Enhancing Formative Assessment Practice and Encouraging Middle School Mathematics Engagement and Persistence

In the transition to middle school, and during the middle school years, students' motivation for mathematics tends to decline from what it was during elementary school. Formative assessment strategies in mathematics can help support motivation by building confidence for challenging tasks. In this study, the authors developed and piloted a professional development program, Learning to Use Formative Assessment in Mathematics with the Assessment Work Sample Method (AWSM) to build middle school math teachers' understanding of the characteristics of high‐quality formative assessment processes and increases their ability to use them in their classrooms. AWSM proved to be feasible to implement in the middle school setting. It improved teachers' practice of formative assessment, especially in their feedback practices, regardless of their pedagogical content knowledge at entry. Results from focus groups suggested that teachers were better able to implement ungraded practice and student self‐ and peer‐assessment after AWSM, and that students were more willing to engage in complex problem solving.     

The long term impact of a coherence based model for mathematics intervention

This article presents a large-scale longitudinal study of hundreds of students across the state of Kentucky that participated in a dual-focus mathematics intervention initiative when they were in the third grade. Rather than an exclusive focus on intervention, this initiative focused on both (i) high quality pull-out intervention and (ii) coherence between pull-out intervention and classroom instruction. The study found that over half of the third grade intervention students that participated in this initiative were classified as “novice” (the lowest possible performance category) on state standardized mathematics assessments at the end of the third grade. However, over the course of the following four years, the novice reduction rate of these students was significantly (p < .01) greater than other novices in Kentucky that did not participate in the initiative. These findings indicate that when implementing intervention initiatives to help students that are struggling with mathematics, it may be important to establish coherence between pull-out intervention and classroom instruction. The long term impact of this approach among traditionally underrepresented minorities suggest that this publication may provide insight into important equity issues where long-term analyses may sometimes be needed to capture the full impact of intervention initiatives.     

Modification and validation of the mixed-format Engineering Concept Assessment for middle school students using many-facet Rasch measurement

Integrating engineering into the K-12 science curriculum continues to be a focus in national reform efforts in science education. Although there is an increasing interest in research in and practice of integrating engineering in K-12 science education, to date only a few studies have focused on the development of an assessment tool to measure students’ understanding of engineering design. Most of the existing measures focus only on knowledge and understanding of engineering design concepts using multiple-choice items with the exception of the mixed-format Engineering Concept Assessment (ECA). Also, advanced measurement models are lacking application in the testing of such mixed-format assessments in science education. This study applied many-faceted Rasch measurement to the modified ECA for eighth-grade (ECA/M8) and a newly constructed rubric applied by five judges across 497 eighth-grade students’ responses after experiencing an integrated learning unit on the engineering design process. The results supported the fit of the items and rubric rating scales to the Rasch specifications. Recommendations are made for item wording, and further reliability and validity testing of the ECA/M8, and use of the ECA/M8 in science education and research.     

“We definitely wouldn't be able to solve it all by ourselves,but together…”: group synergy in tertiary students' problem-solving practices

The ability to address and solve problems in minimally familiar contexts is the core business of research mathematicians. Recent studies have identified key traits and techniques that individuals exhibit while problem solving, and revealed strategies and behaviours that are frequently invoked in the process. We studied advanced calculus students working in groups to identify what strategies they employed and how, including what encouraged the opportunities to invoke them. The study revealed behaviours not included in the original taxonomy, including one that we termed ‘group synergy’. We propose extensions to Carlson and Bloom's original taxonomy to encompass group behaviour and identify the importance of these behaviours in developing problem-solving skills. Finally, we suggest improvements for future problem-solving session iterations, with the goal of promoting opportunity for more expert performance.     

