Algebraic learning and cognition

代数学习和认知

• 批准号: 9292020
• 负责人: DAVID C GEARY
• 金额: $ 42.01万
• 依托单位: UNIVERSITY OF MISSOURI-COLUMBIA
• 依托单位国家: 美国
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-05-22 至 2021-03-31
• 项目状态: 已结题
• 来源: https://reporter.nih.gov/project-details/9292020
• 关键词: Achievement; Address; Algebra; Algorithms; Anxiety; Area; Arithmetic; Attention; Attitude; Behavior; Belief; Child; Cognition; Cognitive; Competence; Complex; Decision Making; Development; Disadvantaged; Employment; Employment Opportunities; Family; Foundations; Geometry; Goals; Individual; Individual Differences; Intervention; Lead; Learning; Life; Link; Longitudinal Studies; Mathematics; Measures; Medical; Memory; Mental Health; Modeling; Occupations; Outcome; Participant; Proactive Inhibition; Psychometrics; Readiness; Risk; Science; Self-Examination; Short-Term Memory; Structure; Students; System; Technology; Testing; Underemployment; Unemployment; Validity and Reliability; Visuospatial; Wages; Work; algebraic equations; base; cognitive ability; cognitive system; college; cost; design; discount; discounting; gender difference; girls; high school; improved; insight; mathematical ability; mathematical learning; ninth grade; novel; physical conditioning; public health relevance; skills; social; teacher; theories; treatment choice

Modified Project Summary/Abstract Section Competence with algebra is the foundation for the mathematics that facilitates reasoned decision making in many aspects of day-to-day life, including medical treatment choices (Reyna et al. 2009), is demanded in high-paying technology and science fields (National Mathematics Advisory Panel 2008), and contributes to employability and wages in many blue collar occupations (Bynner 1997). Yet, only 39% of US high school graduates have the algebraic competencies needed for these endeavors. Improving the algebraic skills of US students will yield individual and wider social benefits, but this goal has been difficult to achieve. One impediment is our piecemeal understanding of algebraic learning and cognition that has resulted in both practical and theoretical costs. Practically, one student may have difficulty due to an undervaluation of the importance of mathematics, another may have poorly developed prerequisite skills, and a third may confuse current learning with prior learning (proactive inhibition). The reasons for algebraic deficits in these students are very different and consequently the interventions to address them would differ as well. No current theory exists that integrates cognitive and non-cognitive processes on algebra readiness and learning, an integration that is needed for the development of measures to better assess individual differences in algebraic learning. In this proposal we develop such a model and use it to organize a comprehensive and deep longitudinal study of individual and gender differences in readiness for algebra and the learning of specific, core algorithmic and spatial-related algebraic competencies. Carefully chosen measures of prerequisite skills, visuospatial memory and cognition, complex spatial ability, proactive interference, and inherent sensitivity to magnitude will be administered to 450 7th graders. Their attitudes about mathematics and their math anxiety, as well as their attentive behavior in mathematics and English (as a contrast) classrooms will be annually assessed in 7th to 9th grade. At the beginning and end of 9th grade, participants will be assessed using psychometric and cognitive measures of algebraic competence generally and competence with algorithmic and spatial-dependent aspects of algebra in particular. The breadth and depth of measures will enable testing of nuanced hypotheses regarding the contributions of different cognitive and memory systems to different aspects of algebraic learning; the dynamic interactions between these systems and developmental change in math attitudes and anxiety as related to engagement in the mathematics classroom and algebraic learning and cognition; and, the cognitive and non-cognitive factors that contribute to gender differences in certain aspects of algebra, specifically girls’ disadvantage in spatial aspects of algebra and their undervaluation of mathematics. The combination will significantly advance our understanding of algebraic learning and cognition, and lead to the development of better assessment measures and targeted interventions to address individual and gender differences in algebraic learning.

修改的项目摘要/摘要部分 与代数的能力是数学的基础 日常生活的许多方面，包括医疗选择（Reyna等，2009），都要求 高薪技术和科学领域（国家数学咨询小组2008），并有助于 许多蓝领职业的就业能力和妇女（Bynner 1997）。但是，只有39％的我们高中 毕业生具有这些努力所需的代数能力。提高代数技能 美国学生将带来个人和更广泛的社会利益，但是这个目标很难实现。一 障碍是我们对代数学习和认知的零星理解，这两者都导致 实用和理论成本。实际上，由于低估了一个学生 数学的重要性，另一个可能具有不佳的先决条件，三分之一可能会承认 当前学习先前的学习（积极抑制）。这些学生的代数防御的原因 非常不同，因此解决这些问题的干预措施也将有所不同。没有当前的理论 存在将认知和非认知过程整合在代数准备和学习上 制定措施需要更好地评估个体差异所需的集成 代数学习。在此提案中，我们开发了这样的模型，并使用它来组织一个全面和 对代数准备的个人和性别差异的深入纵向研究以及学习 具体的，核心算法和与空间相关的代数能力。精心选择的措施 先决条件，视觉记忆和认知，复杂的空间能力，主动干扰以及 对幅度的固有敏感性将对450个7年级学生进行管理。他们参加数学 以及他们的数学动画以及他们在数学和英语方面的专心行为（相反） 教室将每年在7至9年级进行评估。在9年级的开始和结束时，参与者 将使用代数能力的心理测量和认知度量进行评估 尤其是代数的算法和空间依赖方面的能力。广度和深度 措施将使有关不同认知和不同认知和 记忆系统到代数学习的不同方面；这些系统之间的动态互动 数学的发展和动画与数学的参与有关 教室和代数学习和认知；而且，贡献的认知和非认知因素 在代数的某些方面的性别差异，特别是女孩在空间方面的灾难 代数及其对数学的低估。这种组合将大大推动我们的 了解代数学习和认知，并导致更好的评估的发展 措施和有针对性的干预措施，以解决代数学习中的个体和性别差异。