DOI: 10.25549/usctheses-c127-655069
title: Teacher implementation of reform-based mathematics and implications for algebra readiness: a qualitative study of 4th grade classrooms

description: This study looked at 4th grade classrooms to see how teachers implement NCTM standards-based or reform-based mathematics instruction and then analyzed it for the capacity to improve students’ algebra readiness. The qualitative study was based on classroom observations, teacher and administrator interviews, and teacher surveys. The study took the perspective of instruction as interaction and mathematics as a sense making activity. The NCTM Process Standards were used to evaluate learning activities. The  Adding It Up, Strands of Mathematical Proficiency served as a qualitative metric for assessing the likeliness of the instruction to better prepare students in mathematics, specifically for algebra. Together, these standards are the basis for the Common Core State Standards for Mathematical Practice. The study also looked for student engagement in important mathematical content and ideas, particularly those necessary to prepare students for algebra. Furthermore, the study looked for rigor and an opportunity for students to struggle with important mathematics. ❧ The study observed teacher created Cognitively Guided Instruction (CGI) lessons and lessons from Contexts for Learning replacement units. Teachers implemented reform-based mathematics instruction in two ways, in distinct reform-based lessons and integrating some of the reform-based pedagogy in their traditional text-based lessons. Observation lessons revealed that students were genuinely engaged in the Process Standards for over 90% of the instructional time. Learning engaged children in understanding mathematics in the context of real-life situations, accurate computation and algebraic reasoning were stressed. Classroom sociomathematical norms were developing around the Process Standards, which served as distributed scaffolding to support children in their conceptual understanding. The study found evidence to support a bridge between social constructivist theory and reform or standards-based practice. ❧ The study determined that students engaged in qualitatively different activities from traditional classrooms which should positively impact algebra readiness. Learning emphasized important mathematical content and ideas necessary for success in algebra. Students were developing conceptual understandings of arithmetic which were explicitly connected to standard computation methods. ❧ Student solutions expressing mathematical relationships were always conveyed in both words and standard mathematical notation, and frequently in expressions or equations. The study concluded that students were making progress in each of the five Strands of Mathematical Proficiency, providing them more of the tools needed for algebra.The study found that students' engagement with the Process Standards and their trajectory in the Strands of Mathematical Proficiencies will not only serve students wishing to enter the STEM fields, but provide skills useful for academic, career, and personal facets of their life. Commonly mentioned 21st century skills, such as problem solving, critical thinking/reasoning, effective communication, flexible application of knowledge, and creativity are addressed in the Process Standards and Strands of Mathematical Proficiencies, now combined in the CCSS Standards for Mathematical Practice.