低,而高三女生的学习兴趣和学习能力都高于高一、高二年级。3）通过年级因素的多重比较发现,在学习兴趣方面,高二、高三无显著差别,且均高于高一;在学习能力方面,均存在非常显著的差异,且高三最高,高二次之,高一最低。  相似文献   

8.
Problem solving is an important yet neglected mathematical skill for students with autism spectrum disorder and intellectual disability (ASD/ID). In addition, the terminology and vocabulary used in mathematical tasks may be unfamiliar to students with ASD/ID. The current study evaluated the effects of modified schema-based instruction (SBI) on the algebra problem solving skills of three middle school students with ASD/ID. Mathematics vocabulary terms were taught using constant time delay. Participants were then taught how to use an iPad that displayed a task analysis with embedded prompts to complete each step of solving the word problems. This study also examined participant’s ability to generalize skills when supports were faded. Results of the multiple probe across participants design showed a functional relation between modified SBI and mathematical problem solving as well as constant time delay and acquisition of mathematics vocabulary terms. Implications for practice and future research are discussed.  相似文献   

9.
中国古代数学与古希腊数学在思想方法和内容上有着很大的差别，不同的数学观是造成这种差别的重要原因之一。文章对古代中国与古希腊数学观作了明确的阐述，并从多种角度对二者进行了比较和分析。  相似文献   

10.
We show that students rearranging the terms of a mathematical equation in order to separate variables prior to integration use gestures and speech to manipulate the mathematical terms on the page. They treat the terms of the equation as physical objects in a landscape, capable of being moved around. We analyze our results within the tradition of embodied cognition and use conceptual metaphors such as the path-source-goal schema and the idea of fictive motion. We find that students solving the problem correctly and efficiently do not use overt mathematical language like multiplication or division. Instead, their gestures and ambiguous speech of moving are the only algebra used at that moment.  相似文献   

11.
This article shows how multilevel modelling can be used to study institutional variations in the gender differences in achievement. The results presented are from analyses of the degree classifications of 22,433 individuals who graduated in mathematical sciences, from universities in the UK, between 1994/95 and 1999/2000. The analyses were designed to measure gender differences in the achievement of first class honours in mathematical science degrees as a whole and within individual institutions. After allowing for students' entry qualifications, age, type of course and institution attended, no systematic gender difference was detected in the achievement of first class honours in mathematical sciences at any level of entry qualifications. However, there were statistically significant variations between universities in ‘gender difference added’. This variation between institutions in gender difference added was explained by the significant gender differences in the first class degree awards made by Oxford and Cambridge universities, with no significant evidence of gender differences in the first class degree awards made by other institutions.  相似文献   

12.
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   

13.
Temporal processing in dyslexia   总被引：1，自引：0，他引：1  
The temporal processing capabilities of 15 children with dyslexia versus 15 age-matched and 15 reading-matched controls in a word identification task were examined. The hypothesis underlying the present experiment was that word recognition would be inferior in children with dyslexia, relative to controls, when the task demanded the temporal integration (sequencing) of two-syllable words. Such a hypothesis must predict that one-syllable word recognition does not distinguish between these two populations and that these effects cannot be accounted for in terms of eye movement differences. To test this hypothesis, one- and two-syllable words displayed for 100, 300, and 3,000 msec were required to be identified. The results yielded evidence of decreased accuracy of word identification by the children with dyslexia in the two-syllable, 300-msec condition, as predicted. A second experiment was unable to uncover any differences in eye movement behaviors that could account for the effects observed in the first experiment. The results are discussed in terms of potential sequential processing deficits in individuals with dyslexia.  相似文献   

14.
This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language interact. This alternative framework is termed Math- Mediated Language (MML) and argues that the perception of common terms that adults possess is an important part of the knowledge that practitioners possess about linking conceptually related linguistic and mathematical knowledge. Empirical findings from a survey recording participants' reactions to seven categories of terms with mathematical meanings and three categories of distracter terms were analyzed. The data indicated that when asked to think about math, practitioners more readily accessed words for operation terms than relational terms. Additionally, participants demonstrated stronger tendencies toward additive terms conveying addition or subtraction concepts over multiplicative ones conveying multiplication or division concepts. The findings point to patterns in the ways that participants view mathematical language demonstrating that language interacts with even simple interpretations of basic mathematical terminology. The implications of this are that practitioners interpretations of everyday language may influence their ability to see opportunities for teaching mathematical concepts not only in the context of an explicit math lesson but throughout the broader early childhood curriculum.  相似文献   

