Bilingualism and mathematical reasoning in English as a second language

This paper examines the ability of bilingual children to reason deductively in mathematics. In particular, the findings of a recent study of bilingual Punjabi, Mirpuri, Italian and Jamaican 11–13 year old children growing up in England are reported. It is found that first language competence is an important factor in the child's ability to reason in mathematics in English as a second language. This gives considerable support to theories which assert that a cognitively and academically beneficial form of bilingualism can only be achieved on the basis of adequately developed first language skills. However for both English monolingual and bilingual children knowledge of logical connectives in English is a crucial factor. It is suggested that published weaknesses in mathematics found among certain Asian and West Indian pupils may well be due to language factors. Furthermore there are strong cultural forces which predispose differential performance among boys and girls. The implications of the findings for a relevant mathematical education for bilingual children are discussed.     

The effects of IMPROVE on mathematical knowledge, mathematical reasoning and meta-cognition

The purpose of the present study is to examine the effects of IMPROVE, a meta-cognitive instructional method, on students' mathematical knowledge, mathematical reasoning and meta-cognition. Participants were 81 students who studied a pre-college course in mathematical. Students were randomly assigned into one of two groups and groups were randomly assigned into one of two conditions: IMPROVE vs. traditional instruction (the control group). Both groups were exposed to the same learning materials, solved exactly the same mathematical problems, and were taught by the same experienced teacher. The IMPROVE students were explicitly trained to activate meta-cognitive processes during the solution of mathematical problems. The control group was exposed to traditional instruction with no explicit exposure to meta-cognitive training. Results indicate that the IMPROVE students significantly outperformed their counterparts on both mathematical knowledge and mathematical reasoning. In addition, the IMPORVE students attained significantly higher scores then the control group on the three measures of meta-cognition: (a) general knowledge of cognition; (b) regulation of general cognition; and (c) domain-specific meta-cognitive knowledge. The theoretical and practical implications are discussed.     

Algebraic and fractional thinking in collective mathematical reasoning

Educational Studies in Mathematics - This study examines the collective mathematical reasoning when students and teachers in grades 3, 4, and 5 explore fractions derived from length comparisons, in...     

Students' mathematical reasoning in university textbook exercises

Video recordings of three undergraduate students' textbook-based homework are analysed. A focus is on the ways their exercise reasoning is mathematically well-founded or superficial. Most strategy choices and implementations are carried out without considering the intrinsic mathematical properties of the components involved in their work. It is essential in their strategies to find procedures to mimick and few constructive reasoning attempts are made.This revised version was published online in October 2005 with corrections to the Cover Date.     

Early childhood mathematical development: the association between patterning and proportional reasoning

Educational Studies in Mathematics - Insight into early precursors of proportional reasoning is necessary to further our theoretical understanding of mathematical development and to guide early...     

Developing interactive mathematical talk: investigating student perceptions and accounts of mathematical reasoning in a changing classroom context

In recent years there has been an increased focus on the need for teachers to develop learning communities where all students have opportunities to engage in interactive discourse. However, there are few studies that focus on student perceptions and accounts of mathematical reasoning in classrooms with interactive mathematical talk as a focus of reform. A framework of teacher actions to develop classroom and mathematical practices was developed from classroom observations. Photo-elicitation interviews were used to investigate student perception and accounts of mathematical explanations and reasoning. The professional development programme, shifts in the teacher actions, and subsequent shifts in student perception and their recall of their own and peers’ mathematical reasoning over a school year are highlighted. Developing interactive dialogue in the classroom took considerable time and attention. Facilitating change to the way students both participated and understood their obligations required constant, ongoing attention to both the classroom and mathematical practices.     

