SBIR Phase I: Learning to Think Mathematically and Problem-Solve Right From the Start

摘要这个SBIR第一阶段项目将为补充的K-2数学项目产生原型，平板电脑交付，建立数学推理和解决问题的技能。对于学生来说，要想在高薪工作的先决条件--看门人课程中取得成功，推理和解决问题的技能是必不可少的，但大多数学校严格关注计算。为了解决这一全国性的问题，将借鉴联邦政府资助的综合学校数学计划(CSMP)的教学方法和策略。1970年至1990年的研究表明，通过曼斯测试，CSMP学生具有更强的解决新问题的能力。尽管从有天赋的人到有学习挑战的人的结果是显著的，但CSMP？S亲力亲为、个性化的方法在当时成本太高，无法大规模实施。该项目将致力于利用今天的S技术来利用CSMP最强大的方面。学生们将通过反复暴露在类似游戏的环境中解决问题的场景来进行练习。与传统的操控方式不同，五颜六色的玩具积木被用来提出问题、探索概念、发展技能和定义新想法。随着新一代人能够用数学思维，更多的美国人将能够在技术先进的21世纪市场中蓬勃发展，创造就业机会和创造税收。采用专门为平板电脑设计的强大技术(触摸、拖放和加速计)使创造侦探般的冒险成为可能，鼓励学生形成假设、考虑替代方案和检验结论。通过图画和具体的表示，孩子们能够解释和内化许多人认为超出他们理解范围的数学概念。儿时流行的建筑砖的复制品让这种体验看起来像是玩耍，而不是一系列要完成的任务。通过在平板电脑屏幕上移动这些熟悉的物体，孩子们可以看到他们行为的前因后果。自适应学习机制提供了基于性能的自动分级体验--节省了大量的准备和监督时间。自动生成的报告为决策提供数据。第一阶段的研究将集中在技术的可行性、学生的参与度和教师的使用上。在第二阶段，广泛的评估将确定学生是否将共同核心概念内在化，并利用他们日益增长的数学理解来解决问题。传统的定性分析技术将被用来回答研究问题，并为继续研究提供基础。在补充计划已按设计实施的学校，可以进行MANS测试，以确定学生的结果是否与最初的CSMP队列相似或更好。

ABSTRACT This SBIR Phase I project will produce the prototype for a supplementary K-2 math program, tablet delivered, that builds mathematical reasoning and problem-solving skills. For students to succeed in gate keeper courses that are prerequisite to high-paying jobs, reasoning and problem-solving skills are essential, yet the majority of schools focus strictly on computation. To address this nationwide problem, the pedagogy and strategies from the federally-funded Comprehensive School Mathematics Program (CSMP) will be appropriated. Studies (1970-1990) show that CSMP students had greater ability to solve novel problems as measured by the MANS test. Although results were significant from the gifted to the learning challenged, CSMP?s hands-on, personalized approach was too costly at the time to implement on a larger scale. This project will address harnessing today?s technology to leverage the strongest aspects of CSMP. Students will work through repeated exposures to problem-solving scenarios presented in game-like settings. Rather than traditional manipulatives, colorful toy building bricks are used to pose problems, explore concepts, develop skills, and define new ideas. As new generations are able to think mathematically, considerably more Americans will be able to thrive in the technologically sophisticated 21st century marketplace, fostering jobs and generating tax revenues.Employing powerful technologies devised exclusively for the tablet (touch, drag-and-drop, and accelerometers) makes possible the creation of detective-like adventures that encourage students to form hypotheses, consider alternatives, and test conclusions. Resplendent with pictorial and concrete representations, children are able to interpret and internalize mathematical concepts many think are beyond their comprehension. Replicas of popular childhood building bricks make the experience seem play-like rather than a series of tasks to be completed. By moving these familiar objects across the tablet screen, children see the cause and effect of their actions. Adaptive learning mechanics deliver auto-graded experiences based on performance -- saving considerable preparation and supervisory time. Automatically generated reports provide data for decision-making. Phase I research will focus on the viability of the technology, student engagement and teacher use. During Phase II, an extensive evaluation will determine if students internalize Common Core concepts and use their growing understanding of mathematics to solve problems. Traditional qualitative analysis techniques will be used to answer research questions and provide a foundation for continued studies. In schools where the supplementary program has been implemented as designed, the MANS test can be administered to ascertain if students have similar or better outcomes than the original CSMP cohort.