Differential effectiveness by gender of instructional methods on achievement in mathematics at tertiary level

In order to investigate the effect of methods of teaching on achievement in mathematics of first year National Certificate of Education (NCE) students in Nigeria, a sample of 165 students comprising 71 males and 94 females, was exposed to three methods of teaching in a second semester basic mathematics course. The three methods were the traditional lecture method, interactive method with individual use of materials and interactive method with group use of materials. Analysis of covariance showed a significant interactive effect of gender and method of teaching on student achievement. Further analysis showed that the use of interactive methods with group use of materials favoured males while interactive method with individual use of materials favoured females. Implications of the results for teaching of tertiary mathematics are discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Differential contribution of specific working memory components to mathematics achievement in 2nd and 3rd graders

The contribution of the three core components of working memory (WM) to the development of mathematical skills in young children is poorly understood. The relation between specific WM components and Numerical Operations, which emphasize computation and fact retrieval, and Mathematical Reasoning, which emphasizes verbal problem solving abilities in 48 2nd and 50 3rd graders was assessed using standardized WM and mathematical achievement measures. For 2nd graders, the central executive and phonological components predicted Mathematical Reasoning skills; whereas the visuo-spatial component predicted both Mathematical Reasoning and Numerical Operations skills in 3rd graders. This pattern suggests that the central executive and phonological loop facilitate performance during early stages of mathematical learning whereas visuo-spatial representations play an increasingly important role during later stages. We propose that these changes reflect a shift from prefrontal to parietal cortical functions during mathematical skill acquisition. Implications for learning and individual differences are discussed.     

The effects of cooperative homework on mathematics achievement of Chinese high school students

This study examined the effects of cooperative homework on mathematics achievement, taking into account team characteristics. Results of analysis of covariance (ANCOVA) showed that three-member teams high in ability (three high achievers or two high achievers plus one middle/low achiever) seem preferable in organizing cooperative learning for mathematics homework. Middle and low achievers all benefited from cooperative mathematics homework, whereas high achievers did not although they still maintained their top position in mathematics achievement.     

Powerful tasks: A contribution to a high level of acting and reflecting in mathematics instruction

Mathematics instruction contains two conflicting demands: on the one hand, the demand for economical efficiency and for well-developed motorways and, on the other hand, the demand that pupils should investigate and discover for themselves and have the freedom to pave their own ways. It is argued that tasks with a certain richness and quality offer some steps towards a constructive handling of this dilemma. The author tries to develop some properties of powerful tasks and to sketch the structure and philosophy of one concrete system of powerful tasks for the concept of angle. The main part of this paper presents seven examples of powerful tasks: five from the system of tasks and two with regard to pupils' working with 2-D-graphic systems. The construction of powerful tasks is viewed as a valuable contribution to bringing the theory and practice of mathematics education closer together.     

高中数学综合题解法探索

高中数学综合题通常具有如下特点:(1)题目本身或解题过程中涉及某个学科的多个知识点,或几个学科的不同知识点;(2)解题过程要应用多种基本的数学方法或解题技能技巧,在培养和考查能力方面提出较高的要求.常见的综合题有单科内的综合,也有跨科的综合.在各层次的练习题和考试题中,综合题常以解答题形式出现,但在选择题、填空题中也不乏具有小巧特色的小型综合题.     

An empirical investigation of differences between mathematics specialists and non-specialists at the high school level in Cyprus: A Logistic regression Approach

AN EMPIRICAL INVESTIGATION OF DIFFERENCES BETWEEN MATHEMATICS SPECIALISTS AND NON-SPECIALISTS AT THE HIGH-SCHOOL LEVEL in Cyprus – The data obtained from high-school seniors for the Third International Mathematics and Science Study (TIMSS) for the country of Cyprus appear to be contradictory. Although Cypriot students did not perform well in mathematics in elementary school, middle school, and in the non-advanced sectors of high school, students in advanced mathematics courses in high school managed to perform exceptionally well. In seeking to account for this apparent disparity, the present study examines the differences between mathematics specialists and non-specialists at the high-school level and discusses the implications that these have for teaching practice. It shows how students educated in an environment that might not be optimal for producing high-achieving students in mathematics and science in elementary and middle school (according to the TIMSS) might nonetheless manage to excel in these fields at the end of their schooling. In conclusion, the authors address the implications of their study for similar educational systems in other developing countries.     

Relationships of some socio-personal factors to mathematics achievement of secondary school and university students in Bophuthatswana

Poor matriculation mathematics results in Bophuthatswana led us to make exploratory efforts to identify possible non-pedagogical factors responsible for such results. Two small scale studies were carried out to examine relationships of socio-personal variables to mathematics achievement. Study 1 looked into the impact of socioeconomic background, school alienation, sex, self-concept and attitude toward mathematics on mathematics performances of secondary school pupils, while study 2 was aimed at examining relationships of dogmatism and mathematics anxiety to mathematics achievement of first-year university students. The data of these two studies invite the attention of mathematics educators to the importance of attitude toward mathematics, mathematics anxiety, and dogmatism in mathematics achievement of Bophuthatswana secondary school and university students.     

