There are important relationships and convergences are found between the CCSS-M Standards for Mathematical Practices and the CCSS-E/LA student-centered expectations, referred to as the "portrait of students who meet the standards”.
The student portrait detailed within the CCSS-ELA standards is detailed as student “capacities” and has similarities with the mathematical practices in the CCSS-M. The ELA capacities include:
E1. They demonstrate independence.
E2. They build strong content knowledge.
E3. They respond to the varying demands of audience, task, purpose, and discipline.
E4. They comprehend as well as critique.
E5. They value evidence.
E6. They use technology and digital media strategically and capably.
E7. They come to understanding other perspectives and cultures.
The CCSS-M standards for mathematical practices include:
M1. Make sense of problems and persevere in solving them.
M2. Reason abstractly and quantitatively.
M3. Construct viable arguments and critique the reasoning of others.
M4. Model with mathematics.
M5. Use appropriate tools strategically.
M6. Attend to precision.
M7. Look for and make use of structure.
M8. Look for and express regularity in repeated reasoning.
The Standards for Mathematical Practices describe varieties of expertise that mathematics educators at all levels should seek to develop in their students. These practices rest on important “processes and proficiencies” with longstanding importance in mathematics education. The first of these are the NCTM process standards of problem solving, reasoning and proof, communication, representation, and connections. The second are the strands of mathematical proficiency specified in the National Research Council’s report Adding It Up: adaptive reasoning, strategic competence, conceptual understanding (comprehension of mathematical concepts, operations and relations), procedural fluency (skill in carrying out procedures flexibly, accurately, efficiently, and appropriately) and productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).
Similarities Between CCSS-Mathematics Practices and NGSS Science and Engineering Practices
Similar to CCSS-ELA 1, in which students demonstrate independence, the CCSS-M1 emphasizes students’ making sense of problems and persevering in solving them. Another example is seen in comparing E4, which focuses on students’ comprehending as well as critiquing and M3, which addresses constructing viable arguments and critiquing the reasoning of others. Another example of the parallels is seen in comparing E5—students’ valuing evidence with M6—attending to precision. Still another is found in E6—students’ using technology and digital media strategically and capably and M5—using appropriate tools strategically.
There are intentional connections among the CCSS-ELA portrait/capacities and the CCSS-M mathematical practices enable teachers to foster critical habits of mind across the disciplines.
© 2012 California State University
Concept and design by the Center for Distributed Learning