The Effects of Self-Regulation,Motivation, Anxiety,and Attributions on Mathematics Achievement for Fifth and Sixth Grade Students

For this quantitative study, a total of n = 761 students (58.1% female) from selected fifth- and sixth-grade mathematics classrooms in Alabama were surveyed in order to investigate the relationships between self-regulated learning, motivation, anxiety, attributions and achievement in mathematics. Data analyses revealed that significant contributions are made by motivation and anxiety on both test score and mathematics grade for fifth grade students. Specific factors (e.g., self-efficacy, worry, other, and failure) were related to academic performance while failure attribution was significantly related to mathematics grade. As for sixth grade students, data analyses showed relationships exist between motivation, anxiety and academic performance with specific factors (i.e., self-efficacy, intrinsic value, and worry) significantly predicting both test score and mathematics grade for sixth graders. The findings underlie the importance of motivation and anxiety for students and how these constructs interact to facilitate self-regulation over the course of developing expertise in a domain, such as mathematics.     

Productive and ineffective efforts: how student effort in high school mathematics relates to college calculus success

Relativizing the popular belief that student effort is the key to success, this article finds that effort in the most advanced mathematics course in US high schools is not consistently associated with college calculus performance. We distinguish two types of student effort: productive and ineffective efforts. Whereas the former carries the commonly expected benefits, the latter is associated with negative consequences. Time spent reading the course text in US high schools was negatively related to college calculus performance. Daily study time, however, was found to be either a productive or an ineffective effort, depending on the level of high school mathematics course and the student's performance in it.     

Assessing Logo programming among Jordanian seventh grade students through turtle geometry

The present study is concerned with assessing Logo programming experiences among seventh grade students. A formal multiple-choice test and five performance tasks were used to collect data. The results provided that students’ performance was better than the expected score by the probabilistic laws, and a very low correlation between their Logo programming performance and school mathematics achievement was revealed. Most of the made misconceptions were due to geometrical aspects rather than Logo primitives, and were concentrated on the angle of rotation, the angle of complete rotation and the angle of regular polygon. In addition, students’ problem-solving ability was limited while conducting some Logo programming tasks, and acceptable in others. In regard to the results, it is recommended that teaching Logo programming should be used in different contexts that enhance students’ learning, and develop problem-solving processes.     

独立学院大学数学课程体系改革与实践

以华中科技大学文华学院为例,介绍了通过开设选修课、改革大学数学教学内容、改革大学数学教学方法等方式,对大学数学课程进行教学改革的一些做法和体会.通过这些改革,提高了学生学习大学数学的积极性,取得了一定的成效.     

The relationship between mathematical problem-solving skills and self-regulated learning through homework behaviours,motivation, and metacognition

Studies highlight that using appropriate strategies during problem solving is important to improve problem-solving skills and draw attention to the fact that using these skills is an important part of students’ self-regulated learning ability. Studies on this matter view the self-regulated learning ability as key to improving problem-solving skills. The aim of this study is to investigate the relationship between mathematical problem-solving skills and the three dimensions of self-regulated learning (motivation, metacognition, and behaviour), and whether this relationship is of a predictive nature. The sample of this study consists of 323 students from two public secondary schools in Istanbul. In this study, the mathematics homework behaviour scale was administered to measure students’ homework behaviours. For metacognition measurements, the mathematics metacognition skills test for students was administered to measure offline mathematical metacognitive skills, and the metacognitive experience scale was used to measure the online mathematical metacognitive experience. The internal and external motivational scales used in the Programme for International Student Assessment (PISA) test were administered to measure motivation. A hierarchic regression analysis was conducted to determine the relationship between the dependent and independent variables in the study. Based on the findings, a model was formed in which 24% of the total variance in students’ mathematical problem-solving skills is explained by the three sub-dimensions of the self-regulated learning model: internal motivation (13%), willingness to do homework (7%), and post-problem retrospective metacognitive experience (4%).     

Integrating design problems in mathematics curriculum: an architecture college case study

This paper reports an attempt to improve results in the mathematics course in one of the architecture colleges in Israel through practise in applications. The effect of integrating structure design problems in the calculus curriculum on students' achievements and attitudes was examined. The applied topics in the curriculum were connected to calculus topics and studied through problembased learning activities. The integrated curriculum was implemented and the learning results in experimental and control groups were assessed by means of achievement tests, attitude questionnaires and student interviews. The learning achievements in the experimental group proved to be significantly higher than in the control group. The positive impact of learning applications on motivation, understanding, creativity and interest in mathematics is indicated.     

Mathematics in the home: Homework practices and mother-child interactions doing mathematics

Parents are a largely untapped resource for improving the mathematics performance of American children, which lags behind the performance of children from other nations. The purpose of the research reported here was to assess homework practices in the home, and to examine interactions between mothers and their 5th grade children as they worked challenging mathematics problems (pre-algebra equivalence problems). Results indicated that children spent on average 23 min per day on mathematics homework, with an average of 8 min of help from parents. Videotapes of mother-child interactions indicated that mothers varied considerably in the quality of the mathematics content that they conveyed while teaching, and in the quality of their scaffolding of the material for the child. As expected, mothers who themselves had more mathematics preparation performed better in conveying mathematical content and in scaffolding. Mothers with more mathematics self-confidence also performed better. The results suggest that children face inequities in the parental resources available to them for math learning; these inequities might be remedied by school-family partnership programs.     

