Working on arithmetic word problems when English is an additional language

There has been little research in the UK into how students learning English as an additional language (EAL) learn mathematics. This article reports results from a three‐year study of the participation of learners of EAL in Year 5 in an arithmetic word problem task. The research, drawing on ideas from discursive psychology, used discourse analysis to explore patterns of attention in students' interaction as they worked in pairs or threes. The article briefly describes four patterns of attention: to genre, to mathematical structure, to narrative experience and to written form. Further analysis explored how students used attention as part of the social activity involved in working on the task. The rest of the article illustrates how students used attention to narrative experience to make links between word problems and their own experience, as well as to negotiate their relationships with each other.     

Where have all the students gone? Participation of doctoral students in authentic mathematical activity as a necessary condition for persistence toward the PH.D.

The mathematics community in the U.S. has become concerned about the state of doctoral education, including concerns about high attrition rates and the small numbers of women and students from some racial and ethnic groups. This paper proposes a model of doctoral student persistence and attrition, in which student participation in the life of the department and discipline lead to increased student integration, which is crucial for students' success. Ten faculty members and eighteen graduate students were interviewed about their interests,conceptions, and experiences within mathematics, in a case study of one mathematics department. In this department, students experienced four types of obstacles to their participation: obstacles stemming from the program structure, obstacles to participation in class, obstacles to participating with faculty outside of class, and obstacles stemming from faculty beliefs about teaching and learning. Implications for the retention of mathematics doctoral students are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Do they really need to raise their hands? Challenging a traditional social norm in a second grade mathematics classroom

In an attempt to examine dialogue within a second grade classroom, students were encouraged to participate in whole-class mathematics discussions without raising their hands before speaking. Beneficial social and sociomathematical norms developed in place of this traditional social norm. Effects of this change on the dialogue and written mathematical explanations of a class of second grade students are described. Focus was placed on student participation in whole-class discussions. The study helped to determine the effects of student-centered dialogue on students' mathematical explanations and justifications as demonstrated in the students' discussions, participation, and written expression related to their mathematics learning.     

The construction of word meaning in a multicultural classroom. Mediational tools in peer collaboration during mathematics lessons

In this article, we examine the construction of word meaning by students during collaborative activities in a multicultural classroom at a Dutch primary school. The analysis is based on recordings of student talk in small groups of four or five students during mathematics lessons. Difficulties with specific terms and expressions frequently arose during group work. Students could easily ask each other about the meaning of difficult words as a part of the collaborative activities they were accustomed to. In the groups with both Dutch and minority children, the minority students addressed their Dutch classmates as language experts. Conversations about language difficulties also occurred in the groups with only minority students. The conversations about word meaning revealed four patterns: (1) ignoring a question about the meaning of a word, (2) showing the meaning using gestures, (3) explaining, or (4) discussing word meaning. In none of the cases were the language problems solved by referring to the everyday meaning of the word. Instead, the conversations focussed directly on the specialised meaning which the word had in the context of the mathematics lesson. This means that the children used the mathematical discourse as a mediational tool for constructing a mathematical meaning of the words.     

Effect of School Decentralization and School Climate on Student Mathematics Performance: The Case of Hong Kong

For more than a decade, the Government of Hong Kong has instituted a policy of school decentralization aimed at devolving authority to all stakeholders, including the representatives of School Sponsoring Bodies, principals, teachers, parents, and community members. This study examines the relative contribution of two dimensions of school decentralization – teacher participation and school autonomy – to students' mathematics performance, and examines the role of school climate as a mediating variable between decentralization and performance. Data for the present study come from the second cycle of the Programme for International Student Assessment (PISA 2003), which is a large international assessment measuring 15-year-old students' literacy performance across over 40 countries and regions around the world. Using multi-level analysis, the study finds that teacher participation is more important than school autonomy for student mathematics performance in Hong Kong. In addition, the effect of teacher participation on students' performance is mediated by four major school climatic factors – sense of belonging, disciplinary climate, students' morale and student behaviour – in Hong Kong's secondary schools.     

