This study will design a curricular framework for developing children's algebraic thinking across Grades K-2, with a particular focus on understanding how to support the teaching and learning of algebra with students in at-risk settings.
Research indicates that students need sustained algebra instruction throughout Grades K-12 mathematics education, if their informal intuitions about mathematical structure and relationships are to be transformed into the more formal ways of mathematical thinking. Currently, however, no research-based models are available to guide the development, characterization, and assessment of young children's algebraic thinking, particularly at the start of formal schooling. This study will design a curricular framework for developing children's algebraic thinking across Grades K-2, with a particular focus on understanding how to support the teaching and learning of algebra with students in at-risk settings. Study outcomes will include a prototype Grades K-2 instructional sequence, related assessments, and characterizations of progressions in students' thinking as they advance through the instructional sequence. The impact of this work would be to provide a critical roadmap for teaching and learning algebra in Grades K-2 that can clarify and deepen the role of algebra in the elementary grades, strengthen current college and career readiness standards and practices, and provide curricular support for elementary teachers in systematically developing children's algebraic thinking.
The study will use design research to develop and empirically test a K-2 Early Algebra Learning Progression prototype for diverse learners. The context for this study is a North Carolina elementary school, which consists of a student population that is 64% non-white, with 63% categorized as low SES and 27% as English Language Learners. The sample consists of approximately 60 Grades K-2 students. To empirically test the prototype's framework, learning goals, and instructional sequence, classroom teaching experiments (CTEs) will be conducted in conjunction with individual student interviews. These interviews will be conducted at three time points (pre, mid, and post) during the CTEs. Qualitative methods of analysis will be used to identify themes regarding children's understanding of core algebraic thinking practices and concepts in CTE and interview data. Quantitative methods will also be used to identify patterns of growth in students' algebraic thinking from interview data. Results will be used to refine the framework, goals, and sequence, as well as to identify levels of sophistication in children's thinking as they advance through the sequence. Interview assessments conducted during the CTEs will be analyzed for psychometric soundness to ensure they are valid and reliable. In particular, inter-rater reliability measures will be used to ensure that coding of interview data is consistent, internal consistency estimates of reliability will be calculated and used to remove or modify items, and stability of the assessment items will be examined through within-subject correlations of common items and used to remove or modify items. For validity, observed item difficulty will be correlated with predicted item difficulty by the project's expert advisory board to identify items that need modification or deletion.