Enriching Science and Math Through Engineering

This case study reviewed the collaborative efforts of university engineers, teacher educators, and middle school teachers to advance sixth‐ and seventh‐grade students' learning through a series of project‐based engineering activities. This two‐year project enriched regular school curricula by introducing real‐world applications of science and mathematics concepts that expanded opportunities for creativity and problem‐solving, introduced problem‐based learning, and provided after‐school programming (for girls only) led by engineering students from the local university. This engineering education initiative showed significant impact on students' (1) confidence in science and mathematics; (2) effort toward science and mathematics; (3) awareness of engineering; and (4) interest in engineering as a potential career. With regard to gender, there were no significant differences between boys' and girls' responses. The girls' confidence in their own skills and potential, however, was significantly more positive than the boys' confidence in the girls. These results gave rise to new questions regarding mentor/mentee relationships and the overall effect of “girls only” mentoring.     

A Multi‐Method Investigation of Mathematics Motivation for Elementary Age Students

This paper presents the results of a multi‐method study examining elementary students with high self‐reported levels of mathematics motivation. Second‐ through fifth‐grade students at a Title One school in the southeastern United States completed the Elementary Mathematics Motivation Instrument (EMMI), which examines levels of mathematics motivation across three subscales: (a) Math Anxiety, (b) Self‐Efficacy, and (c) Value of Math. Results from this quantitative phase were used to identify a sample for a qualitative phase examining how students who report high levels of motivation perceive mathematics. The resulting qualitative phase utilized a phenomenological design to explore mathematics motivation for a particular set of students in a fifth‐grade setting. Findings indicate that elementary students with high mathematics motivation value mathematics as a present and future oriented discipline and value teachers that deemphasize testing as a measure of success.     

问题驱动 多元表征的概念教学探究——对偶线性规划教学案例设计

数学与应用数学(师范)专业中的《运筹学》具有跨学科、实践性的课程特点,目标在于培养职前教师用数学方法解决实际问题的能力.结合义务教育阶段新课程标准中"四基"的提出这一背景,本文将以线性规划部分(运筹数学)对偶线性规划概念的引入这一知识模块为例,探讨通过问题串形式进行问题驱动、多元表征的概念教学过程.即遵循问题驱动—兴趣驱动—问题意识发展—提出和解决新问题,依据数学与外部联系、数学内部联系两条主线设计教学和学习,探索如何通过问题驱动、多元表征的结构化教学过程引导学生的学习方式发生改变,增强探究学习的动机,发展问题解决能力.课堂教学实践证明效果优于以往单一的讲授式教学法,一定程度上提高了学生的学业成绩、应用问题的兴趣和问题解决意识.     

高等数学教学现状调查分析

高等学校扩大招生后,非数学专业的数学教育面临很多问题,大部分人把这些问题归结为学生质量的下降造成的,这是不公正的.教学过程是一个系统的过程,从对1995级和2005级同一份高等数学(下册)试卷的考试情况进行分析,虽然可以显现出学生的差异,但这些差异不全是学生的质量的问题,应该与教学环境、教学要求、教学方法、师资条件以及社会发展环境等相关联,同时与学生的学习兴趣、学习能力是密不可分的.调查分析这些因素对当代学生的学习和数学教学的影响程度到底有多大,是有效提高大学数学教学质量的前提.     

Extracting factors for students’ motivation in studying mathematics

The purpose of this article is to identify factors that statistically explain the variation and the measures on the level of motivation of a sample of mathematics students in a university. Specifically, this analysis will identify groups of similar items and reduce the number of variables used in a study. This article explains the use of exploratory factor analysis in extracting factors of personal belief and motivational factors among students in learning mathematics. The adaptation of these factors can be used for assessing academic performance in relation to motivation level. By identifying these factors, the mathematics educators or researchers will be able to find ways to improve the condition of the factors and also to further investigate the factors based on confirmatory approaches.     

Three modes of STEM integration for middle school mathematics teachers

Of the four subjects in an integrated science, technology, engineering, and mathematics (STEM) approach, mathematics has not received enough focus. This could be in part because mathematics teachers may be apprehensive or unsure about how to implement integrated STEM education in their classrooms. There are benefits to integrated STEM in a mathematics classroom though, including increased motivation, interest, and achievement for students. This article discusses three methods that middle school mathematics teachers can utilize to integrate STEM subjects. By focusing on open‐ended problems through engineering design challenges, mathematical modeling, and mathematics integrated with technology middle school students are more likely to see mathematics as relevant and valuable. Important considerations are discussed as well as recent research with these approaches.     

