Supporting the development of algebraic thinking in middle school: a closer look at students’ informal strategies

This study investigated how 31 sixth-, seventh-, and eighth-grade middle school students who had not previously, nor were currently taking a formal Algebra course, approached word problems of an algebraic nature. Specifically, these algebraic word problems were of the form x + (x + a) + (x + b) = c or ax + bx + cx = d. An examination of students’ understanding of the relationships expressed in the problems and how they used this information to solve problems was conducted. Data included the students’ written responses to problems, field notes of researcher-student interactions while working on the problems, and follow-up interviews. Results showed that students had many informal strategies for solving the problems with systematic guess and check being the most common approach. Analysis of researcher-student interactions while working on the problems revealed ways in which students struggled to engage in the problems. Support mechanisms for students who struggle with these problems are suggested. Finally, implications are provided for drawing upon students’ informal and intuitive knowledge to support the development of algebraic thinking.     

发展中的我国中学物理"四个类型实验"

分析总结了半个世纪来我国中学物理教学“4个类型实验”的历史、内涵、功能和教法。     

多项式的最大公因式的一种新求法

本文介绍了一种利用数域上矩阵的初等行变换求一组一元ｎ次多项式的最大公因式的方法．     

多循环脉冲爆震发动机流场数值研究

针对二维带有收敛扩张喷管的脉冲爆震发动机模型，采用带基元化学反应的Euler方程组和H2、空气的9组分20基元反应，对发动机在前六个工作循环的流场进行了数值模拟。通过对前几个循环流场进行比较，发现脉冲爆震发动机在第五个循环后流场就基本稳定，单循环得到的流场和多循环稳定后的流场有很大的差别，同时喷管对发动机内流场影响特别大。     

氢氧混合气体爆轰波的真实化学反应模型数值模拟

采用高精度的ENO格式和基于基元化学反应的真实化学反应模型求解氢氧混合气体一维爆轰波的精细结构。采用直接起爆方法得到稳定传播的爆轰波 ,计算的爆轰波阵面参数和实验相当符合。对爆轰波反应区化学反应的研究表明 ,参与反应的不同组分具有不同类型的变化特征。网格尺寸影响的研究表明 ,计算结果的精度随着网格尺寸的增加而增加 ,并能保持较好的收敛性。移动网格研究结果表明 ,网格运动速度和爆轰速度接近时 ,两者的相互作用对计算结果产生一定影响。     

初中学生血吸虫病检查结果与影响因素分析

目的调查和分析江西南昌地区血吸虫病流行区初中学生血吸虫病情况,及相关影响因素。方法 2015年8月至2016年8月,将江西南昌地区血吸虫病流行区中的19个重点县分为血吸虫病传播控制区和血吸虫病疫情控制区,其中传播控制区调查人数1 569名,疫情控制区调查人数1 723名,对所有的学生均采取问卷调查措施。结果疫情控制区初中学生血吸虫病检查率明显高于传播控制区初中学生血吸虫病检查率,数据比较差异具有统计学意义(P0.05);血防知识知晓及格率越高,检查率越高;学校血防教育频次越高,检查率越高;血防部分教育频次及格率越高,检查率越高,数据比较差异均具有统计学意义(P0.05)。结论江西南昌地区血吸虫病流行区初中学生血吸虫病检查率较低,需要加强对初中学生的健康教育,实现提高初中学生血吸虫病检查率的目的。     

Finding Alignment: The Perceptions and Integration of the Next Generation Science Standards Practices by Elementary Teachers

Preparing elementary‐level teachers to teach in alignment with the eight Next Generation Science Standards (NGSS) practices could prove to be a daunting endeavor. However, the process may be catalyzed by leveraging elements of teacher science instruction that inherently attend to the practice standards. In this study, we investigated the science instruction of three grade 3–5 elementary‐level teachers. We used observation, interviews, and surveys to determine the level to which the teachers perceived they taught and engaged in teaching science aligned with the eight NGSS practices. We found that the teachers were partially, and intrinsically implementing several of these practices in their instruction, and at the same time could not articulate the eight NGSS practices. Our results suggest there may be ample opportunity to build on the current science instruction of elementary‐level teachers to bring their instruction into alignment with the NGSS. We found that teachers’ perceive professional development, school culture, and access to additional instructional resources to be essential to their adoption of the NGSS practices.     

求弹性半平面问题基本解的一个新方法

本文所提到的弹性半平面问题的基本解是一个满足特殊条件的弹性半平面的应力位移解答。这些条件为:(1)半平面内一点处作用有集中力X,Y或集中力偶M;(2)半平面边界为自由或固定边。利用平面弹性的复变函数方法,文中把弹性半平面基本解的问题归结为下列问题,使一个特定解析函数和另一个解析函数的共轭值在半平面边界上相等。对上述转化后的问题,只要利用复变函数的性质,不难从基本解的第一部分推导出基本解的第二部分。其中,基本解的第一部分是弹性全平面的本基解。从而,半平面问题基本解可以方便地得到。此外,文中还首次给出了:(1)集中力偶作用于半平面内一点时的基本解;(2)当半平面边界固定情况下的基本解。     

Disappearing x: When solving does not mean finding the solution set

This study deals with preservice elementary teachers’ responses to linear equations and inequalities that had infinite solution sets. In particular, these tasks dealt with situations where the variable is eliminated during standard symbolic manipulation. The results reveal that infinite solution sets proved difficult for the participants, particularly when prompted to solve the linear equations and inequalities. When the direction prompt was changed, there was increased success in finding the correct solution set. The directional prompts changed the types of solution strategies as well as the nature of responses. In addition, participants stated the belief that different, mathematically equivalent prompts required different, non-equivalent, types of solutions and allowed for different solution strategies.