2011年林纾研究刍议

去年的林纾研究,有旧的热点（翻译）,有新的景观。令人欣喜的是,林纾研究的阵地得到了拓展,福建俨然成为林纾研究的＂大本营＂。解决研究比例上的失衡,林纾研究的未来将会更美好。     

‘I like it instead of maths’: how pupils with moderate learning difficulties in Scottish primary special schools intuitively solved mathematical word problems

This study by Lio Moscardini of the University of Strathclyde shows how a group of 24 children in three Scottish primary schools for pupils with moderate learning difficulties responded to word problems following their teachers' introduction to the principles of Cognitively Guided Instruction (CGI). CGI is a professional development programme in mathematics instruction based on constructivist principles developed at the University of Wisconsin‐Madison. The study found that the sample group of pupils were able to develop their understanding of mathematical concepts through actively engaging in word problems without prior explicit instruction and with minimal teacher adjustments. The pupils' conceptual understandings demonstrated by their solution strategies within CGI activities were generally not consistent with classroom records of assessment. The results were encouraging in illustrating the capacity of the sample group of pupils with moderate learning difficulties to reveal their mathematical thinking and considers the importance of this insight for instructional decision making.     

小学生数学语言表达中的错误分析与对策

数学语言在数学教学中起着桥梁的作用。对小学生数学语言表达中常见的错误进行归类剖析,主要有：概念不清、形量不分、乱造术语、分类混乱、增减条件、互相矛盾、重复罗嗦、生活语言与数学语言混淆等。提出要加强教师的素养,指导学生表达,提供平台让学生多说。     

Contrasting Approaches to the Acquisition of Mathematical Skills: Japan and England

Abstract

International differences in mathematical attainment among secondary school age pupils are well documented, indicating that the performance of pupils in England lags behind that of many other countries: in particular, the average attainment of 13‐ and 18‐year‐old pupils in Japan is significantly higher than that of the corresponding cohort of pupils in England. The causes of the poor performance at secondary schools in England, it is argued, may be found partly in the inferior foundations of mathematical understanding at primary schools, aggravated by the ‘linearity’ of mathematical development and the cumulative effect of failure. Although cultural influences at the societal level and curriculum influences at the governmental level are largely beyond the control of the school, yet the other main influence on mathematical development, namely classroom practice, is determined to a great extent by the class teacher, and can be adapted to improve conceptual learning. By considering the current practice in the teaching of mathematics to six‐year‐olds in Japan within the context of available research evidence relating to effective teaching, and comparing this with the practice in England, areas of possible change can be identified which are largely within the control of the individual class teacher and through which standards of attainment might be improved. This article is based on observations of mathematics teaching to six‐year‐old children in Japan and England in 1995, in the state or public sector of education.     

数学运算规则样例学习的理论探索

概述了问题解决样例学习研究的进展,评述了已有样例学习理论的价值,提出了学生可以通过数学运算样例学习新的运算规则的理论解释,并用自己已有的实验研究结果论证了理论解释的科学性。认为学生可以通过精心设计好的数学运算样例并根据已知的数学运算规则顿悟或推断出新的数学运算规则。关键运算步骤的样例设计是数学运算规则样例学习的关键。根据数学运算规则的逻辑特点,可以分别采用分解法、逆运算法和解释法设计运算样例中的关键步骤,从而促进学生对新运算规则的顿悟和运用。     

Implementing Effective Group Work for Mathematical Achievement in Primary School Classrooms in Hong Kong

The Hong Kong Education Bureau recommends that primary school pupils’ mathematical achievement be enhanced via collaborative discussions engendered by group work. This pedagogic change may be hindered by Confucian heritage classroom practices and Western-dominated group work approaches that predominate in Hong Kong. To overcome these obstacles, we introduced a relational approach to group work in a quasi-experimental study. Our sample included 20 teachers randomly allocated to experimental (12) and control (8) conditions and their 504 mathematics pupils (aged 9–10). The relational approach focused on the development of peer relationships in a culturally appropriate manner and was implemented over 7 months. Pupils were pre-/post-tested for mathematical achievement and systematically observed, and the teachers were assessed for subject knowledge and pre-/post-tested for pedagogic efficacy. Analysis of covariance (ANCOVA) and hierarchical linear modeling (HLM) results show enhanced mathematical achievement, supported by improved peer-based communication skills and time-on-task for the experimental pupils. Experimental teachers raised their pedagogic efficacy. Results indicate the potential of the relational approach for boosting academic achievement via enhanced child-peer-teacher interaction and the need to reassess the role of peer-based latent collectivist learning in Confucian heritage classrooms.     

