数学定义的基本要求

对数学概念下定义的基本要求、定义的实质和思想方法进行探讨。把形式逻辑关于真实定义的四条规则用来作为数学定义的基本要求是不恰当的，可以针对数学的三类基本概念中的不变个体制定具体的定义规则。可消去性准则和非创新性准则的思想应当在中学数学教材教法的逻辑内容中得到反映。     

Teacher-student relationship and mathematical problem-solving ability: mediating roles of self-efficacy and mathematical anxiety

Abstract

This study investigated the mediating roles of self-efficacy and anxiety on the effects of teacher–student relationship on mathematical problem-solving ability. A total of 1667 fifth graders from central China participated in the large-scale survey. The findings indicated that (1) teacher–student relationship had a direct and positive effect on students’ mathematical problem-solving ability; (2) the positive link between teacher–student relationship and mathematical problem-solving ability was partially mediated through self-efficacy; (3) the teacher–student relationship affected students’ mathematical problem-solving ability through self-efficacy and maths anxiety, but the effect of self-efficacy on mathematical anxiety was smaller. Implications for the importance of teacher–student relationships in education as well as suggestions for future research are discussed.     

“细看”数学问题解决过程中的惯性思维

本文通过对数学问题解决过程中惯性思维存在现状的分析和探讨,对指导学生跳出惯性思维局限作初步的研究。旨在为教师和研究者提供帮助,解决学生在学习过程中存在的各种思维障碍。     

Ambivalent occupational identities under modern workplace demands: the case of Swiss retail apprentices

This article investigates how Swiss retail apprentices construct their occupational identities under modern workplace affordances. The Swiss retail sector has become more competitive in recent decades; as a consequence, retail businesses look for skilled and responsible employees who are flexible in regard to work tasks and schedules. The article focuses on apprentices’ experiences and sense-making, and specifically examines how retail work conditions not only generate pressure and insecurity, but also offer possibilities for personal identification. Results are based on a qualitative study with retail apprentices involving interviews, focus groups, and observations in vocational education and training schools. Retail apprentices strongly identify with the skilled nature of retail work and even the demand for continuous skill development to ensure that they remain employable. However, they are more critical of the flexible way in which their work is organised and develop divided sense-makings around the demands for responsible autonomy. In short, retail work is perceived in ambivalent ways, oscillating between valorising some of the realities of retail work and suffering from others. The discussion points to the kinds of working and learning conditions within companies that hinder apprentices’ ability to cope with the demands of the modern retail workplace.     

Balancing competing demands: Enhancing the mathematical problem posing skills of prospective teachers through a mathematical letter writing initiative

Responding to mathematical problems is a core activity in classrooms. The problems that teachers select determine the mathematical content, processes and nature of mathematical inquiry occurring in classrooms and thereby contribute to the development of mathematical skills and dispositions. Selecting, designing or reformulating mathematical problems is a critical skill, then, for prospective and practising teachers. This study explores the influence of a mathematical letter writing initiative in developing the problem posing skills of 28 prospective primary teachers. We examine the characteristics of mathematical problems designed by prospective teachers, and their understandings of what constitutes a good mathematical problem, prior to and following completion of a 12-week letter writing initiative with 10–11-year-old children. Analysis of the data reveals the benefits of engaging in the initiative as evidenced in improvements in several problem characteristics. There was an increase in the number of multiple approach and multiple solution problems and in the level of cognitive demand of problems posed. The challenge of posing non-traditional problems, alongside the competing demands of building in opportunities for success, may have diminished participants’ ability to evaluate and attend to the cognitive demand of problems.

     

简单两步计算的应用题的基本训练

目前学生普遍感到解答应用题难、解答复合应用题就更难。如何教好简单应用题是最关键的一环。在教学简单应用题时需要一定的训练 ,才能提高解题能力 ,我常使用的解题训练主要有以下一些方法。一、抓关键词、句的训练。应用题是数量关系和语言文字的综合体。因此解答应用题必须具备坚实的语言文字基础 ,如果学生连题都读不通 ,那就谈不上正确的解答。例如 :一年级一班有 13名“三好学生” ,二班和一班同样多 ,两班一共有多少名“三好学生” ?让学生读题后 ,问这道题说了什么事 ?是哪个年级的事 ?有几个班 ?如果学生答不出来 ,再读 ,并让学生…     

Emotional and motivational relationship of elementary students to mathematical problem-solving: a person-centered approach

European Journal of Psychology of Education - Recent literature has shown that achievement emotions, their regulation, and perceived competence play a compelling role in mathematics learning and...     

多元函数积分计算方法的数学思想研究

多元函数积分是学生掌握的重点和难点,其积分种类多,计算方法非常繁杂。本文总结了多元函数多种积分计算方法的数学思想,并指出这些思想都来源于人们的日常生活经验。教学实践表明这有助于学生理解和掌握这些方法。     

Transfronteriza pre-service teachers managing,resisting, and coping with the demands of mathematical discourse

This article reports on a case study of a college class for pre-service teachers on the US–Mexico border in which students participated in in-depth discussion around mathematical problems every day. This pedagogical approach promotes the socialization of students into and through the specialized discourse of mathematics. The focus of this paper is on the experience of transfronterizo students in that course. Transfronterizos are Mexican residents who periodically cross the border to attend school. For these students, whose educational background in Mexico allowed them to develop proficiency in elementary mathematical discourse in Spanish, their socialization experience includes ways in which they draw on language, and other social and learning experiences in Mexico. The focus of this paper is an assignment called Thinking Logs, a genre that required the use of mathematical discourse for teaching. Drawing on data gathered from participant observation of the course, interviews, analysis of study session discourse, and genre analysis, I highlight agentive ways that each participant used in their own socialization process. I show how participants improvised writing of models, asked for clarification in the first language, and even resisted the discourse. Students who resisted the demands might incur negative effects. Furthermore, I argue that the role of the guidance from an expert (such as a professor) is imperative in a socialization process, and I offer implications for ways that teachers can guide second language writers to develop mathematics discourse.     

