An exploratory study contrasting high- and low-achieving students' percent word problem solving

This study evaluated whether schema-based instruction (SBI), a promising method for teaching students to represent and solve mathematical word problems, impacted the learning of percent word problems. Of particular interest was the extent that SBI improved high- and low-achieving students' learning and to a lesser degree on the indirect effect of SBI on transfer to novel problems, as compared to a business as usual control condition. Seventy 7th grade students in four classrooms (one high- and one low-achieving class in both the SBI and control conditions) participated in the study. Results indicate a significant treatment by achievement level interaction, such that SBI had a greater impact on high-achieving students' problem solving scores. However, findings did not support transfer effects of SBI for high-achieving students. Implications for improving the problem-solving performance of low achievers are discussed.     

An investigation of 3rd‐grade Taiwanese students’ performance in number sense

The main purpose of this study was to investigate the number sense performance of 3rd‐graders in Taiwan, and to diagnose areas of weakness or deficiency in number sense development. A total of 808 3rd‐graders participated in this study. The results indicated that these students did not perform well on each of the five number sense components (correct rates approx. 34%), and they appeared worst on the performance of “Judging the reasonableness of computational results”. Boys and girls did not show any appreciable difference in their ability to solve number sense problems. The importance of number sense should be highlighted both by teachers and in textbooks and more time and opportunity provided for students to work on this type of exercise at lower grade levels. This would require that “drill and practice” exercises in mathematics should not indeed be over‐ taught, and the teaching of number sense to children should begin as early as possible.     

A Study of the Performance of 5th Graders in Number Sense and its Relationship to Achievement in Mathematics

In order to investigate the performance of number sense and its relationships with mathematics achievement of Taiwanese students who had just completed the 5th-grade mathematics curriculum, a computerized number sense scale has been developed. This number sense scale includes four factors which are recognizing relative number size, using multiple representations of numbers and operations, judging the reasonableness of estimates of computed results and recognizing the relative effect of operations on numbers. A total of 1,212 students in Taiwan participated in this study. The main findings of this study are summarized as follows. First, the students perform best on “recognizing relative number size” and perform worst on “judging the reasonableness of estimates of computed results”. This finding is consistent with previous studies. It shows that students in Taiwan seem quite poor on judging the reasonableness of estimates of computed results. Second, female students, on average, have higher scores on recognizing the relative number size than male students, even though only a small effect size is found. And, third, the achievements of the students in mathematics are significantly correlated with their number sense, as measured by the average grade for the academic year of 5th-grade students.     

Explicit teaching of meta-strategic knowledge in authentic classroom situations

Meta-strategic Knowledge (MSK) is a sub-component of metacognition that is defined in the present study as general, explicit knowledge about thinking strategies. In the present study we shall focus on the control of variables thinking strategy. Following an earlier study (Zohar & Peled 2007) that showed considerable effects of explicit instruction of MSK in laboratory setting, this study explores whether these effects are preserved in authentic classroom situations. Participants were 119 8th grade students from 6 classes of a heterogeneous school. Equal numbers of low-achieving and high-achieving students were randomly assigned into experimental and control groups. The findings showed dramatic developments in students’ strategic and meta-strategic thinking following instruction. The effect of the treatment was preserved in delayed transfer tests. Our findings show that explicit teaching of MSK had a strong effect on low achieving students. The implications of the findings for learning and instruction are discussed.     

Relationships among computational performance,pictorial representation,symbolic representation and number sense of sixth‐grade students in Taiwan

Twenty classes in ten schools with 627 sixth‐grade students in five cities in Taiwan participated in this study. The research provides information on the performance differences among written computation, pictorial representation, symbolic representation and number sense. The results of One‐way ANOVA analysis indicate that significant difference was found among WCT, PRT, SRT and NST tests, with F=536.327, p=0.000. The a posteriori comparisons show for each pair (WCT vs PRT, WCT vs SRT, WCT vs NST, PRT vs SRT and SRT vs NST) significant difference at the 0.001 level (p=0.000), except for the pair comparison between PRT and NST. This implies that these Taiwanese students were highly skilled in written computation but their written skills were not equally transferred to use of non‐computational paths that depended on symbolic representation, pictorial representation and number sense to solve similar problems.     