浅议西英四种过去时态的对比

西班牙语和英语同属印欧语系,但不属于同一语族,因此在语法上,特别是动词时态上有较大的区别。该文通过对西班牙语的简单过去时、过去未完成时和英语的一般过去时、过去进行时的对比,探讨它们在动词时态上表达的不同点和相同点,进而为我们学习语言,尤其是学习西班牙语提供帮助。     

Building middle school students' understanding of proportional reasoning through mathematical investigation

This article describes and shares an innovative pedagogical practice that holds promise in contributing to the teaching and learning of proportions in middle school. The teaching and learning of mathematics with understanding framework was used as a vehicle to help 21 seventh grade students reason proportionally. The findings of this unit suggest that the classroom culture, which encouraged the students to make connections between their existing and new ideas and reflecting and communicating their thinking, contributed to their emerging understanding of proportions. The use of an authentic and non-routine task involving liquid measurements also heightened their interest, curiosity and enthusiasm, thereby contributing to their excitement about the mathematics they were learning.     

The relation between types of assessment tasks and the mathematical reasoning students use

The relation between types of tasks and the mathematical reasoning used by students trying to solve tasks in a national test situation is analyzed. The results show that when confronted with test tasks that share important properties with tasks in the textbook the students solved them by trying to recall facts or algorithms. Such test tasks did not require conceptual understanding. In contrast, test tasks that do not share important properties with the textbook mostly elicited creative mathematically founded reasoning. In addition, most successful solutions to such tasks were based on this type of reasoning.     

Spanish and English Early Literacy Profiles of Preschool Latino English Language Learner Children

Research Findings: The purpose of this study was to examine within-group individual differences in the code-related and oral language abilities of an economically stressed Spanish-speaking English language learner (ELL) preschool sample and to evaluate the predictive relationship of these differences to later listening comprehension. Latent class analysis was used to identify similarities in both the latent and outcome variables to form classes of students with similar profiles on the measured variables. Our 1st finding confirmed the existence of 4 distinct psychometrically validated profiles: (a) Low English Language, Average Spanish Language, Mixed Spanish Code-Related (prevalence 19.4%); (b) Average English Language, Strengths in Spanish Language and Spanish Code-Related (24.2%); (c) Mixed English and Spanish Language, Low Spanish Code-Related (prevalence 34%); and (d) High English Language, Average Spanish Language, Mixed Spanish Code-Related (prevalence 22%). The resulting profiles demonstrated that English and Spanish code- and language-related domains of emergent literacy developed unevenly across the Spanish-speaking ELL preschoolers. Relative strengths and weaknesses in code- and language-related skills were also found to be meaningfully related to end-of-year listening comprehension—a precursor to reading comprehension. Finally, profiles yielded meaningful variability along sociodemographic variables. Practice or Policy: Implications, limitations, and directions for future research are discussed.     

A Cross-Linguistic Investigation of English Language Learners' Reading Comprehension in English and Spanish

This study investigated the associations of oral language and reading skills with a sample of 282 Spanish-speaking English language learners across 3 years of elementary school. In the 3rd grade, the English and Spanish decoding measures formed two distinct but highly related factors, and the English and Spanish oral language measures formed two factors that showed a small positive correlation between them. The decoding and oral language factors were used to predict the sample's English and Spanish reading comprehension in the 6th grade. The decoding and oral language factors were both significant predictors of reading comprehension in both languages. The within-language effects were larger than the cross-language effects and the cross-language effects were not significant after accounting for the within-language effects.     

Disclosure of students’ mathematical reasoning through collaborative technology-enhanced learning environment

Education and Information Technologies - We focus on students’ mathematical reasoning in a technology-enhanced collaborative learning environment. We adopt a dialogical approach to analyze...     

Effects of a rubric for mathematical reasoning on teaching and learning in primary school

Rubrics are assessment tools that help students gain complex competencies. Our quasi-experimental study aimed to evaluate whether rubrics help teachers teach and assess mathematical reasoning in primary school and whether such an instrument might support student learning. In two Swiss cantons, 762 students in 44 5th- and 6th-grade primary classes worked on their reasoning competencies, and half of them additionally employed our standards-based rubric. All of the teachers received a 1-day training and participated in the final project evaluation. To standardise and support the teachers during the implementation phase, they received a detailed curriculum. An achievement test and questionnaires for students and teachers were administered before and at the end of the intervention. The results of our quantitative longitudinal analyses indicate that the rubric fosters the teachers’ perceived diagnostic skills but only indirectly impacts their use of formative feedback. Based on the students’ perceptions, however, we observed a direct effect of the rubric on formative feedback and student self-assessment. Effects on students’ outcomes could not be observed, but there are indications of effects mediated by self-regulation and self-efficacy.     

