From Classroom Lessons to Learning Trajectories: Mathematics + Computational Thinking

• In Event: 41.049 - Stories From the Field: Integrating Computational Thinking Across Curricular Domains

Abstract

Purpose. A primary reason for integrating computational thinking (CT) and computer science (CS) into mathematics instruction is to address underrepresentation of people from diverse backgrounds in computing. Integration sidesteps students self-selecting out of computing experiences (Weintrop, et al., 2015) as all students typically take math classes. Additionally, school schedules are packed, making it difficult to add new content. Including computing in existing courses avoids this issue (Israel et al., 2015; Weintrop et al., 2015). However, there is lack of guidance in how to develop such integration. The purpose of this study was to begin to develop learning progressions that integrate mathematics and CT.

Theoretical Framework. Work on integrating CT and mathematics comes from a long history of work on how computational construction can support students in exploring academic content (e.g., Papert, 1980). The current study focuses on how CT can be integrated into mathematics at the elementary level. This work assumes a balance model of integration (Kiray, 2012) to conceptually represent the type of integration that can occur at the elementary level. As Kiray (2012) noted, there is a difference between theory and practice; even if teachers predetermine the level of integration they want to achieve, once in practice, the curriculum may not be fully integrated.

Methods.
Integrated Lesson Development: Five teachers with experience in K-5 CS/CT with support from university faculty developed the integrated units using the Everyday Mathematics 4 (EDM4) curriculum. The computing platform used was Scratch (https://scratch.mit.edu/), a block-based programming environment designed for children.
Data Sources: Data sources included integrated mathematics and CS/CT lesson plans, teacher interviews, and classroom observations. Data collection occurred during two instructional phases. Lesson plans included the Common Core State Standards for Mathematics, CT standards, critical content, students’ instructional materials, and assessments.
Data Analysis: Analysis involved coding themes in the lesson plans related to mathematics and CT and the balance between mathematics and computing instructional time. A spreadsheet was created with cells for lesson components, standards, goals, and assessments. Additionally, mathematical and computing content were coded for level of integration. The research team then conducted member checks with the teachers followed by a focus group to gain perspectives about themes related to cross-grade CT/mathematics instruction.

Results. Findings revealed that mathematics instruction was dominant and CT was important but secondary. Additionally, teachers generally did not move to CT lessons until students mastered mathematics content. Cross-grade CT concepts included looping, conditionals, decomposition, iterative design, and debugging. Within each category, concepts were introduced with increasing complexity. For example, within iterative design, the progression included: Using concrete representations of code, introducing how to design a program and then refining it for efficiency, and developing pseudo code and preplanning in writing code.

Significance, This study provides an initial insight into how mathematics and CS/CT can be integrated at the elementary level. The emerging trajectories and integrated units can be refined and amended to develop a more complete set of integrated materials that teachers can implement across the grades.

Authors

• Maya Israel, University of Illinois at Urbana-Champaign

• Quentin Wherfel

• Jelena Pokimica, University of Illinois at Urbana-Champaign