Investigating the Benefits of Using Worked Examples to Improve Mathematical Explanations for Students Who Struggle

当学生解释他们在数学中的解决方法时，他们能够与先前的知识建立联系，建立新的见解，并加深他们对正在学习的数学的理解。有数学困难的学生(成绩低于25%的学生)在解释他们的解题方法时，很难清楚地表达他们对数学原理的理解。学习和理解小学高年级的分数对学生来说尤其具有挑战性，而且经常阻碍学生在初中和高中数学进步的过程中学习。该项目的目的是为在数学方面有困难的学生改进数学解释，特别是分数。为了实现这一点，该项目将调查工作例子(即已经解决的问题)的好处，作为一种机制，以改进对挣扎的学生的解释。该项目将开发专注于分数概念的样例材料，用于五年级有数学困难的学生，并检查这种教学方法是否在干预过程中提高学生的数学解释能力。拟议的项目包括三个阶段：开发工作、两个短期随机对照试验(RCT)和可行性初步研究，然后是多点随机对照试验。首先，团队将开发各种类型的工作示例(正确与不正确的解决方案；一种与两种解决方案)，以解决关键分数概念和五年级标准中的运算。然后，研究人员将进行两个短期RCT，以确定哪些样例类型最有希望为有数学困难的学生开发解释。最后，将进一步开发样例材料，并将其作为教学组件嵌入到先前验证的分数干预中。将在可行性试点中审查干预经验教训，随后将进行多地点随机对照试验。80名符合条件的学生将被随机分配接受小组小组干预、样例干预或一切照常进行控制。学生数据将包括分数、概念和程序的测量，以及书面和口头解释的评估。对工作记忆和注意力的评估也将包括在内。将使用治疗仪器的保真度和班级观察系统收集实施数据。数据分析程序涉及一个两级分层模型，并将明确说明在治疗条件下的小组教学小组中的学生嵌套，而不是在控制条件下的嵌套。将通过添加条件与先前分数知识、工作记忆和注意力的交互作用来进行调节分析。该项目得到了EHR核心研究计划(ECR)的支持，该计划支持STEM教学和学习的基础研究。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

When students explain their solution approaches in mathematics, they are able to make linkages with prior knowledge, build new insights, and deepen their understanding of the mathematics they are learning. Students with mathematics difficulties (those performing below the 25th percentile) struggle to articulate their understanding of mathematical principles as they explain their solution approaches. Learning and understanding fractions in upper elementary school is especially challenging for students and often impedes learning for students as they advance in middle and high school mathematics. The purpose of the project is to improve mathematical explanations for students who struggle in mathematics, specifically with fractions. To accomplish this, the project will investigate the benefits of worked examples (i.e., already worked-out problems) as a mechanism to improve explanations for students who struggle. The project will develop worked example materials focused on fractions concepts for use with students with mathematics difficulties in Grade 5 and examine whether this approach to instruction enhances students’ mathematical explanations during intervention. The proposed project consists of three phases: development work, two short-duration randomized controlled trials (RCTs), and a feasibility pilot study followed by a multi-site RCT. First, the team will develop various types of worked examples (correct vs. incorrect solutions; one vs. two solutions) that address critical fractions concepts and operations in Grade 5 standards. Researchers will then conduct two short-duration RCTs to determine which worked example types are most promising for developing explanations for students with mathematics difficulties. Finally, worked example materials will be further developed and embedded as an instructional component into a previously validated fractions intervention. Intervention lessons will be examined in a feasibility pilot, which will be followed by a multi-site RCT. Eighty eligible students will be randomly assigned to receive small-group fractions intervention with worked examples or business-as-usual control. Student data will include measures of fractions concepts and procedures and assessments of written and verbal explanations. Assessments of working memory and attention will also be included. Implementation data will be collected using fidelity of treatment instruments and the CLASS observation system. Data analysis procedures involve a two-level hierarchical model and will explicitly account for the nesting of students in small instructional groups in the treatment condition but not in the control condition. A moderator analysis will be conducted by adding the interaction of condition with prior fractions knowledge, working memory, and attention. This project is supported by the EHR Core Research Program (ECR) which supports fundamental research on STEM teaching and learning.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.