Abstract The study explored the impact of Please Go Bring Me-COnceptual Model-based Problem Solving (PGBM-COMPS) computer tutoring system on multiplicative reasoning and problem solving of students with learning disabilities. The PGBM-COMPS program focused on enhancing the multiplicative reasoning and problem solving through nurturing fundamental mathematical ideas and moving students above and beyond the concrete level of operation. This is achieved by taking advantages of the constructivist approach from mathematics education and explicit conceptual model-based problem solving approach from special education. Participants were three elementary students with learning disabilities (LD). A mixed method design was employed to investigate the effect of the PGBM-COMPS program on enhancing students’ multiplicative reasoning and problem solving. It was found that the PGBM-COMPS program significantly improved participating students’ problem solving performance not only on researcher developed criterion tests but also on a norm-referenced standardized test. Qualitative and quantities data from this study indicate that, in addition to nurturing fundamental concept of composite units, it is necessary to help students to understand underlying problem structures and move toward mathematical model-based problem representation and solving for generalized problem solving skills.

中文翻译：

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基于概念模型的数学计算机导师对学习障碍学生乘法推理和问题解决的影响

摘要 本研究探讨了请带我来-基于概念模型的问题解决（PGBM-COMPS）计算机辅导系统对学习障碍学生乘法推理和问题解决的影响。PGBM-COMPS 计划侧重于通过培养基本的数学思想和使学生超越具体的操作水平来增强乘法推理和解决问题的能力。这是通过利用数学教育中的建构主义方法和特殊教育中基于显式概念模型的问题解决方法来实现的。参与者是三名有学习障碍（LD）的小学生。采用混合方法设计来研究 PGBM-COMPS 程序对增强学生乘法推理和解决问题的影响。结果发现，PGBM-COMPS 计划不仅在研究人员制定的标准测试中，而且在以规范为参照的标准化测试中，都显着提高了参与学生的问题解决能力。本研究的定性和数量数据表明，除了培养复合单位的基本概念外，还需要帮助学生理解潜在的问题结构，并朝着基于数学模型的问题表示和解决问题的普遍解决问题迈进。