A comparison of public and private schools in Spain using robust nonparametric frontier methods

This paper uses an innovative approach to evaluate educational performance of Spanish students in PISA 2009. Our purpose is to decompose their overall inefficiency between different components with a special focus on studying the differences between public and state subsidized private schools. We use a technique inspired by the non-parametric free disposal hull and the application of robust order-\(m\) models, which allow us to mitigate the influence of outliers and the curse of dimensionality. Subsequently, we adopt a metafrontier framework to assess each student relative to the own group best practice frontier (students in the same school) and to different frontiers constructed from the best practices of different types of schools. The results show that state-subsidised private schools outperform public schools, although the differences between them are significantly reduced once we control for the type of students enrolled in both type of centres.     

A Case Study of the Effectiveness of Teacher Experience in the Use of Explanation‐Based Assessment in High School Physics

This article reports on the results of a study involving an innovative assessment program initiated to investigate student predictions and revised explanations regarding a variety of optical phenomena. The assessments were administered via videotape to two classes of high school physics students from different high schools. Two high school teachers with similar educational and teaching backgrounds administered the tapes to the two groups of students. The school environments and the ability levels of the two student groups were similar. The students of the teacher with greater experience with this new form of assessment provided considerably more substantive explanations to the phenomena presented on the videos. The results of the case study suggest that the introduction of new forms of assessment in science education, although desirable, will require significant reordering of the goals and strategies of science teaching.     

The Cumulative and Residual Impact of a Systemic Reform Program on Teacher Change and Student Learning of Science

This longitudinal, five‐year study of teachers and students who had participated in a systemic reform program in science explored if (1) teacher change in practice realized during a three‐year program is sustained one, two, and three years following the program, (2) student performance on state science assessments two years following studying with teachers at this school still demonstrated significant differences from students who attended the control school, and (3) student performance continued to be enhanced for both White and Minority students. Student achievement was assessed using the Discovery Inquiry Test in Science during sixth through eighth grades and the Ohio Graduation Test was used in 10th grade. The same students completed the test in grades 6–8 and 10th grade. Students from the Program school significantly outperformed students who attended the control school on the 10th grade state assessment in science. Findings in this study revealed the ability for sustained, whole‐school, professional development programs to have a cumulative and residual impact on teacher change and student learning of science.     

What Factors Affect Attitudes Toward Women in Science Held by High School Biology Students?

To achieve the goal of science for all Americans, students of both genders must believe that careers in science are equally appropriate for women. Yet male and female students in high school science classes do not have the same views of women in science. This study investigated the influence of 17 factors on high school students' attitudes toward women in science. Data were collected from 844 students enrolled in biology classes in an urban school district in Georgia. Multiple regression determined that the 17 factors significantly influence students' attitudes toward women in science, accounting for 28% of common variance. The four most significant factors - student gender, science ability, level of education the student plans to complete, and career interest-accounted for 24.6% of total variance. Female students who have high science ability, plan to complete high levels of education, and who have career interests in science showed more favorable attitudes toward women in science. Males with low science ability, low levels of education they plan to complete, and no interest in science as a career had the least favorable attitudes toward women in science. Male students with less positive attitudes toward science careers for women need to be included in programs aimed at encouraging all students to consider science careers.     

普通高中教育投入绩效评估实证研究——基于江门市47所高中调查的多层数据

基于江门市47所高中调查的多层数据,运用多层统计分析模型,进行普通高中教育投入绩效评估的实证研究,结果表明:中考成绩与学校绩效之间呈负相关态势;高考成绩最重要的决定因素是学生先前的知识储备和起始能力水平;教育经费投入对高考成绩有显著正影响;学校师资质量对提高学生学业成就有正影响;在47所学校中,有18所学校教育绩效较好,有27所学校教育绩效还有待进一步提高,相应的教育资源的配置需要进一步优化等,并提出相应的政策建议.     

