Common Core State Standards for Mathematics content and practice clearly drive classroom lessons. While real-world contexts and connections to the critical areas of focus provide a purpose for learning, time in lessons over the course of a unit is balanced between standards aimed at procedural fluency, conceptual understanding, and application of concepts. Students name the mathematical content and practice targets for their learning and describe how they relate to content learned previously and what’s to come.
All students focus on mathematical sense making and reasoning. All students are supported in explaining facts and procedures, justifying mathematical thinking, and making generalizations. To these ends, classroom structures enable daily equitable engagement with mathematical ideas through private reasoning time, accountable structured talk, writing, and problem-solving.
Curriculum & Pedagogy
Multiple representations of mathematics – visual, numerical/symbolic, physical/manipulative, verbal – support students’ sense making. Mathematically worthwhile tasks empower students to develop conceptual understanding and apply content and practice standards. As such, they are not simply drawn from the adopted text or a supplemental resource of interest but are carefully selected, revised, or crafted to be of high cognitive demand and aimed precisely at the intended learning target(s). The CCSS Learning Progressions and recommended CCSS resources are employed in teacher planning as teachers anticipate student strategies and misconceptions.
In line with the learning target(s) and success criteria, evidence of learning is elicited from all students at planned transitional points in each lesson through structured student math talk, relevant gestures, construction of tables/ charts/drawings, demonstration with manipulatives, calculations, and/or written work. Teachers watch and listen to students, noting/charting patterns of responses to select and sequence ideas to be shared with the full class as a form of feedback, advancing the day’s learning goals. Evidence of student progress is also used to respond to observed student needs through individual and small group additional targeted instruction.
Classroom Environment & Culture
Equity in student engagement with mathematics is ensured through the classroom structures, culture, and instructional strategies. Students ask each other questions, compare and share their mathematical thinking, and debate mathematical ideas. Mathematics serves as the source of authority in the classroom rather than social status. Effort and growth are valued, contributing to tolerance for productive disequilibrium. The physical arrangement of the room ensures access to mathematical tools/manipulatives and to classmates for collaboration.