Mathematics Standards are not isolated concepts. Standards relate to one another both within and across grades. Therefore, the Standards Maps illustrate the coherent structure that is fundamental to college-and-career ready standards. The goal of providing this to educators is to assist them in identifying gaps in a students knowledge by tracing a standard back through its logical prerequisites, visualizing and understanding how supporting standards relate to the major work of the grade, and tackling ways in which they can build student understanding by linking together concepts within and across grades.

The Common Core State Standards in mathematics were built on progressions: narrative documents describing the progression of a topic across a number of grade levels informed both by research on children’s cognitive development and by the logical structure of mathematics. The progressions can explain why standards are sequenced the way they are, point out cognitive difficulties and pedagogical solutions, and give more detail on particularly challenging areas of mathematics. These documents also provide a transmission mechanism between mathematics education research and standards.

Elementary and Middle School Mathematics: Teaching Developmentally provided an unparalleled depth of ideas and discussion to help teachers develop a real understanding of the mathematics they will teach and the most effective methods of teaching various mathematics topics. This text reflects the NCTM and Common Core State Standards and the benefits of problem-based mathematics instruction. It is structured for maximum flexibility, offering 23 chapters that may be mixed and matched to fit any course, professional development or teaching approach. This comprehensive, practical text offers readers a strong theoretical perspective reflecting the most current research on how students learn mathematics, ways to best teach it, and many conceptual and problem-based activities to engage students.

Research in mathematics education has consistently found that understanding and skills are best developed when students are allowed to wrestle with new ideas, to create and defend solutions to problems, and to participate in a mathematical community of learners. This student-centered, problem-based approach to learning is a central theme of Van De Walle’s book. Learning how best to help children believe that mathematics makes sense and that they themselves can make sense of mathematics is an exciting endeavor and a lifelong process. It requires knowledge gained from research, the wisdom shared by professional colleagues, and the insightful ideas that come from daily experiences with students.

Various performance tasks are highlighted to support conceptual understanding, procedural understanding, mathematical reasoning, and problem-solving. The overview highlights key understandings, provides a description of the activity and provides a link or visual description. These tasks can serve as supplements to the school assigned curriculum. In addition, it can help teachers assign learning activities that allow students to demonstrate their knowledge, understanding, and proficiency

As mentioned in Leverage Leadership, standards alone are meaningless until you are clear on how they are assessed. “Assessments, therefore, are the roadmap to rigor.” Participants in the Math Network are thus provided a bank of assessment items drawn from previously released items from their state assessment or similar source to ensure that teachers use this to answer the question of what they need to teach in order for students to be successful on the rigorous assessment items. In addition, having a bank of items allows teachers to test what they intended to teach instead of gearing assessments only to the needs of students. By focusing on assessment items teachers can go straight to the end game, analyze the questions, break down specific skills needed to promote student success.