During the last several decades, mathematics reform has emphasized the goal of ensuring that students develop both conceptual and procedural understanding in mathematics. The current mathematics reform, Common Core State Standards for Mathematics (National Governors Association and the Council of Chief State School Officers [NGA Center & CCSSO], 2010), promotes this goal, with procedural knowledge building upon a strong conceptual base. This study uses content analysis to investigate the extent and ways in which Houghton Mifflin Harcourts Go Math! K-8 (HMH, 2016) supports teachers in building procedural fluency from conceptual understanding when teaching equivalence of fractions.Krippendorfs (1980) framework for content analysis guided this study. I identified a priori codes, and allowed for emergent codes, that characterize quality mathematical instruction. Careful analysis of the teacher editions of the textbook series revealed that, if the teacher instructions are to be followed with fidelity, students are not given opportunities to create and share their own strategies for solving tasks designed to help them learn equivalence of fractions. Neither are they given opportunities to make connections among strategies. All connections are introduced by the teacher. Although the teacher editions promote transitions from visual models to algorithms, they provide inconsistent use of problem-solving practice tasks and equal-sharing problems, two methods that are strongly supported by the research literature for developing procedural fluency from conceptual understanding in equivalence of fractions. Finally, the teacher materials include multiple instances in which the same or similar language and terms are used for mathematical and pedagogical practices found in mainstream research and professional literature, yet the practices were to be implemented in ways contrary to mainstream interpretations.Overall, Go Math! K-8 (HMH, 2016) provided little support to teachers in helping students build procedural fluency from conceptual understanding. A teacher-driven, rather than student-driven, approach to instruction was emphasized, thus minimizing opportunities for students to engage in the kinds of tasks and discourse recommended in the literature. The ways in which mathematical language and terms were implemented contrary to mainstream research interpretations can easily cause confusion among educators. The dearth of authentic problem-solving practice was inconsistent with quality mathematics instruction that supports students conceptual and procedural understanding.



College and Department

David O. McKay School of Education; Teacher Education

Date Submitted


Document Type





conceptual understanding, latent content analysis, mathematics instruction, procedural fluency, reform perspective, textbook analysis