Math Instruction What’s in and What’s out

What’s in and What’s out! Common Core Instruction

No. 1 thing that is in… Knowing what math is used for!!

Make sense of problems and persevere in solving them What’s InWhat’s Out Teachers facilitate discussion in problem solving. Students are involved in classroom discourse with one another, making conjectures and planning solutions. Students are actively engaged and are visibly thinking – students are DOING math. Teachers are allowing time for productive struggle. Teacher lecturing/demonstrating for an extended period of time Students passively taking notes Students are following PROCEDURES Quiet classrooms

Reason abstractly and quantitatively What’s In What’s Out Students are encouraged to provide a range of representations and solutions of math problem situations. Opportunities for students to make sense of quantities and their relationships in problem situations. Engaged in problems that require flexible use of properties of operations and objects. Students are expected to do certain problems using a certain method Formulaic problems that require little critical thinking. Students attending only to the memorization of rules/procedures.

Constructing viable arguments and critiquing the reasoning of others. What’s InWhat’s Out Students are given opportunities to make conjectures – inquiry. Students are given opportunities to construct arguments and critique arguments of others in writing and through dialogue. Students are encouraged to justify their conclusions and communicate them to others. Students work independently in silence. Assignments are based strictly on procedures and following algorithms. Teacher telling students how to solve problems.

Model with Mathematics What’s InWhat’s Out Opportunities to apply the mathematics they know to everyday life, society and the workplace. Rich tasks that focus on conceptual understanding and relationships. Students analyze relationships and draw conclusions based on assumptions. Manufactured “real- life” problems that only require knowing a formula. Problems focused only on procedures and concepts

Use appropriate tools strategically What’s InWhat’s Out Problem solving tasks that require students to consider a variety of tools for solving (tools might include pencil/paper, concrete models, ruler, protractor, scientific or graphing calculator, spreadsheet, various software programs, etc.) The use of technology tools to explore and deepen the understanding of concepts. The use of calculators is never allowed. Limited access to mathematical tools in the classroom. The use of technology is not an integral part of the learning environment.

From What’s Out to What’s In Making the shift

Make sense of problems and persevere in solving them What We Want to See Examples Teachers facilitate discussions in problem solving. Students are involved in classroom discourse with one another, making conjectures and planning solutions. Students are actively engaged in solving problems and thinking is visible. Teachers are allowing time for problem solving and practice. Open-minded problem with no solution pathway evident; may have more than one right answer. Collaborative work environment in which students are discussing and sharing ideas. Teacher asks probing questions to facilitate discussion. Teacher gives students help grappling with problems.

Reason abstractly and quantitatively What We Want to See Examples Students are encourages to provide a range of representations and solutions of math problem situations. Opportunities for student to make sense of quantities and their relationships in problem situations. Engaged in problems that require flexible use of properties of operations and objects. Tasks that allow for pausing during the manipulation process; students show understanding of what symbols represent. Provide rich tasks that require the use of symbols. Students regularly consider units involved in problem situations.

Constructing viable arguments and critiquing the reasoning of others What We Want to See Examples Students are given opportunities to make conjectures and explore the truth of their conjectures. Students are given opportunities to construct arguments and critique arguments of others in writing and through dialogue. Students are encouraged to justify their conclusions and communicate them to others. Tasks that allow students to analyze situations by breaking them into cases. Tasks that require students to justify, defend/refute and communicate examples and counterexamples. Classroom environment encourages the exchanged of ideas between students – with facilitation from teacher.

Model with mathematics What We Want to See Examples Opportunities to apply the mathematics they know to everyday life, society and the workplace. Rich tasks that focus on conceptual understanding and relationships. Students analyze relationships and draw conclusions based on assumptions. Problem solving situations that require students to develop essential questions. Problem solving situations that require students to use a variety of mathematical concepts.

Use appropriately tools strategically What We Want to See Examples Problem solving tasks that require students to consider a variety of tools for solving (tools might include pencil/paper, concrete models, ruler, protractor, scientific or graphing calculator, spreadsheet, various software programs, etc). Students are familiar with appropriate tools and make sound decisions about when each tool might be helpful. The use of technological tools to explore and deepen the understanding of concepts. Problems solving situations that require students to use technology. Problem solving situations that involve concrete models. Technology is used to enhance solutions, not distract from. Students are encouraged to share their own ideas about using technology to solve problems.

Attend to precision What We Want to See Examples Opportunities for students to explain and/or write their reasoning to others. Students use and clarify mathematical definitions in discussions and in writing. Students calculate accurately and efficiently, understand and state the meaning of symbols, and express numerical answers with a degree of precision. Performance tasks with rubrics. Students work collaboratively using correct academic language. Students examine claims and make explicit use of definitions.

Look for and make use of structure What We Want to See Examples Opportunities and time for students to explore patterns and relationships to solve problems. Teacher facilitates conceptual understanding through problem solving. Problems that encourage the use of patterns. Students are given time to investigate and use intuition.

Look for and express regularity in repeated reasoning What We Want to See Examples Problem situations that allow students to explore regularity and repeated reasoning. Through the use of regularity, students are led to generalizations which may include formulas. Students notice if calculations are repeated, and look both for general methods and for shortcuts. Problems that encourage multiple methods. Problems that require multiple steps/sub- problems to work through.

Possibilities The Common Core State Standards offer the possibility and potential for all students to access math curriculum…it is up to us to do our part to ensure that happens.