**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

The Linked Learning Advantage: Using Linked Learning to Implement the Common Core State Standards

A Stanford Center for Opportunity Policy in Education Policy Brief, October, 2012

This brief examines the Common Core State Standards and their implications for Linked Learning, an innovative high school reform approach in California that prepares students for college and career by connecting learning in the classroom with real-world applications outside of school. This brief aims to address the ways in which the common standards align with and can be adopted by Linked Learning teachers, schools, and districts to ensure that all their students are ready for success in college, careers, and citizenship.

Download the Linked Learning Advantage PDF here

The Common Core State Standards and Teacher Preparation – The Role of Higher Education

A Discussion Paper from the Science and Mathematics Teacher Imperative (SMTI)/ The Leadership Collaborative (TLC) Working Group on Common Core State Standards

Higher education plays multiple roles in ensuring the success of the Common Core State

Standards. This brief describes an action agenda for the role of higher education institutions in this collective work, including:

- Aligning higher education curriculum with K–12 curriculum
- Preparing and educating teachers, both prospective and practicing
- Conducting research on issues of teaching and learning the Common Core State Standards
- Establishing and sustaining long-term partnerships with other actors and agencies in the educational system

Download the Role of Higher Education PDF here

top of pageWebinar sponsored by California State University, Office of the Chancellor and Hosted in WestEd's SchoolsMovingUp

This webinar was sponsored by the CSU Chancellor's Office and hosted by WestEd's SchoolsMovingUp on January 30, 2014. In this webinar archive, a team of panelists from CSU, the Oakland Unified School District (California), and the math program at WestEd share perspectives on the Common Core State Standards for Mathematics. The webinar highlights the shifts in practice required of classroom teachers, as well as the implications for coursework in teacher preparation programs. **Archive Link (WebEx)**

CCSS-Math Changes, Impacts, and Responses in K-12 and CSU from Julie Duffield on Vimeo.

Dr. Ivan Cheng, Department of Secondary Education, CSU Northridge

This site contains archived presentations by Ivan Cheng from recent California Mathematics Council (CMC) meetings. You will find information on how assessments under CCSS-M will shift, advice on teaching with a “non-Common Core” text book, and example activity sheets that support development of the mathematical practices required under CCSS-M.

Click Here to view Dr. Cheng's example

**Responsive Teaching in Science**

Dr. Fred Goldberg, Professor of Physics, San Diego State University

Responsive Teaching refers to the practices of attending and responding to the substance of students' thinking. Teachers make decisions about next moves based on their sense of what students have been saying and doing, and they often entail adapting plans and objectives within a particular lesson while still working toward larger learning goals. This website is a prototype of curriculum and professional development to support responsive teaching and includes many video clips from elementary classrooms showing responsive teaching in action, professional development Case Studies, a Responsive Teaching Toolbox for managing and assessing classroom activities, Suggested Readings, and a section on “Responsive Teaching and the NGSS”.

**"Surveys Fail to Measure Grasp of Scientific Practice"**

Dr. Irene Salter, Chair, Science Education Department, CSU Chico

Dr. Leslie Atkins, Professor, Science Education Department, CSU Chico

There is debate in the science education literature about how best to improve students' understanding of the nature of science: Can an "immersion" experience in the process of doing science like scientists outperform explicit instruction on the nature of science? We report on a course in which students engaged in sophisticated scientific practices, and yet student responses to a standard nature of science survey showed surprisingly few pre-post changes. We argue that this data suggest that when students do science like scientists do, they gain a grasp of scientific practice that cannot be measured by declarative means such as surveys and interviews.

Physics Education Research Conference 2012, Philadelphia, PA: August 1-2, 2012

Volume 1513, Pages 362-365

**Web Resources in STEM Education-Examples Recommended by CSU Faculty **

Dr. Madeleine Jetter, Associate Professor, MAT Coordinator, Department of Mathematics, CSU San Bernardino recommends the following sites illustrating the use of Lesson Study for teachers of Mathematics:

Learning from the practices of others is a powerful way to improve teaching. Here, you can explore real mathematics teaching and learning by exploring everyday classrooms where educators are working to refine their mathematics teaching practices.

The Chicago Lesson Study Group provides a forum for teachers to learn about and practice lesson study as a way to steadily improve student learning.

Includes an overview of Lesson Study, videos and resources for getting started.

This article documents teacher learning through participation in lesson study, showing how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students' autonomous problem-solving, and 5) increasingly used multiple representations for solving mathematics problems.

The webinar took place on March 27^{,}2014. An overview of the Next Generation Science Standards (NGSS) and key changes from previous standards were reviewed. A team of panelists from Santa Clara COE, the Oakland Unified School District (California), and the from both CSU Sacramento and CSU Fresno presented examples about their work in NGSS.

Highlights include examples from K-12 classrooms implementing change in response to the NGSS, science preparation in the CSU system, and course requirements and content for the future. Panelists shared examples on engineering/literacy in CSU classes as potential examples for K-12.

NGSS Changes, Impacts, Responses in K-12-CSU from Julie Duffield on Vimeo.

View the WebEx URL to also access the chat

View the related webinar resources for this event

View the related webinar PowerPoints and PDFs for this event

© 2012 California State University

Concept and design by the Center for Distributed Learning