Development and Analysis of a Mathematics Aptitude Test for Gifted Elementary School Students

This paper describes the development and preliminary analysis of a mathematical test targeted for high mathematical ability elementary school students, the Stanford Education Program for Gifted Youth (EPGY) Mathematical Aptitude Test (SEMAT). A version was administered to 248 students, 9–11 years old, in EPGY. The SEMAT was developed because no other satisfactory test was designed or normed for this population. Most standardized tests assess mathematics proficiency for the general population so that gifted students' scores cluster in the few top percentiles. The SEMAT discriminated among this extreme upper end. Item response theory determined proficiency estimates, which were then used as scores to predict various outcomes in EPGY. The SEMAT proved to be a strong predictor of acceleration in EPGY.     

Factors contributing to academic achievement: a Bayesian structure equation modelling study

In Iran, high school graduates enter university after taking a very difficult entrance exam called the Konkoor. Therefore, only the top-performing students are admitted by universities to continue their bachelor's education in statistics. Surprisingly, statistically, most of such students fall into the following categories: (1) do not succeed in their education despite their excellent performance on the Konkoor and in high school; (2) graduate with a grade point average (GPA) that is considerably lower than their high school GPA; (3) continue their master's education in majors other than statistics and (4) try to find jobs unrelated to statistics. This article employs the well-known and powerful statistical technique, the Bayesian structural equation modelling (SEM), to study the academic success of recent graduates who have studied statistics at Shahid Beheshti University in Iran. This research: (i) considered academic success as a latent variable, which was measured by GPA and other academic success (see below) of students in the target population; (ii) employed the Bayesian SEM, which works properly for small sample sizes and ordinal variables; (iii), which is taken from the literature, developed five main factors that affected academic success and (iv) considered several standard psychological tests and measured characteristics such as ‘self-esteem’ and ‘anxiety’. We then study the impact of such factors on the academic success of the target population. Six factors that positively impact student academic success were identified in the following order of relative impact (from greatest to least): ‘Teaching–Evaluation’, ‘Learner’, ‘Environment’, ‘Family’, ‘Curriculum’ and ‘Teaching Knowledge’. Particularly, influential variables within each factor have also been noted.     

Perceived Helpfulness and Amount of Use of Technology in Science and Mathematics Classes at Different Grade Levels

Use of technology in science and mathematics classes has been increasing, but there are differences in the amount of use of and students' perceptions of its helpfulness across grade levels and subject areas. Technology was reported as used only occasionally. Technology was used most often to understand or explore in more depth concepts taught in class. The second most frequent use was as a tool of investigation or assessment. The lowest reported use of technology was as tool of communication. Students in middle school classes perceived technology as less helpful than did students in elementary or high school classes. Students in mathematics classes perceived technology as more helpful than did students in science classes. Girls perceived technology as more helpful than did boys. Additionally, teacher and student perceptions of amount of use varied with teachers reporting more use than students.     

Effects of State Tests on Classroom Test Items in Mathematics

Classroom tests from nine eighth‐grade mathematics teachers were collected from the 2003–04 and 2005–06 school years. These years represent one school year prior to the eighth‐grade Ohio Achievement Test (OAT) in mathematics being implemented and the year after the eighth‐grade OAT in mathematics was implemented, respectively. In addition, teachers were interviewed to determine factors that influence classroom assessment practices. Classroom assessment data were compared between the two years, and interview data were examined, to investigate the impact that the new state test was having on classroom assessment practices. An average of 87% of teachers' classroom assessment items were at the lowest depth of knowledge level during both years. Teachers relied heavily on curriculum materials for their test items, and these items tended to only assess students ability to recall basic facts or perform straightforward procedures. The presence of a state test did not entice teachers to assess students at higher depth of knowledge levels.     