Pupils' mathematical performance in grades 3 and 6. A longitudinal study

The main purpose of this study was to analyse how pupils, differing in achievement levels in mathematics, performed operations with numbers and solved mathematical problems. What strategies did they use in different grades when they performed the operations and solved the problems correctly, and what types of errors were involved when they solved an item incorrectly? What types of errors disappear and what types of errors remain at a later grade? Five groups of pupils, comprising a total number of 900, who have shown different developments in mathematical achievement from grades 3 to 6 have been studied. When the pupils solved items correctly they used the same strategies irrespective of their total results. However, when they made errors they used a number of different strategies. The results of this study implicate that it is very essential that the teaching be individualised and built upon how the pupils think when solving mathematical problems.     

Classroom studies into cognitive style in mathematics for pupils with dyslexia in special education in the Netherlands, Ireland and the UK

The project reported here was designed to explore the cognitive style used by pupils with dyslexia when answering a range of mathematical questions. The research involved 132 pupils aged between 9 and 13 years, including 66 pupils in mainstream and 66 pupils in specialist schools, in three countries in Europe.
Detailed studies of the methods used by pupils attempting the given questions on a test of cognitive style suggested that they fell into two main categories. These pupils were observed when completing the test and their responses were categorised accordingly. The resulting numerical data were then analysed for differences between pupils within each country and between their non-dyslexic counterparts.
The results showed significant differences in the balance of cognitive styles employed by pupils with dyslexia as opposed to their non-dyslexic counterparts. Also there were interesting differences occurring between the pupils with dyslexia within the three countries on initial testing. Further differences were established after a six-month intervention period, suggesting that the characteristics of different curriculum models do have an impact upon pupils' flexibility as learners.     

Information processing by intellectually gifted pupils solving mathematical problems

What differences may be found in the way gifted pupils, as compared with average pupils from the second form of lower secondary education, process information while solving mathematical problems? Gifted pupils apparently solved the problems better, faster and needed less assistance than average pupils. A global distinction of the subprocesses orientation, execution and evaluation also allows for the conclusion that in most cases the gifted pupils processed information in a different fashion. The yield of this line of research should be the improvement of education in two respects. For one, the results may induce teachers to adapt their teaching to gifted pupils. Secondly they may try to teach average pupils to process information like gifted pupils typically would.     

Socially shared metacognition of dyads of pupils in collaborative mathematical problem-solving processes

This study investigated how metacognition appears as a socially shared phenomenon within collaborative mathematical word-problem solving processes of dyads of high-achieving pupils. Four dyads solved problems of different difficulty levels. The pupils were 10 years old. The problem-solving activities were videotaped and transcribed in terms of verbal and nonverbal behaviours as well as of turns taken in communication (N = 14 675). Episodes of socially shared metacognition were identified and their function and focus analysed. There were significantly more and longer episodes of socially shared metacognition in difficult as compared to moderately difficult and easy problems. Their function was to facilitate or inhibit activities and their focus was on the situation model of the problem or on mathematical operations. Metacognitive experiences were found to trigger socially shared metacognition.     

辽宁省小学生近五年体质健康状况分析研究

采用文献资料、访谈调查及数理统计等研究方法对辽宁省小学生近五年体质健康状况进行比较与分析,旨在对小学阶段培养良好的生活习惯和文明健康的生活方式,促进学校、家庭、社会的有效引导和保障作用服务,为相关部门制定青少年体质健康促进政策提供理论参考。     

Curiosity killed by SATs: an investigation of mathematics lessons within an English primary school

By taking both pupils’ and teachers’ actions as the point of departure, this study aimed to understand governance within a primary school classroom. Video footage was recorded in an English primary school in which mathematics happened to be the focus. This data was analysed to identify the directions of both governance and self-governance and to help understand the consequences for pupil and teacher subjectivities. Our findings revealed the central role of national testing and inspection policy in constituting staff as ‘evidence hunters’ and pupils as ‘confessant and unafraid producers of evidence’. Both staff and pupils were complicit in creating sufficient space for everyone to fulfil their obligation to be accountable to the school’s senior leadership team (SLT), school inspectors and national attainment tests. As a consequence, mathematical knowing was simplified into a discipline of reproducing testable calculation, in which other possibilities of mathematical knowing were foreclosed.     

The effect of standardized test information on teachers’ assessment of ability in their classes

Abstract

The responses of three groups of teachers to a rating task in which they were asked to indicate how many of their pupils were “bright”, “above average”, “below average” and “dull” were compared. In two of the groups, teachers had been provided with test information based on performance on nationally standardized ability and attainment tests. In the third group tests had been administered but no results were provided.

