对日本精英教育的怀旧及其借鉴作用——日本数学家藤田宏教授访谈录

日本数学家、数学教育家藤田宏教授对日本数学精英教育的观点主要有:日本需要真正的精英教育;提倡大众教育的前提下,进行精英教育;从旧制高中教育中体会到成功的教育经验,以传统精神为基础,同时吸收西方现代文明;精英教育应该从文化教育直至研究生院教育;数学教师必须接受精英教育,具备精英教育意识;精英教育不应仅限于大学的数学教师,也适用于中学教育中的数学教师.     

对我国数学认知结构研究的反思

我国数学认知结构二十余年的研究经历了基于认知发展理论的实验研究、理论探索与发展、理论深化与实证研究兴起3个阶段,取得了明显的成绩.但是,研究中还存在着研究起点偏失、理论深度不够、基础问题研究发展缓慢、某些问题无人问津、研究力度分布不均、研究方法有所失当等问题.今后的研究应着力于理论体系的建构与完善、研究内容深度的挖掘与广度的拓展和研究方法的更新与融合这3个方面.     

高中生数学问题解决图示归纳方式的比较研究

类比迁移是进行数学发现和解决数学问题的重要思维方法,是培养数学创造性思维的一个重要途径.学优生更多的是依靠源靶问题的结构性特征,图示归纳的方式是消除性的;学困生往往依赖源靶问题的表面特征,图示归纳的方式是保留性的.数学教学中要加强学生正确运用类比迁移策略的意识,重视帮助学困生形成完善的数学知识网络.     

高师数学系开设数学双语课的调查分析与建议

对开设过数学双语课的任课教师进行访谈,发现:开设数学双语教学课型单一,课程时间安排难以保证;无统一教材,随意选用;开设数学双语教学费时费力,英语化程度不高;教师与学生的英语水平参差不齐;教学评价没有相关标准;数学双语教学属于新生事物,经验较少.建议:今后加大对数学双语课教学的理论与实践研究力度;出版或引进相关的数学双语教学用书;制定数学双语教学的评价标准;进行数学双语师资的培训;把数学双语教学持续开展下去.     

Prior knowledge in mathematics and study success in engineering: informational value of learner data collected from a web-based pre-course

The article describes the development and evaluation of a web-based pre-course in mathematics, delivered to four cohorts of engineering students at a German university. Based on demographic, personal, and learning-related data relationships between students’ preconditions, their learning gains in the pre-course, and study success in the degree programme were analysed. The results support the existing literature in that domain-related prior knowledge and secondary school achievement play a dominant role regarding study success in engineering. The analyses also showed that the influence of cognitive predictors could only be compensated for by a strong learner engagement. At-risk students with high pre-course learning gains showed significantly better first-year performance. The number of self-tests a student attempted was positively related to pre-course learning gains and even to first-year performance, suggesting that this variable is a good indicator of student engagement.     

Improving mathematics results: does teachers’ academic optimism matter? A study of lower secondary schools

Educational effectiveness research has provided evidence about the importance of teacher beliefs and attitudes for teaching and learning. This study builds on the concept of academic optimism, which combines 3 aspects of a teacher’s professional creed: self-efficacy, trust, and academic emphasis. The study explores the functioning of the collective and individual measures of academic optimism in the Czech environment and studies its impact on students’ outcomes. The analyses are based on pilot data from 39 schools, 325 teachers, and 1,316 Grade 9 students and on the data from the Czech Longitudinal Study in Education (CLoSE), covering 163 schools, 1,469 teachers, and 4,798 students. The individual measure was selected for further studies based on 2-level confirmatory factor analysis. Two-level structural equation modelling showed a significant impact of a school’s academic optimism on students’ achievement even after controlling for prior achievement and socioeconomic status at both the student and the school level.     

Programming and Mathematics in an Upper-Level University Problem-Solving Course

We discuss teaching and learning situations that surfaced when computer programming and mathematics were brought together in a course where students write computer code to explore mathematics problems. Combining programming and mathematics creates a rich ecosystem which, on top of traditional mathematics activities (writing solutions, proofs, etc.), offers simulation and experimentation, invites discussions about structure, requires logic and testing strategies, and handles mathematics objects with an added feeling of reality. Focusing on novice and inexperienced programmers, we look for answers to the practice-oriented question, “How do students reason through their difficulties when using programming to explore a mathematics problem?” Following literature review and methodology, we build the programming model, which we use to study students' experiences as they approach a mathematical problem by writing computer code. Our research is based on analyzing students' in-class work and class notes, author's observations of students working on their computers, and his interactions with students in class and elsewhere. In the four case studies that we present we touch upon students' difficulties in working with complex conditional statements and recurrence relations. As well, we discuss cases where resolving a programming issue demands posing and answering mathematical questions.     

Attending to Precision: Mathematical Definitions in Courses for Pre-Service and Practicing Teachers

In this article we address the Common Core State Standard for Mathematical Practice: Attend to Precision. We describe work in mathematics content courses for pre-service and inservice teachers focused on developing teachers’ understanding of mathematical definitions. We discuss teachers’ work in developing definitions for students at various levels of mathematics, in generalizing a definition in order to extend the domain to which it may be applied, and in correcting teachers’ misconceptions. The work discussed in this article is consistent with the recommendations of the Conference Board of the Mathematical Sciences for the mathematics education of teachers. In explicit response to contemporary mathematics education research, the author presents constructive assessment prompts which lend themselves to formal study by mathematics education researchers.     

An example of the use of dynamic mathematics software to create problem-solving environments that serve multiple purposes

Problem-solving is regarded as a major component of mathematical performance, and well-designed problem-solving-based learning environments have the potential to assist students in developing a meaningful understanding of mathematical concepts and procedures. In this respect, given its various features, dynamic mathematics software has been regarded by mathematics educators as a promising tool for designing such environments. This study presents an example of the use of technology to create a dynamic learning environment through a discussion of the pedagogical value of a problem selected for an activity, followed by the implementation sequence of the problem-solving activity in the classroom. The students’ experiences during the implementation of the activity are also discussed; and finally, an additional version of the problem is recommended for use in the classroom.     

A microworld-based role-playing game development approach to engaging students in interactive,enjoyable, and effective mathematics learning

In traditional teacher-centered mathematics instruction, students might show low learning motivation owing to the lack of applied contexts. Game-based learning has been recognized as a potential approach to addressing this issue; however, without proper alignment between the gaming and math-applied contexts, the benefits of game-based learning could be limited. Therefore, this study aims to develop a microworld-based educational game, which provides simulated contexts encouraging students to explore, discover, and solve practical problems using the mathematics knowledge gained in the class. A quasi-experimental design was implemented in the learning activity of the “Speedy World” unit in an elementary school mathematics course to examine the effectiveness of the proposed approach. A total of 107 sixth graders participated in the experiment. The experimental results showed that the students who learned with the microworld-based gaming approach had better learning achievement and motivation in the mathematics course than those who learned with the conventional technology-enhanced learning approach. In addition, the students also showed that they highly accepted the microworld-based game for learning mathematics. The findings of this study provide good evidence for the importance and necessity of associating authentic applied contexts with gaming contexts in developing computer educational games for mathematics.