An Analysis of Incident/Accident Reports from the Texas Secondary School Science Safety Survey, 2001

This study investigated safety in Texas secondary school science laboratory, classroom, and field settings. The Texas Education Agency (TEA) drew a random representative sample consisting of 199 secondary public schools in Texas. Eighty‐one teachers completed Incident/Accident Reports. The reports were optional, anonymous, and open‐ended; thus, they are unique in capturing the strengths and weaknesses of safety practices in school science settings as perceived by the teachers. Pertinent findings include: a) incidents and accidents (mishaps) increased from 8% to 62% as the class enrollment increased from <14 students to >24 students (p < 0.05), b) mishaps increased from 11% to 66% as classroom space per student decreased from >60 ft² per student to <45 ft² per student (p < 0.05), c) mishaps increased from 11% to 47% as room size decreased from >1200 ft² to <800 ft² (p < 0.05) d) 35% of teachers did not have adequate safety training within the last year, and e) 69% of teachers had a written safety policy. The findings of this study can be used to develop science classroom, lab, and field safety guidelines on a classroom, school, district, state, and a national level.     

Student and Teacher Perspectives Across Mathematics and Science Classrooms: The Importance of Engaging Contexts

Substantial recent focus has been placed upon the competitiveness of American students in increasingly global economies and entrepreneurial enterprises. As concerns center on students’ educational preparedness and their efforts at continued learning, researchers acknowledge the importance of student engagement with school. In order to foster engaged learners, teachers must be able to determine and monitor their students’ levels of engagement. The current study examined the alignment of perceptions of engagement by students, teachers, and outside observers across middle and high school mathematics and science classrooms. Results indicated significant teacher‐student differences in perceptions of student cognitive engagement across mathematics and science classrooms with teachers consistently perceiving higher levels than students. Moreover, most effect sizes were moderate to large. A subsequent multi‐level analysis indicated that while teacher perceptions of student cognitive engagement were somewhat predictive of student reported cognitive engagement, academic engagement ratings by outside observers were not.     

Students’ self-regulation of emotions in mathematics: an analysis of meta-emotional knowledge and skills

Over the past decade, the concept of self-regulated learning has broadened to include motivational, volitional, and emotional components next to (meta-)cognitive ones. In this article, we present a meta-emotion perspective as an essential component of a conceptual framework on self-regulation that fully acknowledges the role of emotions. Against this background, a study is presented that attempts to contribute to the clarification of the relevance and the functioning of students’ meta-emotional knowledge and emotional regulation skills in school-related mathematical activities. It investigates the coping strategies that 393 students of the second (age 14) and fourth (age 16) year of secondary school report to use to regulate their emotions in three different mathematical school settings (i.e., a mathematics test, a difficult mathematics homework, and a difficult mathematics lesson). More specifically, it aims (1) to document the nature and frequency of the reported coping strategies, and (2) to explore—for the three different mathematical school settings—relationships between these reported coping strategies and personal characteristics (i.e., students’ familiarity with the particular school settings, their track in secondary education, their achievement level, their age, and gender). The results indicate that students report to know and to make use of several coping strategies in school-related mathematical activities, and reveal that the use of these strategies is related to specific person-related characteristics. In conclusion, we elaborate on how schools and teachers can stimulate students to acquire appropriate strategies and skills to self-regulate their emotions.     

Connecting mathematical creativity to mathematical ability

This study aims to investigate whether there is a relationship between mathematical ability and mathematical creativity, and to examine the structure of this relationship. Furthermore, in order to validate the relationship between the two constructs, we will trace groups of students that differ across mathematical ability and investigate the relationships amongst these students’ performance on a mathematical ability test and the components of mathematical creativity. Data were collected by administering two tests, a mathematical ability and a mathematical creativity test, to 359 elementary school students. Mathematical ability was considered as a multidimensional construct, including quantitative ability (number sense and pre-algebraic reasoning), causal ability (examination of cause–effect relations), spatial ability (paper folding, perspective and spatial rotation abilities), qualitative ability (processing of similarity and difference relations) and inductive/deductive ability. Mathematical creativity was defined as a domain-specific characteristic, enabling individuals to be characterized by fluency, flexibility and originality in the domain of mathematics. The data analysis revealed that there is a positive correlation between mathematical creativity and mathematical ability. Moreover, confirmatory factor analysis suggested that mathematical creativity is a subcomponent of mathematical ability. Further, latent class analysis showed that three different categories of students can be identified varying in mathematical ability. These groups of students varying in mathematical ability also reflected three categories of students varying in mathematical creativity.     