No differences between the groups were found in terms of the extent to which teacher ratings of ability levels correspond with mean ability test scores. In addition, teachers, irrespective of the group to which they belonged, were found to display a tendency to place more pupils in the above average categories than the below average categories. Finally, no support was found for an hypothesis which suggested that test information would differentially affect the ratings of teachers of classes with pupils who were typical and untypical with respect to age.

The fact that the correlation between mean ratings and mean test scores were found to be fairly high in all three groups (they ranged from .51 to .60) suggests a reason for the failure of test information to impact on teachers’ judgements. The degree of agreement between teachers and tests that the correlations reveal means that there is less scope for a convergence of ratings on tests to occur than might otherwise be the case.     

The use of mathematical symbolism in problem solving: An empirical study carried out in grade one in the French community of Belgium

This article relates to an empirical study based on the use of mathematical symbolism in problem solving. Twenty-five pupils were interviewed individually at the end of grade one; each of them was asked to solve and symbolize 14 different problems. In their classical curriculum, these pupils have received a traditional education based on a “top-down” approach (an approach that is still applied within the French Community of Belgium): conventional symbols are presented to the pupils immediately with an explanation of what they represent and how they should be used. Teaching then focuses on calculation techniques (considered as a pre-requisite for solving problems). The results presented here show the abilities (and difficulties) demonstrated by the children in making connections between the conventional symbolism taught in class and the informal approaches they develop when faced with the problems that are put to them. The limits of the “top-down” approach are then discussed as opposed to the more innovative “bottom-up” type approaches, such as those developed by supporters of Realistic Mathematics Educations in particular.     

谈如何在小学数学教学中培养学生独立思考的习惯

在当今多元化教育模式下,教师侧重于培养小学生自我探索、独立思考的能力,格外重视小学生逻辑思维能力的培养,让学生在潜移默化中形成独立思考的习惯。小学阶段的数学教育教学对学生来说非常重要,教师要让学生养成独立思考的习惯,提高独立思考的能力,要学会活学活用知识,避免死板地吸收数学内容。     

The use of mathematical strategies: factors and features affecting performance

The study investigates the use of general mathematical strategies by pupils of junior high school age. The form of response required pupils to describe their reasoning and to articulate their reasons for the choice of particular strategies. Main effects were found for cognitive level, year level, and sex. The sex effects is in contrast with similar effects from most other mathematical studies in that girls outperformed boys at each year level.A second part of the study involves the characterization of responses by means of a qualitative hierarchy: The Solo Taxonomy. Features of responses representing different levels of functioning are discussed and used to suggest related implications for curriculum and teaching.     

Visuospatial working memory in adolescents with poor performance in mathematics: variation depending on reading skills

The first purpose of this study was to investigate whether the visuospatial working memory (VSWM) skills of 15–16‐year‐old pupils with difficulties in mathematics differ from those of their normally achieving peers. The goal was to broaden the view of the complex system of VSWM. A set of passive and active VSWM tasks was used. The study’s second purpose was to investigate whether pupils with mathematical difficulties differed in their VSWM skills based on whether they had signs of reading deficits or not. Results indicate that the pupils with poor performance in maths showed poorer performance on certain VSWM tasks. The group with deficits only in maths had less capacity for storing passive visual simultaneous information, while the group with difficulties both in maths and reading had deficits in both storing (passive visual and visuospatial information) and processing, and had less ability to control irrelevant visuospatial information compared to their peers of the same age. The results indicate a general VSWM deficit in pupils with both mathematics and reading problems and a specific VSWM deficit in pupils with only mathematics problems.     

Assessing pupils’ intelligence through self,parental, and teacher estimates

This study examined the accuracy of self‐ and other‐estimated intelligence in relation to tested cognitive ability and gender. Three groups of raters were examined: 187 (102 male, 85 female; mean age 14.33 years, SD = .32) pupils of single‐sex comprehensive schools, 109 (55 mothers and 54 fathers) parents, and six teachers of the pupils. Pupils estimated their own overall IQ, while their parents and teachers estimated the pupils’ overall, mathematical, spatial, and verbal abilities. Self‐ and other‐estimates were compared to each other, and to the child’s psychometric test scores in verbal, quantitative, and figural/non‐verbal reasoning ability. Results suggested that participants were reasonably accurate at estimating pupils’ intelligence – teachers significantly more so than parents, and pupils significantly more so than fathers. Although both parents significantly overestimated their child’s IQ, this overestimation was more pronounced in fathers.