An evaluation of the Supplemental Instruction programme in a first year calculus course

Supplemental Instruction (SI) incorporates collaborative learning in small, peer-led, group settings in order to integrate instruction in learning and reasoning skills with course content. Several meta-analyses speak to the efficacy of SI but fail to address selection bias due to ability/motivation and gender. In this study, SI was paired with a first year calculus for non-majors course. An ANCOVA indicated that: ability/motivation, as measured by prior grade point average, was a useful predictor of course letter grade; gender differences were statistically significant but trivial; and, SI participation was statistically and practically significant, a 1.8 letter grade improvement after correction for selection bias. For the pass/fail analysis, a sequential binary logistic regression indicated there was a sizable statistically significant improvement with SI participation after accounting for gender and ability/motivation selection biases. The odds of success were 2.7 times greater for the SI participants. No gender differences of any significance were found.     

Developing Middle School Students' Interests in STEM via Summer Learning Experiences: See Blue STEM Camp

It is a well‐known fact that, in general, many students have a lack of interest and proficiency in mathematics and science. Therefore, it is imperative that we prepare and inspire all students, specifically students of underrepresented populations, to learn science, technology, engineering, and mathematics (STEM) content. Now in its fourth year, See Blue STEM Camp was created in order to expose middle‐level students to a variety of STEM fields and STEM professionals through hands‐on project‐based learning experiences in order to increase their interest in STEM. This paper describes the structure and the activities of the camp. In this innovative project, we utilized an embedded mixed methods study design to investigate the extent middle level students' attitudes, perceptions, and interest in and toward STEM fields and careers changed after participating in an informal learning environment of a five‐day day camp held on the campus of a major university in the mid‐south. The results revealed an increase in their motivation and interest in STEM fields; in fact, there was 3% increase from pre to post in interest in STEM careers. The data also revealed that a majority of the participating middle school students found the STEM content sessions “fun” and engaging, specifically citing the hands‐on experiences they received.     

Chinese and English Mathematics Language: The Relation Between Linguistic Clarity and Mathematics Performance

In Study 1, 48 judges rated the clarity of Chinese, English, and "Chinglish" (Chinese words translated into English) mathematical words-for example, the Chinglish version of the Chinese word for quadrilateral is "four-side-shape." Native Chinese-speaking judges achieve greater agreement on the relative clarity of Chinese words than do native English-speaking judges on the relative clarity of English words. More Chinese words are rated clear than are English. Chinglish mathematical words tend to be rated more clear than English. The inherent compound word structure of the Chinese language seems well suited to portray mathematical ideas.

In Study 2, we examined the relations among the clarity of Chinese mathematical terms, U.S. urban junior high school students' Chinese reading ability, and their mathematics performance. There is a strong correlation between Chinese reading ability and performance on test items with mathematics words rated clear by Chinese judges. The relative clarity of mathematical terms in the Chinese language may contribute to Chinese-speaking students' understanding of mathematics and to superior mathematics performance.     

Mathematics achievement and interest in mathematics from a differential perspective

In this article, we present results of an empirical study with 500 German students of grades 7 and 8. The study focussed on students' mathematics achievement and their interest in mathematics as well as on the relation between these two constructs. In particular, the results show that the development of an individual student's achievement between grade 7 and grade 8 depends on the achievement level of the specific classroom and therefore on the specific mathematics instruction Interest in mathematics could be regarded a predictor for mathematics achievement Moreover, our findings suggest that the students show hardly any fear of mathematics independent of their achievement level.     

Digital game‐based learning for K–12 mathematics education: A meta‐analysis

Digital games (e.g., video games or computer games) have been reported as an effective educational method that can improve students' motivation and performance in mathematics education. This meta‐analysis study (a) investigates the current trend of digital game‐based learning (DGBL) by reviewing the research studies on the use of DGBL for mathematics learning, (b) examines the overall effect size of DGBL on K‐12 students' achievement in mathematics learning, and (c) discusses future directions for DGBL research in the context of mathematics learning. In total, 296 studies were collected for the review, but of those studies, only 33 research studies were identified as empirical studies and systematically analyzed to investigate the current research trends. In addition, due to insufficient statistical data, only 17 out of the 33 studies were analyzed to calculate the overall effect size of digital games on mathematics education. This study will contribute to the research community by analyzing recent trends in significant DGBL research, especially for those who are interested in using DGBL for mathematics education.     

Chinese and English Mathematics Language: The Relation Between Linguistic Clarity and Mathematics Performance

In Study 1, 48 judges rated the clarity of Chinese, English, and “Chinglish” (Chinese words translated into English) mathematical words-for example, the Chinglish version of the Chinese word for quadrilateral is “four-side-shape.” Native Chinese-speaking judges achieve greater agreement on the relative clarity of Chinese words than do native English-speaking judges on the relative clarity of English words. More Chinese words are rated clear than are English. Chinglish mathematical words tend to be rated more clear than English. The inherent compound word structure of the Chinese language seems well suited to portray mathematical ideas.

In Study 2, we examined the relations among the clarity of Chinese mathematical terms, U.S. urban junior high school students' Chinese reading ability, and their mathematics performance. There is a strong correlation between Chinese reading ability and performance on test items with mathematics words rated clear by Chinese judges. The relative clarity of mathematical terms in the Chinese language may contribute to Chinese-speaking students' understanding of mathematics and to superior mathematics performance.