Self-concept a game changer for academic success for high-achieving Australian Indigenous and non-Indigenous students: Reciprocal effects between self-concept and achievement

Indigenous Australians are highly disadvantaged educationally and on all socioeconomic indicators, but graduating from university largely closes this gap. However, despite clear examples of Indigenous success, little research has focused on the drivers of success of high-achieving Indigenous students to emulate their success. Thus, the explicit purpose of our study is to identify psychological drivers of Indigenous academic success for high-achieving students and compare these to those of high-achieving nonIndigenous students. To accomplish this purpose, we test the reciprocal effects model (REM) of self-concept and achievement for high-achieving Indigenous students (N = 493) and matched nonIndigenous students (N = 586) in primary and secondary schools. Academic achievement and self-concept were reciprocally related over three annual time waves, supporting the REM for high-achieving Indigenous and nonIndigenous students. Furthermore, results were invariant over two within-person facets (time and content-domain—math vs. English) and two between-person facets (Indigenous vs. nonIndigenous, and primary vs. secondary students). The results have important policy/practice implications for the drivers of success for high-achieving Indigenous students, education of high-achieving students more generally, and self-concept theory and research.     

A case study of reading instruction in a Philippine classroom

In this article, we describe the reading practices in a public and high-achieving 6th grade English classroom in the Philippines. By utilizing a four resources model, we discuss the different roles that students assume in this classroom. Students in this class are mainly code breakers and text users and have limited opportunities to assume the other two roles of the four resources model. This case study provides a different view of reading, specifically a view of a culture of reading wherein higher status is given to oral reading performance rather than comprehension. We describe the way a high-achieving 6th grade Philippine classroom perceives reading. Through this article, we would like to contribute to the research literature on Philippine education and increase our knowledge of reading practices as they are conceived and practised in this particular classroom.     

The effectiveness of student team-achievement division (STAD) for teaching high school chemistry in the United Arab Emirates

Education in the United Arab Emirates (UAE) faces major problems which may hinder its future development. These include low achievement in science and a negative attitude toward science subjects, which have resulted in a high number of student dropouts from the science track in high school. It is believed among UAE educators that the main reason is the way science that has been taught in its schools. A solution to this problem depends on finding effective teaching methods, which maintain student achievement, improve students' attitude and provide opportunities to develop essential scientific skills. The effectiveness of Student Team-Achievement Division (STAD) for teaching science to high school classes in the UAE was investigated. The sample was selected randomly. A representative group of UAE high school students was chosen from the northern province, which includes urban areas, and from the eastern province, which includes rural areas. The study involved sixteen tenth grade classes. During the second semester of the academic year 1998/1999, three units in the chemistry curriculum were covered. This study was designed to investigate the effectiveness of STAD in teaching high school chemistry in the UAE and to find out which groups, gender, area, and ability benefitted most.     

9～12岁儿童估算策略选择的发展特点

认知心理学家和数学教育工作者对于估算在人们日常生活中的作用已形成广泛共识.9～12岁儿童估算策略选择的发展特点有:在估算时能选择多种策略,且策略的使用频率不相同,取整使用最频繁,其次是先补偿,转换和分解策略的使用频次最小;随着问题难度的增加,估算策略选择的最佳击中率降低;随着年龄的增长,估算策略选择的个数增加,估算策略选择的最佳击中率上升;估算策略的选择不存在性别差异。     

What fills the gap between discrete and dense? Greek and Flemish students’ understanding of density

It is widely documented that the density property of rational numbers is challenging for students. The framework theory approach to conceptual change places this observation in the more general frame of problems faced by learners in the transition from natural to rational numbers. As students enrich, but do not restructure, their natural number based prior knowledge, certain intermediate states of understanding emerge. This paper presents a study of Greek and Flemish 9th grade students who solved a test about the infinity of numbers in an interval. The Flemish students outperformed the Greek ones. More importantly, the intermediate levels of understanding—where the type of the interval endpoints (i.e., natural numbers, decimals, or fractions) affects students’ judgments—were very similar in both groups. These results point to specific conceptual difficulties involved in the shift from natural to rational numbers and raise some questions regarding instruction in both countries.     