PUTTING CONTEXT IN CONTEXT: AN EXAMINATION OF THE EVIDENCE FOR THE BENEFITS OF ��CONTEXTUALISED�� TASKS

The professional literature in mathematics education is replete with calls to use tasks that are ‘authentic’, ‘relevant’ and related to ‘real life’ and the ‘real world’. Such activities are frequently advocated for their potential to motivate and engage students, but evidence of their ability to do so is rarely presented. This paper examines evidence in relation to the effectiveness of context problems in achieving their intended purposes and thereby contributing to enhanced student participation, engagement and achievement in mathematics education. It is argued that context problems are not a panacea and that categorising problems as contextualised or de-contextualised is less helpful than the consideration of more salient aspects of tasks that impact on their effectiveness. Such aspects also relate to the purposes for and affordances and limitations of particular tasks in relation to the purposes they are intended to serve, along with attention to the contexts in which students learn mathematics. Examples of theoretical and empirical programs built on these considerations are reviewed in terms of their potential to enhance participation, engagement and achievement in school mathematics.     

Student performance and attitudes using personalized mathematics instruction

This study investigated the effects of personalized instruction on the achievement and attitudes of Taiwanese students on two-step mathematics word problems. A total of 136 fourth-graders in a Taiwanese public school participated in the study. Subjects initially completed a Student Survey on which they chose their favorite foods, sports, stores, classmates, and other selections. The most popular items were then used to create personalized math word problems for the pretest, personalized instructional program, and posttest. Subjects were blocked by ability based on their pretest scores and were randomly assigned within ability levels to either a personalized or nonpersonalized version of the print-based instructional program. After finishing the program, subjects completed a student attitude survey and the posttest. A repeated-measures univariate analysis of variance revealed that subjects in the personalized treatment made significantly greater pretest-to-posttest gains than those in the nonpersonalized treatment. Subjects also performed significantly better on the personalized pretest and posttest problems than on the nonpersonalized problems. Personalized subjects and higher-ability students both had significantly more positive attitudes toward the instructional program than did their nonpersonalized and lower-ability counterparts. This research was conducted while he was a doctoral student at Arizona State University.     

Using video-based anchored instruction to enhance learning: Taiwan's experience

The purpose of this study is to investigate the effects of computer-assisted videodisc-based anchored instruction on attitudes toward mathematics and instruction as well as problem-solving skills among Taiwanese elementary students. Results from a t-test indicate a significant main effect on student attitudes toward mathematics. Results from a two-way Repeated Measures ANOVA show that students' problem-solving skills improve significantly with anchored instruction. Results also indicate that all the students benefit from the effects of anchored instruction on their problem-solving performance regardless of their mathematics and science abilities. The findings suggest that video-based anchored instruction provide a more motivating environment that enhanced students' problem-solving skills. This study is significant because it establishes an example of video-based anchored instruction for Taiwanese students and also provides empirical evidence of its effects on affective and cognitive responses among fifth graders in learning mathematics. This study is helpful to educators who want to help students learn to think and learn throughout technology.     

论数学教学中学生的参与意识

数学作为一门基础而又非常重要的学科,学生应消化基础知识,掌握解题技巧和思想方法。在教学实践中教师要时刻注意给学生提供参与的机会,体现学生的主体地位,充分发挥学生的主观能动作用,才能收到良好的教学效果。     

The Role of Beliefs and Motivational Variables in Enhancing Word Problem Solving

A Word Problem Enrichment programme (WPE) has been found to increase student word problem solving performance when facing non-routine and application problems. However, it is unknown if the WPE has an impact on student beliefs about word problem solving and how the WPE works for students with different motivation in learning mathematics. This study investigated the impact of the WPE on student beliefs about word problem solving by using Latent Profile Analysis and Structural Equation Modelling to analyse relations among the different cognitive, motivation, and belief factors. A total of 170 fourth- and sixth-grade students from elementary schools participated. Results showed that the effects of WPE are various depending on students’ initial motivation level. The impacts of the WPE on student beliefs were found only in students with a low initial motivation level, while its impacts on student problem-solving performance were found only in students with a high initial motivation level.     

