Teaching the partial products algorithm with the concrete representational abstract sequence and the strategic instruction model

Elementary standards include multiplication of single-digit numbers and students advance to solve complex problems and demonstrate procedural fluency in algorithms. The ability to illustrate procedural fluency in algorithms is dependent on the development of understanding and reasoning in multiplication. Development of multiplicative reasoning provides the foundation for advanced mathematics and algebraic reasoning. For students who struggle in mathematics, instruction in multiplication algorithms should ensure conceptual understanding so that students have a foundation for success in advanced mathematics. The concrete representational abstract (CRA) sequence addresses conceptual understanding and the strategic instruction model (SIM) supports procedural knowledge. The current pilot study combined these methods to teach elementary students the partial products algorithm. Twelve students in grades four and five participated in the study, receiving instruction from teachers in their school during an intervention period. Within a pre-experimental design, using pre- and postintervention data, students showed a significant change in performance. The article will describe and show how teachers implemented the CRA-SIM interventions and discuss implications for practice.     

书刊市场 数码印刷的巨大商机

有关书刊市场,最重要的莫过于它为胶印和数码印刷提供的市场机遇了。胶印在这个市场机遇中占据着最大的份额,而数码印刷则面临着实实在在的增长机遇。     

数码照片市场一个真正的大机遇

上个月,我参加了在美国内华达州拉斯维加斯举行的国际影像器材及电子贸易博览会。有2万多人参观了这次展会,他们中包括许多专业摄影师和数码印刷商。     

与营销及设计人员一起促进业务增长

增加数码印刷收入最有效的方法是与客户的营销人员和设计人员形成伙伴关系．正如施乐公司所绘制的图1所示。     

对佛教体验的再思考:皈依与神迹--佛教体验的"家族相似性"特征

佛教中的体验与“家庭相似性”关联何在,为之辩护的论题包括两部分：（1）与其他方式相比,把皈依概念和神迹概念纳入体验概念可以使我们对佛教体验形成一种更为恰当的观点,而这一观点能够表明佛教的宣称与科学的经验主义的宣称之间的区别（前提1-10）;（2）关于界定体验之所是的“家族相似性”理念,本文结论是,皈依与神迹是对佛教中的体验所作出的非实在论的“家族相似性”定义中的两个要素（前提11-13）.     

We game on skyscrapers: the effects of an equity-informed game design workshop on students’ computational thinking skills and perceptions of computer science

Educational technology research and development - This paper presents a game-design workshop built around a digital art installation featuring video games displayed over a real-world skyscraper to...