四川灾区青少年心理康复特质的差异性研究

本文在回顾心理康复特质文献的基础上,根据自编的青少年心理康复特质问卷,选取四川省彭州市等各受灾程度不等的中学的650名学生进行施测,以探讨四川灾区中学生心理康复特质的差异。本研究采用SPSS16.0进行数据的分析和处理,并运用相关分析、双因子变异数分析统计方法进行统计,所得结果如下：从不同年级的中学生的平均数来看,初一和初二、高一和高二年级的中学生在乐观与希望、问题求助方式、不安全感、安全感维度以及总问卷上的平均分具有不同程度的差异：（1）初中二年级学生具有的乐观与希望、安全感特质好于其他年级的学生;（2）初中二年级学生整体心理康复状况好于其他年级的学生;（3）高中二年级学生比其他年级学生更善于运用问题求助来帮助自己康复。从不同性别的中学生的平均数来看：（1）男女中学生具有的整体心理康复特质没有显著的差异;（2）在遇到突发事件时,女生比男生表现出更高程度的不安全感;（3）女生比男生更多地用问题求助的方式来帮助自己康复,且女中学生比男中学生更能找到问题解决和求助的途径。     

Learning fractions with and without educational technology: What matters for high-achieving and low-achieving students?

Instructional design research promotes interactive and adaptive scaffolds as features of educational technology. Mathematics education research can guide elaborated fractions curricula to develop basic fraction concepts while challenging the natural number bias. Thus, we developed theory-grounded interactive material for learning fractions providing scaffolds in an eBook. Evaluating both, curriculum and scaffolds, we split 745 high-achieving and 260 low-achieving 6th graders into three groups: Scaffolded Curriculum group (using the eBook on iPads), Curriculum group (using a paper copy of our developed material), and Traditional group (using conventional textbooks). Generalized linear mixed models revealed diverse positive effects on the achievement of students in the experimental conditions: Results showed that high-achieving students did benefit from the curriculum, regardless of whether it was presented with or without scaffolds, while for low-achieving students using scaffolds was decisive. This suggests that interactive and adaptive scaffolds can support students in learning mathematical concepts, especially for low-achieving students.     

Classroom interaction in regular and special education middle primary classrooms in the United Arab Emirates

Samir Dukmak is an assistant professor in the Department of Special Education in the Faculty of Education at the United Arab Emirates University. The research reported in this article investigated the frequency, types of and reasons for student-initiated interactions in both regular and special education classrooms in the United Arab Emirates (UAE). These interactions were studied in relation to various variables, including levels of students' academic achievement, their gender, special educational needs and disability. Teacher-initiated interactions were also examined in the study. Eighteen boys and girls from two regular and two special education classrooms were observed. Various types of interaction were identified among students and the results reveal that boys in all groups initiated more interactions than girls, and that high-achieving boys and girls initiated more interactions than their low-achieving counterparts. The findings also reveal that teachers interacted differently with boys versus girls. The reasons prompting students to initiate classroom interaction are highlighted in this research.     

Stressful Life Events Experienced by Academically High-Achieving Females Before the Onset of Disordered Eating

Research on gifted and high-achieving students has shown that they experience some sources of stress that are different from those experienced by general students. This qualitative case study investigated the types of stressful life events experienced by academically high-achieving females before the onset of disordered eating in adolescence. Fourteen academically high-achieving females who had recovered from disordered eating were interviewed and completed a written survey. The results revealed that these high-achieving females reported stressful events in five areas before the onset of disordered eating symptoms. All participants reported stress related to academic issues, yet academic stress is rarely mentioned in the literature on stress and eating disorders. These findings have implications for both prevention and treatment of eating disorders among academically high-achieving females.     

Number Sense Strategies Used by Pre-Service Teachers in Taiwan

This study examined number sense strategies and misconceptions of 280 Taiwanese pre-service elementary teachers who responded to a series of real-life problems. About one-fifth of the pre-service teachers applied number sense-based strategies (such as using benchmarks appropriately or recognizing the number magnitude) while a majority of pre-service teachers relied on rule-based methods. This finding is consistent with earlier studies in Taiwan that fifth, sixth, and eighth grade students tended to rely heavily on written methods rather than using number sense-based strategies. This study documents that the performance of pre-service elementary teachers on number sense is low. If we want to improve elementary students’ knowledge and use of number sense, then action should be taken to improve the level of their future teachers’ number sense.     

