Algebraic learning and cognition

修改项目摘要/摘要部分 代数能力是数学的基础，有助于合理的决策， 日常生活的许多方面，包括医疗选择（Reyna et al. 2009）， 高薪技术和科学领域（国家数学咨询小组2008年），并有助于 就业能力和工资在许多蓝领职业（Bynner 1997）。然而，只有39%的美国高中 毕业生具有这些努力所需的代数能力。提高代数技能 美国学生将产生个人和更广泛的社会效益，但这一目标一直难以实现。一 障碍是我们对代数学习和认知的零碎理解，这导致了 实际和理论成本。实际上，一个学生可能有困难，由于低估的 另一个人可能没有充分发展的先决条件技能，第三个人可能会混淆数学的重要性， 当前学习与先前学习（前摄抑制）。这些学生出现代数缺陷的原因 它们是非常不同的，因此解决这些问题的干预措施也会有所不同。目前没有理论 存在整合认知和非认知过程对代数准备和学习， 为更好地评估个体差异而制定措施所需的整合 代数学习在本建议中，我们开发了这样一个模型，并使用它来组织一个全面的， 深入纵向研究个人和性别差异准备代数和学习 具体的，核心算法和空间相关的代数能力。精心挑选的措施， 先决技能，视觉空间记忆和认知，复杂空间能力，主动干预， 将对450名七年级学生进行对震级的固有敏感性测试。他们对数学的态度 和他们的数学焦虑，以及他们在数学和英语中的注意行为（作为对比） 每年对七至九年级的教室进行评估。在9年级开始和结束时，参与者 将使用一般代数能力的心理测量和认知测量进行评估， 特别是代数的算法和空间相关方面的能力。广度和深度 的措施将使测试的细微差别的假设，对不同的认知和 记忆系统到代数学习的不同方面;这些系统之间的动态相互作用 数学态度和焦虑的发展变化与数学参与有关 课堂和代数学习和认知;以及，认知和非认知因素，有助于 在代数的某些方面存在性别差异，特别是女孩在空间方面处于不利地位， 代数和他们对数学的低估这一组合将大大推动我们的 理解代数学习和认知，并导致更好的评估的发展 采取措施和有针对性的干预措施，解决代数学习中的个人和性别差异。

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.