Collaborative Research: : Collaborative Partnership to Teach Mathematical Reasoning Through Computer Programming (CPR2)

由于计算在STEM学科中的强大创新和应用，STEM+C项目解决了从小学到高中（pre -12）学生对现实世界、跨学科和计算准备的迫切需求。通过计算机编程教授数学推理的合作伙伴关系（CPR2）项目将调查计算机编程是否是七年级和八年级数学课堂教学和学习泛化的有效工具。理解和解释一般的表达对学生来说可能很困难，但这是在STEM学科中进步的关键。未能在中学“掌握”这项技能是在大学和职业生涯中追求STEM的主要障碍。CPR2教学模型（IM）将帮助学生理解，解释，甚至生成一般或代数表达式。该团队开发了一种明确的泛化教学方法，适用于没有编程或正式数学论证背景的学习者。学生将编写小型计算机程序，然后从代码中识别和恢复一般行为。接下来，学生将学习用抽象的数学语言描述这些行为。CPR2 IM的另一个好处是，学习者将获得使用编程作为科学探索工具的经验、技能和信心。这种体验为所有学生打开了一扇门，让他们认识、理解和应用抽象概念，并体验编写自己的计算机程序，从而推动了STEM领域的发展。CPR2 IM有可能为所有学生参与者铺平道路，包括那些目前在计算机科学领域代表性不足的学生，以在未来的STEM研究中取得成功。研究人员将在基于设计的实施研究方法中完善教学模型。在为期两周的暑期培训中，教师们将沉浸在四步模型中，并学习它如何建立泛化所必需的心理框架。然后，教师将在团队的支持下在课堂上实施该模型。最后，研究人员将在试点研究中确定对学生的影响。研究人员假设，参与该项目提供的专业发展的教师将提高他们自己概括数学概念的能力，并将更自如地在课堂上使用计算机编程作为工具。学生和教师将使用计算机编程来探索思想，这将提高他们的能力和信心来思考计算和推广数学概念。教师将沉浸在与来自高中和高等教育机构的专业人士的合作环境中。建立的网络将促进和维持各级数学教育的变化。最终，这将导致教师和学生更广泛地参与编程和计算思维。该奖项反映了美国国家科学基金会的法定使命，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。

As a result of the powerful innovation and application of computing in STEM disciplines, the STEM+C program addresses an urgent need for real-world, interdisciplinary, and computational preparation of students from the early grades through high school (preK-12). The Collaborative Partnership to Teach Mathematical Reasoning through Computer Programming (CPR2) project will investigate whether computer programming is an effective tool for teaching and learning generalization in 7th and 8th grade math classrooms. Understanding and interpreting general expressions can be difficult for students, but it is a key to advancing in STEM disciplines. The failure to "catch" this skill in middle school is a major roadblock to pursuit of STEM in college and career. The CPR2 Instructional Model (IM) will help students come to understand, interpret, and even generate general or algebraic expressions. The team has developed an explicit method for teaching generalization that is intended for learners with no background in programming or formal mathematical argumentation. Students will write mini computer programs and then recognize and recover general behaviors from their code. Next, students will learn to describe these behaviors using abstract mathematical language. An additional benefit of the CPR2 IM is that learners will gain experience, skill, and confidence in using programming as a tool for scientific exploration. This experience advances STEM fields by opening a door for all students to recognize, understand and apply abstractions, and to experience writing their own computer programs. The CPR2 IM has the potential to pave the way for all student participants, including those currently underrepresented in computer science, to succeed in future STEM studies. The researchers will refine the instructional model in a design-based implementation research approach. In a two-week summer institute, teachers will be immersed in the four-step model and learn how it builds the mental frameworks necessary for generalization. The teachers will then implement the model in their classes with support from the team. Finally, researchers will determine the effects on students in an experimental pilot study. The researchers hypothesize that teachers who participate in the professional development offered by the project will improve their own ability to generalize over a mathematical concept and will become more comfortable using computer programming as a tool in the classroom. Students and teachers will use computer programming to explore ideas, which will improve their ability and confidence to think computationally and to generalize over a mathematical concept.The teachers will be immersed in a collaborative environment with professionals from high schools and institutes of higher education. The network created will facilitate and sustain change in mathematics education at all levels. Ultimately, this will lead to broader participation of teachers and students in programming and computational thinking.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.