15.
This study argues that maximizing early childhood educators' abilities to create social opportunities for co-construction of knowledge rests on two understudied assumptions, one theoretical and one empirical. Theoretically this study rejects the notion of language as an impartial conveyor of knowledge in favor of one in which math and language interact. This alternative framework is termed Math- Mediated Language (MML) and argues that the perception of common terms that adults possess is an important part of the knowledge that practitioners possess about linking conceptually related linguistic and mathematical knowledge. Empirical findings from a survey recording participants' reactions to seven categories of terms with mathematical meanings and three categories of distracter terms were analyzed. The data indicated that when asked to think about math, practitioners more readily accessed words for operation terms than relational terms. Additionally, participants demonstrated stronger tendencies toward additive terms conveying addition or subtraction concepts over multiplicative ones conveying multiplication or division concepts. The findings point to patterns in the ways that participants view mathematical language demonstrating that language interacts with even simple interpretations of basic mathematical terminology. The implications of this are that practitioners interpretations of everyday language may influence their ability to see opportunities for teaching mathematical concepts not only in the context of an explicit math lesson but throughout the broader early childhood curriculum.  相似文献   

16.
An attitude toward mathematics questionnaire indicated no real difference in attitudes between two‐ and four‐year colleges. No differences in mathematical competencies, as measured by the Beckmann‐Beal Mathematical Competencies Test for Enlightened Citizens, existed between two‐ and four‐year colleges. The gain in mathematical competency due to taking one precalculus mathematics course was only 1.48 questions, or an increase of only 4.1%.  相似文献   

17.
Combined with emotional expressions, eye gaze can provide essential information to indicate threat in the environment. The current study assessed the effects of eye gaze direction on infants’ neural processing of fearful and angry faces. Event‐related potentials were recorded from thirteen 7‐month‐old infants. Two face‐sensitive posterior components, the N290 and P400, as well as a frontocentral negative component (Nc), indicating attentional arousal, were sensitive to eye gaze direction and emotion. A larger Nc was observed for angry faces with direct compared to averted eye gaze. Fearful faces elicited a larger N290 than angry faces, whereas angry faces elicited a more prominent P400 regardless of eye gaze direction. The findings are discussed in terms of early social cognitive and neural development.  相似文献   

18.
ABSTRACT— Is educational neuroscience a “bridge too far”? Here, we argue against this negative assessment. We suggest that one major reason for skepticism within the educational community has been the inadequate definition of the potential role and use of neuroscience research in education. Here, we offer a provisional definition for the emerging discipline of educational neuroscience as the study of the development of mental representations. We define mental representations in terms of neural activity in the brain. We argue that there is a fundamental difference between doing educational neuroscience and using neuroscience research results to inform education. While current neuroscience research results do not translate into direct classroom applications, educational neuroscience can expand our knowledge about learning, for example, by tracking the normative development of mental representations. We illustrate this briefly via mathematical educational neuroscience. Current capabilities and limitations of neuroscience research methods are also considered.  相似文献   

19.
结合数学与经济学之间的联系,将经济问题转化为数学问题,用数学方法对经济学问题进行分析.从课程目标、学习重点来说,经济数学教学与高等数学的教学有很大的区别.从经济数学教学的课程体系、方式、方法等方面对如何激发学生学习经济数学的兴趣,培养学生的数学思维,从而提高他们的数学应用能力进行一定的探讨.  相似文献   

20.
This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the mathematical texts and the historical text. Before reading the texts, a test of prior knowledge for both mathematics and history was given and after reading each text, a test of reading comprehension was given. The results reveal a similarity in reading comprehension between the mathematical text without symbols and the historical text, and also a difference in reading comprehension between the two mathematical texts. This result suggests that mathematics in itself is not the most dominant aspect affecting the reading comprehension process, but the use of symbols in the text is a more relevant factor. Although the university students had studied more mathematics courses than the upper secondary students, there was only a small and insignificant difference between these groups regarding reading comprehension of the mathematical text with symbols. This finding suggests that there is a need for more explicit teaching of reading comprehension for texts including symbols.  相似文献   

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