The effects of teaching mental calculation in the development of mathematical abilities

Many countries include mental calculation within their curriculum, as the literature shows benefits related to it. However, evidence mainly focuses on the effects of teaching mental calculation on computational fluency. Therefore, the authors aimed to assess the effects of teaching mental calculation on double-digit computation, number line estimation, and computational fluency. Fifty second-grade students from a Uruguayan private school were randomly assigned to a control or treatment condition (n?=?25 each). The treatment group participated in 15 sessions of mental calculation intervention, while the control group received “teaching as usual.” Assessment took place before and after the intervention. The authors found no significant impact of the treatment on the mathematical outcome variables. The results are explained in the context of the available literature and the methodological decisions taken. From a perspective of evidence-based teaching practices, the present study contributes to a better understanding of effective instructional principles.     

Responsiveness to mathematical problem-solving instruction: comparing students at risk of mathematics disability with and without risk of reading disability

This study assessed responsiveness to a 16-week mathematical problem-solving treatment as a function of students' risk for disability. Among 301 third graders, TerraNova scores were used to categorize students as at risk for both reading and mathematics disability (MDR/RDR; 20 control and 12 experimental), at risk for mathematics disability only (MDR-only; 5 and 8), at risk for reading disability only (RDR-only; 12 and 15), or not at risk (NDR; 60 and 69). Interactions among at-risk status, treatment, and time showed that as a function of treatment, MDR/RDR, MDR-only, and RDR-only students improved less than NDR students on computation and labeling, and MDR/RDR students improved less than all other groups on conceptual underpinnings. Exploratory regressions suggested that MDR/RDR students' math deficits or their underlying mechanisms explained a greater proportion of variance in responsiveness to problem-solving treatment than reading deficits or their underlying mechanisms.     

Engineering problem-solving knowledge: the impact of context

Employer complaints of engineering graduate inability to ‘apply knowledge’ suggests a need to interrogate the complex theory-practice relationship in twenty-first century real world contexts. Focussing specifically on the application of mathematics, physics and logic-based disciplinary knowledge, the research examines engineering problem-solving processes as enacted by recent graduates in a range of industrial settings. Theoretically situated in the sociology of education, the Bernsteinian concept of knowledge structures and Legitimation Code Theory epistemic relations are utilised to surface the disciplinary basis of problem solving in different sociotechnical contexts. It is argued that the relationship between the ‘what’ and the ‘how’ of the problem gives rise to significantly different practice ‘codes’ between which successful engineering problem-solvers are required to shift. This paper presents two contrasting case studies which demonstrate the impact of the environment on code-shifting practices. Findings suggest that engineering curricula need to facilitate a more conceptual grasp of contextual complexities.     

Welcome to the era of vague news: a study of the demands of statistical and mathematical products in the COVID-19 pandemic media

Educational Studies in Mathematics - In this article, we report on a typology of the demands of statistical and mathematical products (StaMPs) embedded in media items related to the COVID-19...     

Towards powerful learning environments for the acquisition of problem-solving skills

It is generally agreed that acquiring thinking and problem-solving skills is nowadays a primary objective of general education. Responding appropriately to this challenge requires an answer to the following questions: 1. what does the acquisition of problem-solving skills involve, and 2. how can those abilities be fostered through systematic instruction? This contribution describes a four-step model of skilled problem-solving processes, and gives an overview of three major categories of cognitive skills involved in competent problem solving, namely, the flexible and integrated application of domain-specific knowledge, of heuristic methods, and of metacognitive skills. Furthermore, a framework is presented for the design and elaboration of powerful teaching-learning environments in which such problem-solving skills can be acquired efficiently. Two basic ideas underlying this model are: the view of learning as a constructive process, and the idea of cognitive apprenticeship as an effective and appropriate method for learning and teaching. Finally, some recent research findings supporting the educational significance of the framework are briefly reviewed.     

Gauging the gaps in student problem-solving skills: assessment of individual and group use of problem-solving strategies using online discussions

For the past 3 yr, faculty at the University of New Mexico, Department of Biochemistry and Molecular Biology have been using interactive online Problem-Based Learning (PBL) case discussions in our large-enrollment classes. We have developed an illustrative tracking method to monitor student use of problem-solving strategies to provide targeted help to groups and to individual students. This method of assessing performance has a high interrater reliability, and senior students, with training, can serve as reliable graders. We have been able to measure improvements in many students' problem-solving strategies, but, not unexpectedly, there is a population of students who consistently apply the same failing strategy when there is no faculty intervention. This new methodology provides an effective tool to direct faculty to constructively intercede in this area of student development.