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

SBIR第一阶段项目将为补充K-2数学课程制作原型，交付平板电脑，培养数学推理和解决问题的能力。对于想要在高薪工作的先决条件——门卫课程中取得成功的学生来说，推理和解决问题的能力是必不可少的，但大多数学校都严格关注计算。为了解决这个全国性的问题，联邦政府资助的综合学校数学项目（CSMP）的教学方法和策略将得到拨款。研究（1970-1990）表明，CSMP学生有更大的能力来解决新的问题，通过测量的MANS测试。尽管从天才儿童到学习困难儿童的结果都很显著，但CSMP？当时，这种亲力亲为、个性化的方法成本太高，无法大规模实施。这个项目将解决今天的问题？利用CSMP最强大的方面。学生将通过在游戏设置中反复暴露解决问题的场景来工作。与传统的操作工具不同，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。随着新一代的人能够用数学思考，更多的美国人将能够在技术成熟的21世纪市场上茁壮成长，创造就业机会，创造税收。利用专为平板电脑设计的强大技术（触摸、拖放和加速度计），可以创造侦探般的冒险，鼓励学生形成假设，考虑替代方案，并检验结论。孩子们善于用图形和具体的表述来诠释和内化许多人认为超出他们理解范围的数学概念。仿造童年流行的积木，让游戏体验看起来更像游戏，而不是一系列需要完成的任务。通过在平板电脑屏幕上移动这些熟悉的物体，孩子们看到了他们行为的因果关系。自适应学习机制提供基于性能的自动分级体验——节省了大量的准备和管理时间。自动生成的报告为决策提供了数据。第一阶段的研究将侧重于技术的可行性、学生参与和教师使用。在第二阶段，一个广泛的评估将确定学生是否内化了共同核心概念，并利用他们对数学日益增长的理解来解决问题。传统的定性分析技术将用于回答研究问题，并为继续研究提供基础。在补充项目已经按照设计实施的学校，可以进行MANS测试，以确定学生是否与最初的CSMP队列有相似或更好的结果。

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.