Understanding/Preventing Math Problem/Solving Disability

描述(由申请者提供)：本项目的总体目的是增加对数学问题解决(MPS)的认识，减少数学问题解决障碍的发生率(MPS：需要一个以上步骤的应用题和/或以相对较长的叙述和/或不相关的信息真实地呈现)。一方面，对MPS的研究主要局限于初中生和高中生，没有明显的困难。另一方面，对幼儿数学障碍的研究主要集中在算术上，对算术词问题(需要加/减基本事实的语言上简单的一步问题)也有一些关注。然而，算术应用题并不代表学校课程中超出最低年级或生活要求的数学问题的类型。因此，无论是在学校里还是在校外，对数学障碍的研究结果都很难一概而论。这就产生了在三年级时明确学习MPS残疾(MPSD)的必要性，当学生第一次被期望用更长的叙述和/或无关的信息来解决多步骤问题时。增加数学障碍研究广度的另一个原因是，考虑到MPS的需求，与算术或算术应用题不足相关的概况可能与与MPS不足有关的概况不同。因此，需要关注MPS，以了解和预防数学残疾，因为它在学校发展，与现实世界的能力有关。 该项目使用随机对照试验来测试课堂水平和辅导治疗的有效性，旨在降低MPSD的患病率，并利用每年测试课堂水平和辅导治疗的创新成分。在这些试验的背景下，MPSD的患病率和诊断稳定性是在有或没有阅读障碍(RD)、有或没有使用智商成绩差异以及有或没有预防的情况下进行评估的。本研究探讨了与有或无RD和有或无智商成绩差异的MPSD发展相关的人口统计、学业、注意力和认知特征，并对学生进行了纵向跟踪，以了解随着课程难度从5年级到5年级的加剧，3年级的课堂和辅导预防措施是如何影响结果的。因此，本研究提出四个具体目标：(1)调查与强迫症发展相关的人口学、学业、注意力和认知模式；(2)评估有或没有研发、有或没有研发、有或没有智商差异、有或没有预防的强迫症的患病率和稳定性；(3)为强迫症建立有效的课堂预防；及(4)为有或没有研发风险的强迫症高危学生提供有效的预防性辅导。

DESCRIPTION (provided by applicant): The overall purpose of this project is to increase the understanding and decrease the prevalence of disability in mathematical problem solving (MPS; word problems requiring more than one step and/or presented realistically with relatively long narratives and/or irrelevant information). On the one hand, research on MPS has been confined largely to middle- and high-school students without significant difficulties. On the other hand, research on mathematics disability in younger children has focused primarily on arithmetic, with some attention to arithmetic word problems (linguistically simple one-step problems requiring adding/subtracting basic facts). Arithmetic word problems do not, however, represent the kinds of math problems incorporated in school curricula beyond the earliest grades or those required in life. So, the generalizability of findings to math disability as it occurs in and out of school is tenuous. This creates the need for the explicit study of MPS disability (MPSD) at 3rd grade, when students are first expected to solve multi-step problems with longer narratives and/or irrelevant information. Another reason to increase the breadth of math disability study is that, given the demands of MPS, the profiles associated with deficient arithmetic or arithmetic word problems may differ from those associated with deficient MPS. Consequently, a focus on MPS is required to understand and prevent math disability as it develops in schools and pertains to real-world competence. This project employs randomized controlled trials to test the efficacy of classroom-level and tutoring treatments designed to decrease the prevalence of MPSD, with the contribution of an innovative component tested annually for classroom-level and tutoring treatment. Within the context of those trials, the prevalence and diagnostic stability of MPSD is estimated as it occurs with or without reading disability (RD), with or without using an IQ-achievement discrepancy, and with or without prevention. The demographic, academic, attention, and cognitive profiles associated with the development of MPSD with or without RD and with or without IQ-achievement discrepancy are explored, and students are followed longitudinally to understand how classroom and tutoring prevention efforts at 3rd grade, when complex MPS develops, affect outcomes as curricular difficulty intensifies through the 5th grade. Four specific aims are therefore proposed: (1) investigating the demographic, academic, attention, and cognitive profiles associated with the development of MPSD with or without RD and with or without IQ-achievement discrepancy; (2) estimating the prevalence and stability of MPSD with or without RD, with or without IQ discrepancy, and with or without prevention; (3) building effective classroom-level prevention for MPSD; and (4) identifying effective preventive tutoring for students at risk for poor MPSD outcomes with and without risk for RD.