### Commonalities Among the Practices in Science and Engineering in the NGSS and Mathematics in the CCSS

**Standards of Mathematical Practices**

The Standards for Mathematical Practice 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).

Make sense of problems and persevere in solving them

Reason abstractly and quantitatively

Construct viable arguments and critique reasoning of others

Models with mathematics

Use appropriate tools strategically

Attend to precision

Look for and make use of structure

Look for and make use of regularity in repeated reasoning

### Standards of Scientific and Engineering Practices in the NGSS

This dimension of the NGSS focuses on important practices used by scientists and engineers: modeling, developing explanations, and engaging in argumentation. These practices have too often been underemphasized in K-12 science education. For example, all of the disciplines of science share a commitment to data and evidence as the foundation for developing claims about the world. As they carry out investigations and revise or extend their explanations, scientists examine, review, and evaluate their own knowledge and ideas and critique those of others through a process of argumentation.

Engaging in the full range of scientific practices helps students understand how knowledge develops and gives them an appreciation of the wide range of approaches that are used to investigate, model, and explain the world. Similarly, engaging in the practices of engineering helps students understand the work of engineers and the links between engineering and science.

Asking questions (for science) and defining problems (for engineering)

Developing and using models

Planning and carrying out investigations

Analyzing and interpreting data

Using mathematics and computational thinking

Constructing explanations (for science) and designing solutions (for engineering)

Engaging in argument from evidence

Obtaining, evaluating, and communicating information