The Core Connections courses are built on rich, meaningful problems and investigations that develop conceptual understanding of the mathematics and establish connections among different concepts. The lesson problems are non-routine and team-worthy, requiring strategic problem solving and collaboration. Throughout the course, students are encouraged to justify their reasoning, communicate their thinking, and generalize patterns.
In each lesson students work collaboratively in study teams on challenging problems. The teacher is continuously providing structure and direction to teams by asking questions and giving clarifying instructions. The teacher gives targeted lectures or holds whole-class discussions when appropriate. The teacher has the freedom to decide the level of structure or open-endedness of each lesson. While students are in teams, the teacher checks for understanding by questioning students’ thinking and asking students to justify their solutions. Questioning is informative to both the teacher and the student as it guides the students to the learning target. At the close of each lesson, the teacher ensures that the students understand the big mathematical ideas of the lesson.
The homework in the “Review & Preview” section of each lesson includes mixed, spaced practice, and prepares students for new topics. The homework problems give students the opportunity to apply previously-learned concepts to new contexts. By solving the same types of problems in different ways, students deepen their understanding. CPM offers open access homework support at homework.cpm.org.