In April of 2018, Scott Hendrickson and Sterling Hilton, a professor in Educational Leadership and Foundations presented their findings, CPR for the Common Core: Using the Comprehensive Mathematics (CMI) Framework to Unpack Standards Across a Learning Cycle of Instruction, at the National Council of Supervisors of Mathematics Annual Meeting. Scott Hendrickson is a Teaching Professor who has been at BYU since 2005.
The Comprehensive Mathematics Instruction (CMI) Framework developed by the Brigham Young University Public School Partnership informs teachers on how to align Common Core State Standards along a progression from emerging ideas, strategies and representations towards more robust conceptual, procedural and representational understanding. In this presentation, participants used the CMI Framework to deepen their understanding of a subset of high school standards by selecting, sequencing and connecting these standards across a learning cycle of instruction.
For over 12 years the Comprehensive Mathematics Instruction (CMI) Framework has been used by the presenters to assist K-12 mathematics teachers in making informed decisions when aligning tasks and instructional standards. The framework assists teachers in decomposing standards into their conceptual, procedural and representational components and then sequencing those components along a continuum of understanding from emerging ideas towards more robust understanding. Once standards have been selected, sequenced and connected using the CMI Framework, learning cycles of instruction can be created that move student thinking forward from an initial “developing understanding “ phase of instruction—where ideas surface from students’ engagement in a contextualized problematic situation, through a “solidifying understanding” phase of instruction in which emerging ideas are examined and extended, and culminating in a “practicing understanding” phase of instruction where ideas are used fluently, skillfully and flexibly.
Conceptualizing a learning cycle of instruction in this way leads to deeper understanding of the targeted content standards, while also engaging students in authentic mathematical practices such as persevering in problem-solving, engaging in reasoning and justifying one’s thinking.
The Comprehensive Mathematics Instruction Framework has been developed and implemented by professors from the departments of Mathematics Education, Mathematics, Teacher Education, and Educational Leadership and Foundations along with curriculum directors and mathematics specialists from the five surrounding districts in the BYU Public School Partnership. Their work was guided by a need to articulate a framework for teaching, learning and understanding mathematics. Initially focusing on three questions—What is mathematics? What is mathematics understanding? How do you teach for mathematical understanding?–the CMI BYU-Public School Partnership committee refined this framework through literature research and ongoing professional development with elementary and secondary schools within the partnership school districts: Jordan, Alpine, Provo, Nebo, and Wasatch.
The CMI Framework provides a vocabulary for coaches and grade-level teams when discussing teaching episodes, aids in the aligning of learning targets and goals (the focus of this presentation), provides a lens for describing students’ understanding of mathematics along a continuum of deeper learning and assists teachers in making instructional decisions based on assessment of learning. The development team has found the CMI Framework useful for envisioning mathematics instruction for preservice teachers and clarifying mathematics instruction for practicing teachers.