初中数学教学生活化,让学生在数学中“享受”数学

初中处于基础教育教学的关键阶段,中学生学习数学课程旨在促进中学生全面、持续、和谐发展。如何发挥数学课程学习的作用,引导初中数学教学向生活化方向发展,让学生在数学中享受数学,这已经是众多数学教师教学所共同探讨的热点话题了。因此,本文指出要紧密联系数学教学本身的特点与教学规律,在充分遵循学生数学学习心理特点的基础上,要采取措施增强初中数学教学的生活化,让学生在数学中享受数学。应立足于学生的生活出与亲身经历,通过数学学习将具体的生活实际问题转换成抽象的数学模型应用,确保数学教学内容、教学过程、教学选择等方面的生活化,从而引导学生从生活问题出发强化对数学教学重难点内容的理解,切实培养和提升中学生的逻辑思维能力、科学的情感态度与正确的价值观。     

Effect of pupil factor on mathematics achievement in cambodian urban primary school

It is generally observed in the literature of school effectiveness research that there are two broadly categorized factors influencing pupil achievement. However, the results of the studies based on empirically collected data vary from country to country and from time to time. Premised on this inconsistency of results and gaps in knowledge of this field in Cambodian education, this study was conducted in order to examine the effect of pupil factor on their mathematics achievement. The data were collected from pupils by means of questionnaires and a mathematics test. After controlling such factors as pupils’ poverty during the research design, the results of the step wise regression analysis showed that pupils’ interest in mathematics was a significantly positive contributor to their performance. Pupils’ absence frequency, gender, grade repetition and preschool attendance had significantly negative effects on their mathematics outcome.     

Representation of space and students' conceptions at high school level

At high school level, the teaching of space geometry makes use of graphical representations of objects. But usually the only function of these figures is to illustrate, they are stereotyped and have no real mathematical status, as a study of textbooks shows. They contain many implicit conventions, of different kinds, which can lead students to misconceptions about geometrical objects if they are not mastered. However they can, at a low educational cost, serve as an efficient tool to be used for problem solving. To achieve this I propose to base such drawings explicitly on parallel projection, a principle which produces representations of various types, often coinciding with the usual figures, close to perceptive images, and on which important properties of the objects represented are retained.     

Combined fluency and cognitive strategies instruction improves mathematics achievement in early elementary school

One hundred and seventy-eight second grade students from two states (Georgia and Massachusetts) participated in an experiment in which they were randomly assigned to either (1) a computer program designed to increase fluency in addition and subtraction, (2) a program designed to improve cognitive strategy use for addition and subtraction, (3) a program that combined the fluency and cognitive strategy instruction programs or (4) a control condition. The intervention consisted of 40 half-hour sessions (2 sessions per week for 20 weeks). Prior to the intervention, and immediately following the intervention, the participants were tested on fluency, cognitive strategy use, and mathematics achievement. ANCOVAs indicated that children in the combined fluency and cognitive strategy use condition significantly improved their mathematics achievement in comparison to the control group. When we examined the impact of the intervention as a function of gender, boys appeared to benefit from the intervention, but girls did not.     

Predictive value of attitude,cognitive ability,and personality to science achievement in the middle school

This article examines the factors of attitude toward science, spatial ability, mathematical ability, and the scientific personality, as measured by the Myers-Briggs Type Indicator, in a sample of middle school students. Males and females with science grades of A and B were found to have several characteristics of the scientific personality, good grades in mathematics, but negative attitudes toward science. Males and females with science grades of C and D had a more positive attitude toward science, but poor mathematical and spatial abilities and few characteristics of the scientific personality. There were no sex differences except on the Thinking/Feeling (TF) scale of the Myers-Briggs Type Indicator. As expected females portrayed themselves as preferring the (F) scale, the use of personal values when making decisions and males portrayed themselves as preferring the (T) scale, the use of logical analysis when making decisions.     

导学案在初中数学教学中应用的调查分析和反思

通过对近10年导学案相关文献的调阅,结合调查问卷,分析了目前导学案研究的现状和存在的问题,从学生角度探讨了对导学案的理解和要求,提出了高效导学案设计和实施的原则,对初中数学使用导学案应该注意的问题进行了反思,提出了自己的认识和建议。     

A multilevel analysis of Japanese middle school student and school socioeconomic status influence on mathematics achievement

The author examined the simultaneous influence of Japanese middle school student and school socioeconomic status (SES) on student math achievement with two-level multilevel analysis models by utilizing the Trends in International Mathematics and Science Study (TIMSS) Japan data sets. The theoretical framework used in this study was Bronfenbrenner’s bioecological theory (Bronfenbrenner and Morris 1998). The data sets contained 4,856 students from 146 public and private middle schools. The results indicated that at the student level, different aspects of student SES (i.e., number of books, the possession of computers, paternal, and maternal educational achievements) were positively related to Japanese student math achievement. At the school level, two aspects of school SES (i.e., less populated schools and economically disadvantaged schools) were negatively related to Japanese student math achievement. None of the cross-level interactions were significant, but the random effect for the computer slope was significant. Although this study found both student and school SES effects on student achievement, the proportional reduction of prediction error explained by both student and school SES were was small, meaning the residual variances at student and school levels did not capture the majority of variance explained by math achievement. The implications of theoretical framework and educational policy are discussed.     

浅谈向量在中学数学中的一些应用

向量是中学数学中重要内容之一。文章通过对“特殊向量”（零向量、单位向量）的应用的研究,以及向量在立体几何、平面解析几何解题中的应用的研究,旨在让学生领会向量既具有独特的丰富内涵,又是一种重要的数学工具。