略论经济数学教学内容与方法之改革

在深入分析当代经济数学教学存在的弊端后，提出了经济管理类研究生经济数学的教学内容重点应放在投入产出分析、最优化理论和计量经济方法三个方面的基本设想，并提出了经济数学教学应以提供给学生强有力的基础平台，以培养和提高学生独立从事科学研究能力为目标，以教师讲授、学生讲授、师生互动探讨为主的新的课堂教学模式。     

Building on student mathematical thinking in whole-class discourse: exploring teachers’ in-the-moment decision-making,interpretation, and underlying conceptions

Often, mathematics teachers do not incorporate whole-class discourse of students’ various ideas and solution methods into their teaching practice. Particularly complex is the in-the-moment decision-making that is necessary to build on students’ thinking and develop their collective construction of mathematics. This study explores the decision-making patterns of five experienced Dutch mathematics teachers during their novice attempts at orchestrating whole-class discourse concerning students’ various solution methods. Our goal has been to unpack the complexity of their in-the-moment decision-making during whole-class discourse through lesson observations and stimulated recall interviews. We investigated teacher decision-making adopting a model that combines two perspectives, namely (1) we explored student-teacher interaction with regard to building on student thinking and (2) we explored how the teachers based decisions during such interaction upon their own personal conceptions and interpretation of student thinking. During these novice attempts at orchestrating whole-class discourse, the teachers created many situations for students to articulate their thinking. We found that at certain instances, teachers’ in-the-moment decision-making resulted in opportunities to build on student thinking that were not completely seized. During such instances, the teachers’ decision-making was shaped by the teachers’ own conceptions of the relevant mathematics and by teacher conceptions that centered around student understanding and mathematical goals. Our findings suggest that teachers might be supported in their novice attempts at whole-class discourse by explicit discussion of the mathematics and of their conceptions with regard to student understanding and mathematical goals.

     

A preliminary discourse analysis of constructivist-oriented mathematics instruction for a student with learning disabilities

Reform efforts in mathematics education arose, in part, in response to constructivist works on conceptual learning. However, little research has examined how students with learning disabilities (LD) respond to constructivist-oriented instruction in mathematics, particularly in moment-to-moment interactions. To understand the nature of constructivist-oriented mathematics instruction involving students with LD, the authors conducted a case study to analyze teacher–student interactions during constructivist-oriented small group instruction involving a student with LD. The student demonstrated, to a certain degree, the ability to reason mathematically when provided with appropriate opportunities and prompting. However, given the limited intervention time, his reasoning and problem solving did not seem to go beyond the semiconcrete level of operation, which may have inhibited his solving of complex word problems with large numbers. Findings indicate that more efforts are needed to support students, those with LD in particular, in their transitions from concrete or semiconcrete to abstract conceptual understanding and problem solving.     

The influence of English-Korean bilingualism in solving mathematics word problems

The purpose of this study was to investigate language related difficulties and the language of cognitive processes of English-Korean bilingual students in solving mathematics word problems. Qualitative case study research methodology was used to collect, analyze, and present data. The principle of purposeful sampling was used to select six English-Korean bilingual students. Different types of bilinguals revealed distinct patterns of difficulties and languages in solving mathematics word problems written in English and Korean. Children in the transition stage that is unstable and changing revealed more difficulties in solving the mathematics word problems overall.This article is a summary of doctoral dissertation under the direction of James W. Wilson at the University of Georgia.     

