误差理论中几个问题的讨论

就物理实验教材中有关误差理论概念的延伸、表达,以及有效数据的理解,分别进行了剖析,以便有利于学生学习和教师教学的参考。     

Evaluating students’ conceptual and procedural understanding of sampling distributions

Introductory statistics courses, which are important in preparing students for their daily lives, generally derive inferential statistics from informal knowledge. In this transition process, sampling distributions have an important place, yet research has shown that students often have difficulties with this concept. In order to increase their understanding of sampling distributions, students should have a strong conceptual foundation that is balanced with procedural knowledge. To address this issue, this study was designed to examine the relationship between college students’ procedural and conceptual knowledge of sampling distributions. With this aim in mind, an achievement test consisting of two sections – procedural and conceptual knowledge – was prepared. In answering the questions related to procedural knowledge, the participants were more successful in identifying the relationship between standard deviation of a population and sample means. However, they lacked theoretical knowledge about statements that they had heard or knew intuitively. Simulation activities provided in statistics courses may support students in developing their conceptual understanding in this regard.     

Rheology of Water-in-Oil Emulsions with Different Drop Sizes

Systemic experiments have been conducted to investigate the effect of drop sizes on the rheology of water-in-oil (W/O) emulsions. Three sets of emulsions with different average drop sizes were first prepared and then the corresponding rheologies were determined using a concentric viscometer. Results indicated that the flow behavior of concentrated emulsions changes qualitatively from Newtonian flow to non-Newtonian flow with shear rates. In Newtonian flow regime, a smaller drop size leads to a higher viscosity, and the increments are more pronounced at high dispersed phase volume fractions. Two local remarkable increases of the emulsion viscosity with dispersed phase volume fractions correspond to the percolation and glass-transition, respectively. In non-Newtonian flow regime, emulsions show shear-thinning behavior and can be fitted well by the power law model. For emulsions with volume fractions between 0.132 and 0.325, the flow index and consistency constant show power law relationship with the water content. Furthermore, the shear-thinning effect becomes stronger in the emulsions with smaller drop sizes. A correlation has been successfully developed for determining the clusters’ sizes in W/O emulsions and shows excellent agreement with the experimental data. As a consequence, a microscopic understanding (cluster level) was presented for the shear-thinning behavior of the emulsions in this study.     

化学学科理解视域下的教材单元整体备课*

基于学科理解进行单元整体备课,是教师把握学科知识体系、提升教学设计的站位、实现“素养为本”教学的重要基础。化学学科理解视域下的教材单元整体备课内容主要是对教材内容逻辑顺序与认识思路结构化的系统梳理,确定单元总体与课时教学目标,挖掘教材单元内容所内隐的学科核心素养与教育教学价值,对教学内容、策略进行重构与设计等。对课程标准进行解读理解和对不同教材版本相关内容进行比较整合是提升教材单元整体备课质量的有效途径。     

An exploratory study on student understandings of derivatives in real-world,non-kinematics contexts

Much research on calculus students’ understanding of applied derivatives has been done in kinematics-based contexts (i.e. position, velocity, acceleration). However, given the wide range of applications in science and engineering that are not based on kinematics, nor even explicitly on time, it is important to know how students understand applied derivatives in non-kinematics contexts. In this study, interviews with six students and surveys with 38 students were used to explore students’ “ways of understanding” and “ways of thinking” regarding applied, non-kinematics derivatives. In particular, six categories of ways of understanding emerged from the data as having been shared by a substantial portion of the students in this study: (1) covariation, (2) invoking time, (3) other symbols as constants, (4) other symbols as implicit functions, (5) implicit differentiation, and (6) output values as amounts instead of rates of change.     

A software framework based on a conceptual unified model for evolutionary multiobjective optimization: ParadisEO-MOEO

This paper presents a general-purpose software framework dedicated to the design and the implementation of evolutionary multiobjective optimization techniques: ParadisEO-MOEO. A concise overview of evolutionary algorithms for multiobjective optimization is given. A substantial number of methods has been proposed so far, and an attempt of conceptually unifying existing approaches is presented here. Based on a fine-grained decomposition and following the main issues of fitness assignment, diversity preservation and elitism, a conceptual model is proposed and is validated by regarding a number of state-of-the-art algorithms as simple variants of the same structure. This model is then incorporated into the ParadisEO-MOEO software framework. This framework has proven its validity and high flexibility by enabling the resolution of many academic, real-world and hard multiobjective optimization problems.     

Obstacles and challenges in preservice teachers’ explorations with fractions: A view from a small-scale intervention study

In this study, we implemented one-on-one fractions instruction to eight preservice teachers. The intervention, which was based on the principle of Progressive Formalization (Freudenthal, 1983), was centered on problem solving and on progressively formalizing the participants’ intuitive knowledge of fractions. The objectives of the study were to examine the potential effects of the intervention and to uncover specific difficulties experienced by the preservice teachers during instruction. Results revealed improvement on one measure of conceptual knowledge, but not on a transfer task, which required the teachers to generate word problems for number sentences involving fractions. In addition, the qualitative analysis of the videotaped instructional sessions revealed a number of cognitive obstacles encountered by the participants as they attempted to construct meaningful solutions and represent those solutions symbolically. Based on the findings, specific suggestions for modifying the intervention are provided for mathematics teacher educators.     

Envisioning the infinite by projecting finite properties

We analyze interviews with 24 post-secondary students as they reason about infinite processes in the context of the tricky Tennis Ball Problem. By metaphorically projecting various properties from the finite states such as counting and indexing, participants envisioned widely varying final states for the infinite process. Depending on which properties they attended to, some participants recognized contradictions arising from these infinite projections and sought to resolve the contradictions in non-dismissive ways. The findings indicate that increasing their meta-level awareness of the features of their mental constructions may help students overcome common difficulties with the infinite.