While students are solving complex mathematical problems, they are communicating their thinking and understanding, both formally and informally, whether they are writing or speaking out loud. Communication helps to clarify students’ thinking, prepares them for sharing their ideas in professional settings, and formal or informal feedback that allows for revision. Communication lets teachers and peers assess students’ thinking and depth of understanding. In turn, all students get the chance to improve the quality of their work.
The design of the book recognizes that not all students learn at the same pace. Research-based “spaced practice” addresses this reality by giving students the opportunity, in both classwork and homework, to practice, revisit, and eventually master and then extend ideas that may have been difficult at first. The classroom structure allows considerable opportunities for teachers to work individually with students who need assistance.
The spaced practice structure of the homework assures that students practice ideas and skills over time to consolidate their knowledge for long-term retention. Each homework set contains work with the topics just introduced, as well as problems to practice, extend, and apply previously learned skills and concepts.
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