IdentityThe ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week. It's imperative for teachers to focus on making sure that the students understand the material and not just memorize the procedures.
The first five minutes of the class period set the tone for the entire lesson. Ideally, teachers would start by sharing the agenda for the class period so that students will know the expectations for what will be occurring. Next, teachers could post and articulate the learning objective or essential question to the class so that students know the purpose and, at the end of the lesson, can self-assess whether the objective has been met for them. Finally, the opener might include one or more warm-up problems as a way to review and assess students' prior knowledge in preparation for exposure to the new material.
In the best classroom environment, the teacher is able to show different ways to solve the same problem and encourage the students to come up with their own creative ways to solve them. The more strategies and approaches that students are exposed to, the deeper their conceptual understanding of the topic becomes. Empowering students to create their own problem-solving methods can make the teacher nervous.
