The mathematical vitality of secondary mathematics graduates and prospective teachers: A comparative study

This article links two areas of contemporary interest in mathematics education. These are respectively; mathematical characteristics of prospective teachers, and the notion of levels of understanding.The study reported here considered questions relating to the mathematical appreciation of successful students at both senior secondary (university entrance) and tertiary level. The tertiary students were graduates embarking upon a post-graduate course of teacher-training.It was found that response patterns were stable across a variety of institutions, geographical regions (Australian States), and education systems. Mathematical malfunctions present among secondary graduates were found to exist in substantially the same proportions among the graduate teacher trainees. It was found that the type of understanding sought in this study was not enhanced merely by taking more mathematics courses. The problem of recycling of attitudes and mathematical misconceptions within the secondary teaching structure is addressed, and the question of the approach to the study of mathematics at both secondary and tertiary level is raised as a matter of continuing concern.     

海峡两岸媒介素养教育之比较与启示

信息社会的发展凸显了全球性媒介素养教育的重要性与紧迫性。台湾媒介素养教育起步较晚而成效卓著,目前两岸媒介素养教育无论是在研究方法、教育主体和教育手段方面均有明显差异,台湾媒介素养教育的经验,对大陆媒介素养教育的理论研究和实践开展有一定借鉴意义。     

Learning mathematics and learning to teach: Learning cycles in mathematics teacher education

The reconceptualization of mathematics teacher education based on current mathematics education reform efforts necessitates the elaboration of theoretical frameworks to guide both the practice of and research on teacher education. The author presents a framework which has been useful in shaping two major mathematics teacher education research and development projects. This framework for mathematics teacher learning builds recursively on a framework for mathematics learning which derives from a social constructivist view of learning and incorporates aspects of French didactical theory using the organizing structure of the Karplus Learning Cycle. The framework can be used to think about the content and organization of a particular lesson or of an entire course or program for teachers. Further, it describes the interconnection between different domains of teacher knowledge.     

优差生数学解题认知活动特征的比较研究

运用口语报告技术对优生和差生解同一数学题认知活动的差异进行分析,研究结果表明：优差生数学解题认知活动的差异主要有：数学解题策略运用水平存在差异;在推理过程的缩短性、可逆性和完整性上存在差异;在对问题的表征,特别在心理表征方面存在差异;在对数学材料的记忆方面存在差异;在自我控制技能上存在差异,等等。     

小学数学课堂对话的特点:对专家教师与非专家教师的比较

Using classroom observation and video recording methods, we performed a comparative study on the forms and content of dialogues in the classrooms between expert and novice teachers. Of the 55 lessons surveyed, it was found that expert teachers tend to use analytical and comparative questions more frequently to detect students’ mathematical reasoning. Students and teachers work together to determine the answer to a question and the dialogue in the classroom takes place in a way that students present an answer, the teacher and the other students question the answer, and then the students explain the answer. On the other hand, a novice teacher often tends to give students hints, or utilize simple questions to jog the memory. The novice teacher recognizes students’ logic but does not incorporate them into his/her teaching. In this case, the teacher becomes the sole judge for the appropriateness of the answers and the typical dialogue in the classroom occurs in a way that the teacher asks a question, students answer, and the teacher comments.     

Learning from television and books: A dutch replication study based on salomon's model

According to Salomon's (1981) model, children usually invest less effort in television viewing than in book reading, with the result that information from television is less deeply processed than information from books. The amount of invested mental effort, in its turn, is assumed to depend on the way a medium is perceived. Most children perceive television as an easy medium and books as a difficult one. In this article, Salomon's model and the research in which the model was tested are discussed, and a replication study is presented. The study determines the internal structure of the Dutch versions of Salomon's instruments and tests some predictions following from the model. Unlike their American peers, Dutch children do not unconditionally perceive television as an easy medium.     

体验式学习、“翻转”课堂与MOOC比较研究

"翻转"课堂与MOOC(大规模网络开放课程)都是随着科技进步和教育理念变革产物,它们对传统的教育模式与学习模式都产生了巨大影响。体验式教学也是近些年被广泛应用的教学模式,本论文通过比较这三者的区别与联系旨在探讨它们所具有共通的教育理念以及应用范围。     

Learning from instruction: the case of mathematics

Starting from a brief analysis of adaptive competence in mathematics, this article describes a series of research-based characteristics of the kind of learning processes that should be elicited in students to facilitate and support in them the progressive acquisition of such competence. Four major characteristics are discussed in some detail: learning is constructive, self-regulated, situated or contextual, and collaborative. A rather new approach to transfer of learning is then presented in which transfer is conceived as the preparation for future learning. Throughout the article it is argued that, notwithstanding the progress made in research on learning from instruction, numerous and complex issues and problems remain for continued inquiry.     

Learning for mathematical insight: a longitudinal comparative study on modelling

This paper reports on a longitudinal study of teaching and learning the subject of fractions in two matched groups of ten 9–10-year-old students. In the experimental group fractions are introduced using the bar and the number line as (mental) models, in the control group the subject is introduced by fair sharing and the circle-model. In the experimental group students are invited to discuss, in the control group students work individually. The groups are compared on several occasions during one year. After one year, the experimental students show more proficiency in fractions than those in the control group.     

Sources of self-efficacy in mathematics: A validation study

The purpose of this study was to develop and validate items with which to assess A. Bandura’s (1997) theorized sources of self-efficacy among middle school mathematics students. Results from Phase 1 (N = 1111) were used to develop and refine items for subsequent use. In Phase 2 of the study (N = 824), a 39-item, four-factor exploratory model fit best. Items were revised to strengthen psychometric properties. In Phase 3 (N = 803), a 24-item, four-factor confirmatory factor model fit best. This final model was invariant across gender and ethnicity. Subscales correlated with self-efficacy, self-concept, mastery goals, and optimism. Results suggest that the sources scale is psychometrically sound and could be adapted for use in other domains.     