Promoting moral reasoning and multicultural competence during internship

This paper reports a study designed to increase the moral reasoning and multicultural competence of White students in a counselling internship. An intervention was conducted to determine the effectiveness of using a deliberate psychological education (DPE) approach that incorporated issues of cultural competence, oppression and diversity. This study attempted to discern if the DPE model could make a difference in the promotion of moral reasoning and multicultural competence of counsellor interns. The Intervention Group showed significant gains compared to Comparison Group 1 and 2 in moral reasoning as measured by the Defining Issues Test‐2, as well as significant gains on the Knowledge subscale of the Multicultural Counseling Knowledge and Awareness Scale.     

英语文本阅读中推理发生的认知研究

在英文阅读推理过程中前提决定结论,本文探讨影响前提确定的相关因素。     

Fluid reasoning,working memory and planning ability in assessment of risk for mathematical difficulties

ABSTRACT

The demands on mathematical problem-solving have increased in almost all school systems internationally and may constitute a barrier for children with special educational needs (SEN). This study explored the role of fluid reasoning (FR), working memory (WM) and complex executive function of planning (EF) in children (N = 62) referred for assessment of SEN, and specifically of risk for mathematical difficulties (MD). Performances on FR, WM and complex EF of planning were used to predict risk for MD. Results showed that planning ability predicted children at risk for MD, beyond FR or WM ability, when comparing with children not at risk for MD. It was concluded that assessing the complex EF of planning in addition to FR and WM ability is crucial in identifying children at risk for MD. The importance of understanding how planning ability affects children’s mathematical problem-solving is discussed, in relation to assessment and teaching practices.     

Scientific reasoning during adolescence: The influence of instruction in science knowledge and reasoning strategies

The mechanism linking instruction in scientific topics and instruction in logical reasoning strategies is not well understood. This study assesses the role of science topic instruction combined with logical reasoning strategy instruction in teaching adolescent students about blood pressure problems. Logical reasoning instruction for this study emphasizes the controlling-variables strategy. Science topic instruction emphasizes variables affecting blood pressure. Subjects receiving logical reasoning instruction link their knowledge of blood pressure variables to their knowledge of controlling variables more effectively than those receiving science topic instruction alone—their specific responses show how they attempt to integrate their understanding.     

Writing and reading knowledge of Spanish/English second-generation bilinguals

Written bilingualism represents a particular type of bilingualism that is not frequently approached. The aim of this study was to investigate the writing and reading abilities of second-generation immigrants, Spanish–English bilinguals in South Florida. 58 participants (36 females, 22 males; 18–39 years of age) were selected. Both parents were native Spanish speakers and the home language was Spanish; 37 were born in the United States and 21 were born in a Latin American country, but arrived to the US before the age of 10. Equivalent reading and writing tests were administered both in Spanish and English. Performance was significantly higher in English than in Spanish in the following tests: reading aloud (speed and errors), writing sentences, spontaneous writing number of words, and spontaneous writing errors (spelling and grammatical). When comparing those participants born in the US and abroad, no significant differences were found in Spanish, but in English; participants born in the US did better in reading aloud (errors), and spontaneous writing errors (spelling and grammatical). It was concluded that reading and writing abilities are in general higher in English than in Spanish in this group of bilinguals, which is correlated with the language used in the school they attended. This study emphasize the importance to analyze not only oral but also written bilingualism. Toward the future, it would be particularly important to study written bilingualism in other types of bilingualism.     

论英语网络教育资源的整合

网络的应用已普及到与人们的日常工作、生活和学习密不可分的地步。英语教学尚存在诸多不足。本文就如何整合网络资源推进英语教学进行了分析。