新时期下小学数学课堂提出有效问题的能力培养

一个有效问题的提出,不仅能够在很大程度上激发学生进行积极思考,而且还能培养学生的思考意识。随着新课改的到来,对小学数学课堂提出有效问题的能力培养提出了新的要求。文章就学生问题意识培养、合理引导学生、积极创设问题情境等方面探索了提出问题的能力培养。     

情境教学在小学数学教育中的应用研究

数学新课程的教学设计尤其注重充分发挥学生的主体作用,这就要求教师要在教学中设计合适的教学情境和教学条件,充分调动学生的学习热情和动力,引导学生主动参与到教学之中。本文以情境教学在小学数学教学中作用、实现情境教学的方法和应注意事项为重点,对情境教学在小学数学教育中的应用开展了较为详细的研究。     

Comparing performance: a cross-national investigation into the teaching of mathematics in primary classrooms in England and China

This article presents initial findings from an empirical study of the effectiveness of mathematics teaching (EMT). The article explores the teaching of mathematics in two very different contexts: England and China. Within each country, the target cohort of pupils were those aged 9–10 and overall, 19 teachers, 10 from England and nine from China, participated in the study together with their pupils (n = 562). Two internationally validated instruments were used to collect the data and teacher behaviours were also measured systematically. In addition, structured observation was undertaken in classrooms in both countries. The results show that, on average, Chinese teachers scored higher on effective teaching measures and Chinese pupils outscored their English peers in the tests that were part of the study. This research project is currently collecting qualitative data but its findings, to date, reinforce the findings from previous research studies suggesting that certain teacher behaviours and classroom factors work effectively to improve student learning outcomes.     

Supporting English second-language learners in disadvantaged contexts: learning approaches that promote success in mathematics

In the Australian context, children living in disadvantaged circumstances, whose second language is English, are one of the groups at risk of failing in mathematics. This paper explores the impact purposely developed learning activities (Representations, Oral Language and Engagement in Mathematics Learning activities) have on pupils' mathematics outcomes in the first three years of formal schooling (Foundation, Year 1 and Year 2). The participating group (n = 461) comprised 328 English language learners and 133 mainstream pupils. To ascertain the impact of the learning experience, pre- and post-tests were conducted at the commencement and completion of each school year. The results indicate that all of the children significantly improved, with English as a second language pupils showing the greatest gains, and achieving norm-referenced expectations for their age.     

Cognitive load in algebra: element interactivity in solving equations

Central to equation solving is the maintenance of equivalence on both sides of the equation. However, when the process involves an interaction of multiple elements, solving an equation can impose a high cognitive load. The balance method requires operations on both sides of the equation, whereas the inverse method involves operations on one side only. In an experiment, middle school students (N?=?71) were randomly assigned to the balance and inverse methods to complete a pre-test, an acquisition phase and a post-test. Pre-test and post-test comparisons found that the inverse group outperformed the balance group for those equations that involved high element interactivity. Instructional efficiency measures further confirmed that the balance method imposed higher cognitive load. The inverse method was capable of reducing cognitive load due to the interacting elements.     

The Efficacy of Using Diagrams When Solving Probability Word Problems in College

Previous experiments have shown a deleterious effect of visual representations on college students’ ability to solve total- and joint-probability word problems. The present experiments used conditional-probability problems, known to be more difficult than total- and joint-probability problems. The diagram group was instructed in how to use tree diagrams to solve conditional probability problems; the equation-only group was instructed only in the formulation of equations. Results indicated that the diagram group outperformed the equation-only group on a posttest of 10 near- and far-transfer problems given immediately and as long as 1 week later (Experiment 2). In addition, when rating their experience with the training phase the equation-only group reported significantly higher levels of frustration and lower levels of perceived success than the diagram group.     

Problem solving in mathematics: the significance of visualisation and related working memory

The importance of educational psychologists’ (EPs’) skills to the formulation of evidence-based educational strategies, as well as in response to learning difficulties, is demonstrated here in relation to mathematical problem solving. Initiatives to improve the link between mathematical skills from school to everyday life have drawn significantly on problem solving tasks. Through critical evaluation of research, the relevance of visualisation methods and working memory to problem solving is considered within this article. Studies suggest that differences exist in the effectiveness of particular visualisation methods, but that training can improve their utility and thereby problem solving performance. Additionally, differences between individuals and contexts can influence visualisation use, and some pupils experience specific difficulties in this area. Recommendations are made to enhance the teaching of visualisation as a strategy for problem solving, and to support those pupils with specific difficulties.     

The immediate impacts of preschool attendance on Turkish children’s mathematics achievement

This study was conducted to investigate the immediate impacts of preschool attendance on Turkish children’s mathematics achievement. The participants were 200 children who attended or did not attend preschool. The number and operation task and the geometric shapes sorting task were used as the data collection tools. The children who attended preschool performed significantly better on the number and operation task and the geometric shapes sorting task than the children who did not attend preschool. Indeed, the multivariate regression analysis demonstrated that preschool attendance is the most important predictor of the success of children in number and operation task and the geometric shapes sorting task.     

Online homework impact in undergraduate mathematics and business statistics courses

This evaluation examines the impact on student success rates related to changes in instructional programmes in undergraduate mathematics and statistics courses. Success for students taking courses with a computer-based homework component was compared with success of students who took the course in prior semesters without the computer-based component. Graphical and analytical tools are used to compare results. Results come from multiple semesters of each type of homework application, for both pre-calculus algebra and business statistics courses. Students whose performance is utilised in this study are undergraduate students taking introductory level college mathematics or business statistics courses, with mostly no prior instruction at this level. Comparing the success of the intervention group with the success of the baseline control group, findings support that the students using the computer-based homework instruction are just as successful as those using the traditional method of homework instruction. Utilising the online homework applications, provide several important advantages in today’s universities, including the reduced time for faculty grading, consistency of graded assignments across all sections of a course and most importantly, immediate feedback for students.     

Improved Appreciation of Mathematics Through an IBL Liberal Arts Mathematics Course

Abstract

The author has taught an inquiry-based liberal arts mathematics class using the text “The Heart of Mathematics: An Invitation to Effective Thinking” by Edward B. Burger and Michael Starbird a total of 20 times since Spring 2001. The students in this class have almost all been in non-technical majors and many started the semester with negative or ambivalent attitudes toward mathematics based on their prior experiences. The author has gathered responses from students in this class that illustrate significant changes in their attitudes towards mathematics during the course. In particular, the responses gathered at the end of the semester are often eloquent about understanding the great ideas of mathematics that students confronted in this course and about seeing many more and varied connections between mathematics and the “real world” than they had previously realized existed.