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联系起来，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（那些表现低于第25百分位数的学生）在解释他们的解决方法时，很难表达他们对数学原理的理解。在小学高年级学习和理解分数对学生来说特别具有挑战性，并且经常阻碍学生在初中和高中数学中的学习。该项目的目的是提高数学解释谁在数学斗争的学生，特别是与分数。为了实现这一点，该项目将调查工作示例的好处（即，已经解决的问题）作为一种机制，以改善对学生谁挣扎的解释。该项目将开发工作的例子材料，重点是分数的概念，用于在五年级的数学困难的学生，并检查这种教学方法是否提高学生的数学解释在干预。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），以及可行性试点研究，然后是多中心RCT。首先，该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;一个与两个解决方案），解决5级标准中的关键分数概念和操作。然后，研究人员将进行两项短期随机对照试验，以确定哪些样例类型最有希望为数学困难的学生提供解释。最后，工作的例子材料将进一步开发和嵌入作为一个教学组成部分到以前验证的分数干预。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分数干预与工作的例子或照常控制。学生的资料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。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CLASS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，并将明确说明嵌套的学生在小教学组的治疗条件，但不是在控制条件。将通过添加条件与先前分数知识、工作记忆和注意力的相互作用进行调节分析。 该项目由EHR核心研究计划（ECR）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知识价值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.