Another set of connections is found between the content standards and the practice standards. These connections are absolutely essential to support the development of students’ broader mathematical understanding. To reflect the standards, the Model Content Frameworks emphasize that mathematics is not a checklist of fragments to be mastered, but that doing and using mathematics involves connecting content and practices. (PARCC Model Content Frameworks for Mathematics)
Watch the NCTM video Standards for Mathematical Practice.
There are six Math Practices Expectations that are defined in Math Trailblazers. These six Expectations remain constant throughout the curriculum and define those “habits of mind” that are related to both problem solving and communication. The Math Practices Expectations are written using “student friendly’ language so that students can use them to help them focus on practices related to both problem solving and communication. See Figure 4. Students become more comfortable with these Expectations by reviewing them before, during, and after problem solving and by deciding how well they are met in their work and the work of others. The Math Practices page is divided into two parts: Solving a problem and Showing or telling how I solve a problem. While the Standards for Mathematical Practices have always been an integral part of the curriculum, opportunities for their application are now more explicit and meaningful.
Figure 4: Math Trailblazers Math Practices page
The Standards for Mathematical Practices identify the processes and proficiencies that students should develop as a result of their mathematics education. The Standards for Mathematical Practices embody the National Council of Teachers of Mathematics (NCTM) Process Standards (2000) and five strands of mathematical proficiency outlined in the National Research Council’s Report, Adding it Up (2001). These Standards describe the way in which students should engage in the study of mathematics.
The Math Practices Expectations in Math Trailblazers embody the Standards for Mathematical Practice in the CCSSM. Figure 5 shows the intersection between the Math Practices Expectations in Math Trailblazers and the Standards for Mathematical Practices.
Figure 5: The Intersection between the Math Practices Expectations in Math Trailblazers and the Standards for Mathematical Practices in CCSSM
Figure 6 shows the intersection between those Key Ideas that identify mathematical practices with the CCSSM Standards for Mathematical Practices. In this table, each of the Common Core State Standards for Mathematical Practices are “unpacked” and aligned with the Key Ideas in Math Trailblazers.
Figure 6: Intersection between Key Ideas in Math Trailblazers and the Standards for Math Practices in the Common Core State Standards for Mathematics