Learning mathematics in a second language: A problem with more and less

An investigation into the development of the understanding of the relational terms more and less when used in a mathematical setting is described for two distinet groups of children. The first is a group of Papua New Guinean children attending government schools in Papua New Guinea; English isthe second language for these children. The second is a group of expatriate children attending international primary schools in Papua New Guinea. English is the first language for these children. The language of instruction in both school systems is English. In all, 376 Papua New Guinean children in grades 2, 4, 6, 8 and 10, and 255 expatriate children in grades 2, 4, and 6 were given a test in which the words more and less were used in different contexts. Although analysis of errors suggested that Papua New Guinean and expatriate children tended to make qualitatively similar errors, substantial differences were found in the grade levels by which class mastery of a given meaning could be assumed, with the Papua New Guinean children lagging from 2 to 4 years behind their expatriate contemporaties. This difference appears to have serious educational implications for the learning of elementary mathematics in Papua New Guinea.     

A case study on mathematics anxiety for mathematics of finance course

The DIIA （Diploma in Investment Analysis） students from the FBM （Faculty of Business Management） were required to undertake several MOF （Mathematic of Finance） courses. The passing rates for all of the MOF courses were good except for one course. There are many factors for this low passing rate phenomenon for this particular MOF course. One of the factors is mathematics anxiety as suggested by Richardson in 1971. As a result, this paper is carried out in order to measure the undergraduates＇ level of mathematics anxiety in general and between genders in this one particular course. The outcome is expected to fill in the gap as study of anxiety in MOF is still lacking. A 30-item MARS （Mathematics Anxiety Rating Scale） is adapted and used in this study, because this course is predominant by complex computations. The Ss （samples） of the study are 119 students who undertook this MOF course during the study semester of December 2008 to April 2009 in UiTM （Universiti Teknologi MARA）. It is expected that the findings will show that the Ss have a considerably high mean for mathematics anxiety; and female students have a higher mean of mathematics anxiety as compared to their male counterparts. The study confirms the expectation of the researchers. In terms of the final and overall results, it was expected that the passing percentage be dominated by the male students. However, at the end of the study, the overall performance of the female students was much better compared to their male counterparts.     

Dialogue in the elementary school mathematics classroom: A comparative study between expert and novice teacher

Using classroom observation and video recording methods, we performed a comparative study on the forms and content of dialogues in the classrooms between expert and novice teachers. Of the 55 lessons surveyed, it was found that expert teachers tend to use analytical and comparative questions more frequently to detect students’ mathematical reasoning. Students and teachers work together to determine the answer to a question and the dialogue in the classroom takes place in a way that students present an answer, the teacher and the other students question the answer, and then the students explain the answer. On the other hand, a novice teacher often tends to give students hints, or utilize simple questions to jog the memory. The novice teacher recognizes students’ logic but does not incorporate them into his/her teaching. In this case, the teacher becomes the sole judge for the appropriateness of the answers and the typical dialogue in the classroom occurs in a way that the teacher asks a question, students answer, and the teacher comments.     

A meta-analysis of comparative studies on Chinese and US students’ mathematics performance: Implications for mathematics education reform and research

US and China are reforming mathematics teaching by shifting from students’ attainment of facts and procedures toward development of competencies in reasoning, communication, connections, and problem solving, and application of these in real life contexts. Differences in students’ overall performance, curricula, and teachers’ knowledge and instruction between US and Eastern Asian countries are often used to support US reform with two obvious limitations. First, their performance has not been delineated into specific areas which raise questions about whether overall higher Asian mathematics performance over US is also evident in the specific US reform competencies. Second, Asians are often used as an indiscriminate group with inattention to different schooling and non-schooling factors between countries that might contribute differently to performances. This meta-analysis examines US and Chinese student mathematics performance studies and identifies the strengths and weaknesses in overall and specific competencies. It raises questions about theoretical assumptions, discusses limitations of research designs, and proposes research that may lead to a critical understanding of the quality of mathematics learning.     

Bilingual language proficiency: A comparative study

International Review of Education -     

开放性数学教育实验研究

开放性数学教育以传统数学教育的封闭性为切入口和突破口，坚持开放教育的理念，贯彻全面开放的目标，以学习者为中心，给予学生学习的主动权。经过四年的实验研究，通过主导开放，主体开放，信息开放，方式方法、时空环境开放等措施，取得了一定的成绩。     

A comparative study of children's concentration performance on picture books: age,gender, and media forms

The reading development of children depends on various sensory stimuli, which help them construct reading contexts and facilitate active learning and exploration. This study uses sensory stimuli provided by picture books using various forms of media to improve children's concentration performance. We employ picture books using four forms of media: conventional picture books, pop-up books, talking books, and e-books. Children in young (Grade 3) and senior elementary school students (Grade 6) are recruited as participants. The NeuroSky MindBand (electroencephalogram) is used as a tool to measure children's concentration. The results indicate that children in Grade 3 express higher concentration and interest than children in Grade 6 in picture books, and the effect of gender is greater than that of grade on the level of concentration invested in the picture book media form and exhibits a significant interaction and effects on children's concentration performance. As a result, we suggest that talking books or e-books, which provide multisensory stimuli, should be selected for elementary school boys. In addition, talking books should be selected for girls in young elementary school students, while conventional books should be used for girls in senior elementary school students to avoid distraction caused by excessive media stimuli.