Towards a theory of mathematics homework as a social practice

This article presents a theoretical conceptualization of mathematics homework as a social practice. Rather than considering homework as a task or an artifact, this approach frames homework in terms of the social contexts in which students participate and how students participate in those contexts. This perspective has long been suggested by homework researchers but has not been developed as a framework for understanding homework. Drawing from Wenger’s (1998) social theory of learning and research grounded in sociocultural theory, this conceptualization makes central meaning making and identity development, and puts forth meaning and identity as lenses for understanding students’ participation in the practice of mathematics homework. To further develop this conceptualization of homework, I draw on data from an ethnographic study of the role and meaning of mathematics homework in the lives of middle school students. Case studies of two students are presented to demonstrate the relationships among the meaning of homework, students’ identities, and their participation in the practice of homework. One student’s experiences support him in identifying as a capable mathematics student who is bound for continued academic success through high school to college. Thus, he comes to take on mathematics homework as a means to learn and succeed. The other student’s experiences support him in building an identity that leads him to reject homework. This conceptualization of homework and the case study data have implications for the practice of homework and for theories of students’ motivational dispositions in the context of mathematics homework and learning in general.     

基于应用题解题障碍的认知工具模式设计

通过整理近年来关于小学数学应用题的相关研究,总结学生在应用题解题过程中普遍存在的认知障碍,结合现有解题系统分析研究各类型的认知工具对小学应用题解题障碍的支持,为帮助学生选择合适的认知工具提供借鉴,并在此基础上提出基于问题解决障碍的小学数学应用题解题系统的模型构建,为新的认知工具的设计开发提供新的角度。     

Organization and use of the mental lexicon by deaf and hearing individuals

Two experiments explored the taxonomic organization of mental lexicons in deaf and hearing college students. Experiment 1 used a single-word association task to examine relations between categories and their members. Results indicated that both groups' lexical knowledge is similar in terms of overall organization, with associations between category names and exemplars stronger for hearing students; only the deaf students showed asymmetrical exemplar-category relations. Experiment 2 used verbal analogies to explore the application of taxonomic knowledge in an academically relevant task. Significant differences between deaf and hearing students were obtained for six types of analogies, although deaf students who were better readers displayed response patterns more like hearing students'. Hearing students' responses reflected their lexical organization; deaf students' did not. These findings implicate the interaction of word knowledge, world knowledge, and literacy skills, emphasizing the need to adapt instructional methods to student knowledge in educational contexts.     

福建省高校学生政治参与状况的调查

基于大学生还不是完整意义上的社会人，其政治参与不能仅以政治参与行为进行考量，政治参与意识尚是一个重要指标，因此，调查组采用单变量分析为主的分析方法，从学习政治理论知识、关注社会政治问题、参加政治活动、加入政治团体、投身政治生涯等方面，对福建省4所高校1000名全日制本科生政治参与的基本状况进行抽样问卷调查。结果显示：大学生的政治参与正蓬勃发展，呈现良好态势，但也存在一些倾向和问题，必须引起高度重视。鉴此，调查报告针对调查实况提出了一些建议。冀望促进大学生政治参与朝向好的方向发展。     

Investigating the Unique Predictors of Word-Problem Solving Using Meta-Analytic Structural Equation Modeling

The purpose of the present study is to clarify the contributions of cognitive skills (nonverbal reasoning, language comprehension, working memory, attention, processing speed) and academic skills (mathematics facts retrieval, mathematics computation, mathematics vocabulary, reading comprehension) in performing mathematics word problems among elementary school students. With the two-stage meta-analytic structural equation modeling approach, I synthesized 112 correlation matrices from 98 empirical studies (N?=?111,346) and fitted the hypothesized partial mediation model. Overall, path analysis indicated that language comprehension, working memory, attention, mathematics vocabulary, and mathematics computation were unique predictors of word-problem solving. Subgroup analysis demonstrated different unique predictors for younger and older students to perform word problems (K-2nd grades versus 3rd–5th grades). Implications, limitations, and future directions are discussed.