The effects of explicit teaching of metastrategic knowledge on low- and high-achieving students

This study assessed the effects of explicit teaching of metastrategic knowledge (MSK) on gains of low-achieving (LA) and high-achieving (HA) 5th grade students (N = 41). Gains in reasoning scores of students from the Experimental group (compared to students from the control group) were obtained on the strategic and on the metastrategic level. Gains were preserved in near and far transfer tasks immediately after the end of instruction and 3 months later. Explicit teaching of MSK affected both LA and HA students, but it was extremely valuable for LA students who required a longer period than HA students to reach their top score.     

Factors influencing student perceptions of high-school science laboratory environments

Science laboratory learning has been lauded for decades for its role in fostering positive student attitudes about science and developing students’ interest in science and ability to use equipment. An expanding body of research has demonstrated the significant influence of laboratory environment on student learning. Further research has demonstrated differences in student perceptions based on giftedness. To explore the relationship between giftedness and students’ perceptions of their learning environment, we examined students’ perceptions of their laboratory learning environment in biology courses, including courses designated for high-achieving versus regular-achieving students. In addition, to explore the relationship between students’ perceptions and the extent of their experience with laboratory learning in a particular discipline, we examined students’ perceptions of their laboratory learning environment in first-year biology courses versus elective biology courses that require first-year biology as a prerequisite. We found that students in high-achieving courses had a more favourable perception of all aspects of their learning environment when compared with students in regular courses. In addition, student perceptions of their laboratory appeared to be influenced by the extent of their experience in learning science. Perceptions were consistent amongst regular- and high-achieving students regardless of grade level. In addition, perceptions of students in first year and beyond were consistent regardless of grade level. These findings have critical applications in curriculum development as well as in the classroom. Teachers can use student perceptions of their learning environment to emphasize critical pedagogical approaches and modify other areas that enable enhancement of the science laboratory learning environment.     

小学生数感发展规律与特征的实证研究及其启示

数感是人们对数和数的关系的一种感悟,以及运用数字关系和数字模式进行推理与解决问题的能力.小学生数感发展的总体规律是数感发展水平随着年级(年龄)的增长而逐步提高.数感的构成要素包括数的意义、数的表示、数的关系、数的运算、数的估算、数的问题解决.小学生数感的培养过程要经历3个阶段:学习整数、小数、分数等数的概念及其运算规则;用多种方法来表示数;通过代数式、方程等知识的学习,探索数与形及在实际问题中蕴含的数量关系和规律.     

Strategies of Number Sense in Pre-service Secondary Mathematics Teachers

This paper presents some results of an investigation on the number sense of a group of pre-service secondary teachers from Spain. The objective of this research was to analyze students’ use of strategies associated to number sense and compare them with those obtained in a previous study with pre-service primary teachers in Taiwan, (Yang, Reys & Reys, International Journal of Science and Mathematics Education, 7, 383–403, 2009). Pre-service secondary teachers showed lower success than pre-service primary teachers in a number sense test. Nevertheless, these last based their reasoning mainly on rules and algorithms, while pre-service secondary teachers used more strategies of number sense. In an attempt to delve into the low success shown by of Spanish pre-service secondary teachers, some students were interviewed. Those interviews showed that a deeper work on number sense in the training of these students is needed.     

Primary school students’ strategies in early algebra problem solving supported by an online game

In this study we investigated the role of a dynamic online game on students’ early algebra problem solving. In total 253 students from grades 4, 5, and 6 (10–12 years old) used the game at home to solve a sequence of early algebra problems consisting of contextual problems addressing covarying quantities. Special software monitored the students’ online working when solving the problems. Before and after the intervention a paper-and-pencil test on early algebra was administered. The data analysis revealed that the online working contributed to the students’ early algebra performance. There was a significant gain in performance across all grades. The highest effect was found in grade 6. Out of the three strategy profile clusters that could be distinguished in the whole sample, the cluster dominated by using extreme values and the cluster characterized by the trial-and-error strategy were most influential on the gain in early algebra performance. The students’ level of online working, which was defined as a combination of online involvement and strategy use, appeared to have a marginally significant effect on the gain score for the total sample. Per grade there was no significant effect, yet the levels of online working were significantly related to grade. Free playing was mostly performed in grade 4, looking for answers in grade 5, and exploring relations slightly more in grades 5 and 6. About 17 % of the effect of grade on the gain score was mediated by the level of online working.