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Computational fluency means more than quickly producing correct answers. It requires conceptual understanding and is exhibited through efficiency, accuracy, and flexibility. As you guide your students to mathematical fluency, you will give them many opportunities to construct relationships among numbers to make sense of basic facts and be able to retrieve them.
The Common Core State Standards identify eight mathematical practices that characterize the ways in which mathematically proficient students engage with mathematics. The content standards describe what students are doing in mathematics, and the practices describe how they are doing it.
Asking students questions and inviting them to ask questions of their own can help you discover and address their individual strengths and needs. You can tier questions and problems according to level of challenge, generally progressing from well-rooted, shared understandings toward higher-level work. This allows all students to contribute to the discussion as learning is constructed.
With the tighter focus of the CCSSM comes greater depth and increased rigor. You’ll need to offer students many opportunities to develop conceptual understanding, practice key skills, and apply their skills and understandings to novel situations and problems.
In a collaborative classroom, students share their work, think aloud, ask questions, and work together. For this sharing and collaboration to be effective, they must feel comfortable taking risks and making mistakes.
Just as your students have different learning styles, intelligence strengths, preferred tools, and ways to express themselves, they also have preferences about social interaction. All of these preferences can powerfully affect learning.
The CCSSM emphasize coherence within and across grade levels. This means that students’ experiences with a mathematical topic should be clearly tied to what they have already learned in earlier grade levels and what they will learn in the future. It also means that instruction should be carefully sequenced and that teachers should help students make connections between topics.
The first step in building a strong classroom community is getting to know your students as individuals. When children feel known, understood, and cared about, they are better able to develop relationships with you and with their peers.
The Common Core State Standards for Mathematics prompt teachers to significantly change both what they teach and how they teach it. In a series of posts, we’ll address the three characteristics of the new content standards likely to have the biggest impact on the way you teach math—tighter focus, greater coherence, and increased rigor.