Proof validation and modification in secondary school geometry

Proof validation is important in school mathematics because it can provide a basis upon which to critique mathematical arguments. While there has been some previous research on proof validation, the need for studies with school students is pressing. For this paper, we focus on proof validation and modification during secondary school geometry. For that purpose, we employ Lakatos’ notion of local counterexample that rejects a specific step in a proof. By using Toulmin’s framework to analyze data from a task-based questionnaire completed by 32 ninth-grade students in a class in Japan, we identify what attempts the students made in producing local counterexamples to their proofs and modifying their proofs to deal with local counterexamples. We found that student difficulties related to producing diagrams that satisfied the condition of the set proof problem and to generating acceptable warrants for claims. The classroom use of tasks that entail student discovery of local counterexamples may help to improve students’ learning of proof and proving.     

Effects of variation theory approach in teaching and learning of algebra on urban and rural students’ algebraic achievement and motivation

This study investigates the effect of utilizing variation theory approach (VTA) on students' algebraic achievement and their motivation in learning algebra. The study used quasi-experimental non-equivalent control group research design. It involved 114 Form Two students in four intact classes (two classes were from an urban school, another two classes from a rural school). The first group of students from each school learnt algebra in class which used the VTA, while the second group of students in each school learnt algebra through conventional teaching approach. Two-way analysis of covariance and two-way multivariate analysis of variance (MANOVA) were used to analyse the data collected. The result of this study indicated that the use of VTA has significant effect on both urban and rural students' algebraic achievement. There were evidences that VTA has significant effect on rural VTA students' overall motivation in its five subscales: attention, relevance, confidence, satisfaction and interest but it was not so for urban VTA students' motivation. This study provides further empirical evidence that utilization of variation theory as pedagogical guide can promote the teaching and learning of Form Two Algebra topics in urban and rural secondary school classrooms.     

Science-Related Attitudes of High-ability Students

This study compared college-age student attitudes toward junior high/middle school science classes, teachers, and the value of science content. Subjects represented two groups: academically talented college students majoring in the sciences, and equally talented nonscience college students. The data were compared with responses from noncollegiate young adults, reported in an earlier investigation (Yager & Penick, 1986). Results indicated that science students expressed the most favorable impressions of school science instruction, followed by nonscience students, and then by noncollegiate adults. Although science student attitudes were positive overall, many high-ability students indicated that their secondary science classes were neither exciting nor relevant to daily living. Curricular implications for enhancing students' attitudes are discussed.     

Proof schemes combined: mapping secondary students’ multi-faceted and evolving first encounters with mathematical proof

In this paper, we propose an enriched and extended application of Harel and Sowder’s proof schemes taxonomy that can be used as a diagnostic tool for characterizing secondary students’ emergent learning of proof and proving. We illustrate this application in the analysis of data collected from 85 Year 9 (age 14–15) secondary students. We capture these students’ first encounters with proof and proving in an educational context (mixed ability, state schools in Greece) where mathematical proof is explicitly present in algebra and geometry lessons and where proving skills are typically expected, and rewarded, in key national examinations. We analyze student written responses to six questions, soon after the students had been introduced to proof and we identify evidence of six of the seven proof schemes proposed by Harel and Sowder as well as a further eight combinations of the six. We observed these combinations often within the response of the same student and to the same item. Here, we illustrate the eight combinations and we claim that a dynamic use of the proof schemes taxonomy that encompasses sole and combined proof schemes is a potent theoretical and pedagogical tool for mapping students’ multi-faceted and evolving competence in, and appreciation for, proof and proving.