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.     

新升本院校数学应用专业学生数学素质的调查与分析——以黄淮学院为例

学生的数学素质在很大程度上影响着综合素质,为进行数学专业的教学改革,文章以黄淮学院为例,调查分析了新升本本科院校学生的数学素质.研究表明:学生的数学素质一般,无性别差异,但有年级差异.     

Professional noticing of coordinated mathematical thinking

Over the past three decades, research and policy in many geographic regions has promoted a shift from direct, lecture-oriented mathematics instruction to inquiry-based, dialogic forms of instruction. While theory and research support dialogic instructional approaches, some have noted that the complexities of dialogic teaching make it difficult for teachers to implement. One mechanism by which teachers can improve their decision-making practices in dialogic classrooms is learning to notice (i.e. becoming aware of learners’ processes). While research has contributed frameworks for understanding how teachers notice individual learners’ mathematical thinking, there is little conceptualization regarding how teachers notice group processes in mathematics classrooms, which is integral to dialogic instruction. We offer a noticing framework termed professional noticing of coordinated mathematical thinking that describes how teachers notice group activity in mathematics classrooms. Professional noticing of coordinated mathematical thinking is conceptualized as a bi-dimensional process: noticing groups’ mathematical activity and noticing groups’ coordinated activity. Teachers must become aware of how groups approach the mathematical and collaborative nature of a task, since both of these aspects inform whether learners develop opportunities to learn in groups. The framework describes noticing practices integral to dialogic instruction and promotes inquiry for future research related to teaching moves in dialogic classrooms.     

类比法在“大学数学”教学中的应用

类比方法是用已有的知识和已掌握的技能去解决新问题,从而加深学生对新知识的理解,促进学生对新规律的认识;找出问题、探究问题、解决问题,有助于思想、方法和技巧的开拓与延伸。类比法对提高教学效果和培养学生的创新意识是十分必要的,也是课程改革所倡导的。介绍类比式教学的基本概念,分别大学数学的基础学科和应用学科两类课程来以类比式教学方法的使用情况。运用好类比式教学法将有助于学生加深对数学课程的认识,形成系统全面的知识体系。     

Promoting basic arithmetic competence in early school years–using a response to intervention model

This study investigated whether mathematics education based on a multi-tiered response to intervention (RTI) model can support students' arithmetic competence in primary schools in Sweden. The intent was to identify and support students at risk of failure. In this study, 113 students participated in the intervention, and 30 students participated in the control group. Both groups were followed from Grade 1 to the end of Grade 2 and compared. During the first semester in Grade 1, all students were taught basic addition and subtraction with explicit instructions in Tier 1. Those who did not respond to Tier 1 after one semester were provided support within Tier 2 during the second semester. The same was repeated in grade 2 and the students that did not respond to Tier 2 were supported within Tier 3. At the end of Grade 2, students in the intervention group performed significantly higher on the basic arithmetic competence in the number range 1–9 than the control group. No significant difference was found in a test measuring basic arithmetic competence in the number range 10–19. This study shows that using multi-tiered RTI might be sufficient to identify and support students at risk in early arithmetic competence.     

Middle and high school math teaching for students with mild intellectual disability

The author briefly reviews studies on the math teaching of secondary school students with mild intellectual disabilities. Then, the author demonstrates ways to teach secondary-level mathematics to students with mild intellectual disabilities. In this article, readers will learn about how to use manipulatives, diagrams, and gestures to support students' thinking. Readers will also learn how to make connections between new and challenging math content to students' experiences inside and outside of school to support them as they think through mathematics.     

基于文献计量学的国际基础数学领域作者合作网络分析

系统地统计了基础数学领域10本国际顶级期刊在1981-2011年间发表的所有论文的作者情况,做出了作者合作网络图。并应用社会网络分析方法对最大连通子网络的属性进行了具体分析,对网路的小世界效应、无标度特点、集聚系数等分别进行了计算分析,得到了一些有意义的结论。