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The Impact of the Common Core Standards on Mathematics in Community Colleges

Andres Marti, SFUSD

CMC³ Fall Conference

December 10, 2016

Common Core State Standards for Mathematics (CCSS-M)

CCSS-M Themes

• FOCUS – Developing deep conceptual understanding that lays the foundation for future learning.

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• COHERENCE – Building conceptual understanding over multiple years through research-based learning trajectories.

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• RIGOR – Balancing conceptual understanding (the ability to access concepts from multiple perspectives and apply them to new situations) with procedural skill and fluency.

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Focus and Coherence in Algebra

Rigor

• Rigor is redefined as the ability to access math concepts and apply them to new situations.

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• Rigorous courses must increase students’ depth of understanding and their ability to communicate this understanding.

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• All students in every grade should have rigorous courses that balance conceptual understanding with procedural skill and fluency.

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• No longer means pushing content down into earlier grades.

Standards for Mathematical Practice

1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.

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High School Content Shifts

• Functional approach to algebra.

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• Transformational approach to geometry.

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• Integration of statistics and probability throughout secondary grades.

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• Emphasis on modeling.

CST Test Item

Smarter Balanced (SBAC) Test Item

Rich Math Tasks

A rich math task takes time to solve and lends itself to collaboration and multiple perspectives. Robust use of these tasks creates the context in which students build multiple representations and communicate their reasoning.

Partners:

• Silicon Valley Mathematics Initiative
• Oakland Unified School District
• Complex Instruction Program

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Classifying Solutions to Systems of Equations

Norms:

• Work in the middle
• Everyone touches the cards
• Justify your reasoning aloud
• Stay together

Card Set A: Equations, Tables, Graphs

1. Share the cards between you and spend a few minutes, individually, completing the cards so that each has an equation, a completed table of values and a graph.
2. Record on paper any calculations you do when completing the cards. Remember that you will need to explain your method to your partner.
3. Once you have had a go at filling in the cards on your own:
1. Explain your work to your partner.
2. Ask your partner to check each card.
3. Make sure you both understand and agree on the answers.
4. When completing the graphs:
1. Take care to plot points carefully.
2. Make sure that the graph fills the grid in the same way as it does on Cards C1 and C3.

Make sure you both understand and agree on the answers for every card.

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Card Set B: Arrows

1. You are going to link your completed cards from Card Set A with an arrow card.

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• Choose two of your completed cards and decide whether they have no common solutions, one common solution, or infinitely many common solutions. Select the appropriate arrow and stick it on your poster between the two cards.

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• If the cards have one common solution, complete the arrow with the values of x and y where this solution occurs.

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• Now compare a third card and choose arrows that link it to the first two. Continue to add more cards in this way, making as many links between the cards as possible.

How does this activity help develop math practices?

• Make sense of problems and persevere in solving them.
• Reason abstractly and quantitatively.
• Construct viable arguments and critique the reasoning of others.
• Model with mathematics.
• Use appropriate tools strategically.
• Attend to precision.
• Look for and make use of structure.
• Look for and express regularity in repeated reasoning.

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SFUSD Math Principles

• All students can and should develop a belief that mathematics is sensible, worthwhile, and doable.
• All students are capable of making sense of mathematics in ways that are creative, interactive, and relevant.
• All students can and should engage in rigorous mathematics through rich, challenging tasks.
• Students’ academic success in mathematics must not be predictable on the basis of race, ethnicity, gender, socioeconomic status, language, religion, sexual orientation, cultural affiliation, or special needs.

SFUSD Class of 2014

SFUSD Class of 2015

Tracking

SFUSD Secondary Course Sequence

All secondary schools provide all students the same course sequence aligned to the CCSS-M.

Algebra in 8th and 9th Grade

Core Curriculum

SFUSD Math Core Curriculum is based on groups tasks that focus on making sense of the concepts, supporting multiple abilities, and expanding what “doing math” means beyond procedural fluency.

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Making sense of Solutions to a System of Equations

Teaching Strategies to Encourage Discourse

• Three-Read Protocol

Support English Learners and other students to make sense of quantities and units in text.

• Math Talks

Validate different ways thinking and need to clearly communicate mathematical ideas.

• Participation Quiz

Reinforce norms for working collaboratively in groups and having productive discourse.

• Multiple Abilities Launch

Identify strengths that expand what it means to do math and to be smart in math.

Professional Development for Teachers

• Do math together.
• Experience activities and strategies that give all students opportunities to engage.
• Engage in deep planning that attends to the learning of all students (consider access, rigor, and structures for participation).
• Use video to develop a vision of productive discourse in heterogeneous groups.

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Complex Instruction

• Based on research by Cohen and Lotan addressing status issues in groupwork and strategies to address them.
• Active in half of high schools since 2009, expanded to half of middle schools in 2014.
• Foundation of our support for teachers to make heterogeneous classes work for all students.

Changing Belief Systems of Who Can Succeed in Math

• Core curriculum based on rich math tasks.
• Teaching strategies that encourage student discourse.
• Professional development focused on supporting multiple abilities.
• Policy changes and coaching support for heterogeneous classes.
• Public campaign about growth mindset to address concerns of parents, administrators, and teachers.

Growth Mindset

Questions and Comments

Please share your thoughts, insights, and questions so that I can learn from you too!

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• How can community colleges build upon the shifts described in the CCSS-M?

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• How might you incorporate a growth mindset approach in your teaching?

Thank You!

Andres Marti

Math Content Specialist

martia@sfusd.edu

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Information and resources on our website:

sfusdmath.org

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