High school students’ understanding of the function concept

This paper is a study of part of the Algebra Project's program for underrepresented high school students from the lowest quartile of academic achievement, social and economic status. The study focuses on students’ learning the concept of function. The curriculum and pedagogy are part of an innovative, experimental approach designed and implemented by the Algebra Project. The instructional treatment took place over 7 weeks during the Junior Year of 15 students from our target population. Immediately after instruction, a written instrument was administered followed, several weeks later, by in-depth interviews. The results are that many of our participants achieved a level of knowledge and understanding of functions on a par with beginning college students, including preservice teachers, as reported in the literature. Many conceptual difficulties that have been reported in the research literature were not as prevalent for our participants and some of them were capable of solving difficult problems involving composition of functions. We conclude that, with appropriate pedagogy, it is possible for students in the Algebra Project's target population to learn substantial and non-trivial mathematics at the high school level, and that the Algebra Project approach is one example of such a pedagogy.     

初三学生化学三重表征转化的眼动实验研究

化学三重表征研究一直深受国内外学者的重视,目前,初级表征的研究已有一定的理论基础,但是,次级表征（即不同表征水平之间的转化）的研究仍是研究的弱点和难点。纸笔检测、口语报告研究方法都存在一定的局限。为了从信息加工过程研究三重表征间转化的基本特点,采用眼动分析法对12名初三学生进行3×3两因素混合实验。结果显示：（1）在初三上册期末,学优生基本可以进行三重表征之间的直接转化;（2）学中生符号表征较强且依赖于符号表征,表现出“双通道协同加工”现象,符号—宏观、微观转化水平较强,宏观—微观、符号和微观—符号、宏观转化水平较弱;（3）学困生普遍缺乏三重表征的思维和意识,三重表征间的转化水平较低,相比较而言,符号-宏观、微观表征转化稍强于宏观-微观、符号表征转化和微观-符号、宏观表征转化。     

高中生“绿色应用”素养的测评研究

基于绿色化学对社会可持续发展的重要性,提出科学教育中“绿色应用”素养的理论框架,结合高中生化学学习特征开发测评工具,实施测量,分析处理测试数据,探查了高中生“绿色应用”素养的行为水平。研究发现,高中生“绿色应用”素养水平与其学科能力水平具有较好的一致性,不存在性别差异。测评结果为绿色化学实践提供借鉴和启发,以促进学生“绿色应用”素养的提升。     

Exploring mathematical connections of pre-university students through tasks involving rates of change

This paper reports the results of a research exploring the mathematical connections of pre-university students while they solving tasks which involving rates of change. We assume mathematical connections as a cognitive process through which a person finds real relationships between two or more ideas, concepts, definitions, theorems, procedures, representations or meanings or with other disciplines or the real-world. Four tasks were proposed to the 33 pre-university students that participated in this research; the central concept of the first task is the slope, the last three tasks contain concepts like velocity, speed and acceleration. Task-based interviews were conducted to collect data and later analysed with thematic analysis. Results showed most of the students made mathematical connections of the procedural type, the mathematical connections of the common features type are made in smaller quantities and the mathematical connection of the generalization type is scarcely made. Furthermore, students considered slope as a concept disconnected from velocity, speed and acceleration.     

研究生参与实验室大型仪器管理的探索

阐述了研究生参与大型仪器管理的必要性、运行机制及实施环节,建立了"统一管理,专人负责,用管结合,开放使用"的管理模式.实践证明,这一措施的实施对规范大型仪器管理、提高仪器利用率以及实验室科研项目顺利进行起到了积极促进作用.     

黄葆同归国始末：1950年代留美学生回国因素探析

黄葆同院士（1921-2005）是我国高分子化学领域的资深专家。早年留学美国,1955年回国后一直在中国科学院长春应用化学研究所工作。在乙丙橡胶合成等研究领域走在全国前列。基于对“老科学家学术成长资料采集工程”所存大量书信和日记等的解读分析,论文还原了黄葆同在美留学期间加入进步组织、争取回国的历史过程以及求学经历。并以此为缩影,探讨当时促使留美学生回国的个体与社会因素,具体而微地揭示了那一代中国留学生在困境之中的家国情怀。