Supporting computational thinking for middle school mathematics students through diagrammatic reasoning and representational logic

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This research project studies conjectures about the learning of computational thinking through the development of a curricular and pedagogical intervention. The intervention adds a computational environment to a successful effort called the Algebra Project, and is focused on engaging all students in a predominantly African American middle school in computational thinking. In so doing, this work seeks to develop a remedy for the fact that many low-performing students lack a sufficient contextual understanding of the symbols that they are taught to manipulate in their mathematics courses. This research seeks to demonstrate how the use of various types of computational thinking can increase conceptual understanding, visual reasoning, and representational logic. In pursuit of this outcome, this project is seeking to determine to what extent a specific type of simulation and modeling application can enable teachers and middle-school students to use visual reasoning and spatial logic when analyzing mathematical functions. Students in this intervention will work collaboratively in small groups among themselves, and with near peer mentors and tutors, to examine shared experiences that are grounded in mathematical and computational logic. Through their ongoing collaboration and discourse, the students will determine solutions for various tasks and challenges that they are presented. In addition to using visual reasoning and spatial logic in this work, students will also learn to use Python scripts and functions to aid them in their analyses.This research study will be carried out by using a specific type of Python-based microworld, that combines enactive-iconic representations with an experiential math curricular approach developed by the Algebra Project. The Algebra Project’s curricular approach uses a 5-step collaborative model for mathematics inquiry in the classroom. The first step begins with the students experiencing a shared event. Next, students examine the experience by representing the event pictorially, then through everyday language, then through an agreed upon regimentation of everyday language, and finally through the use of iconic and conventional symbolic representations and equations. This research will extend the Algebra Project’s curricular and pedagogical approach by providing students with enactive-iconic and diagrammatic mathematical constructions that they can manipulate virtually in a computational environment that they can use to further examine the mathematical features and logical structures involved. The results of the previous work of this research team that piloted this approach with a very small number of students in an urban context, found that the students involved developed a greater conceptual understanding of core mathematical ideas, namely equation and function, grounded in visual reasoning and representational logic. Furthermore, indicators suggested improvements in ownership and engagement. The research team had not yet examined the extent to which core elements of computational thinking were developed by the students, and this research will address that issue, as well as expand the content of the mathematics and computational material involved. This project is supported by the CS for All: Research and RPPs program.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.