The Common Core Mathematical Content Standards provide clear but challenging expectations for students stressing conceptual understanding, procedural skill and fluency and problem solving. The Content Standards are centered on the principles of focus and coherence. Focus in the math classroom means going deeper on fewer core mathematical concepts in order to really master them which in turn leads to more meaningful engagements in later grades. Coherence is ensuring that it all fits together in a logical progression across grade levels—that students come into each grade with the foundational preparation necessary to learn new and challenging concepts and that teachers understand how those concepts will build and develop in future grades.
The Common Core Mathematical Practices reflect how students should engage with the math content to master skills and underlying concepts. They require that students be able to speculate, reason, defend and debate their thinking and solve problems in more than one way. Students should have a clear understanding not just of how to do the math but an understanding of why—to be able to apply that math to problems in other disciplines and in real life.
The logical progressions of the Content Standards coupled with the “processes and proficiencies” of the Mathematical Practices provide an excellent foundation to help students make sense of math. But as noted by the Common Core designers themselves:
Standards by themselves cannot raise achievement. Standards don’t stay up late at night working on lesson plans, or stay after school making sure every student learns—it’s teachers who do that.
As we prepare our students for college and career readiness in an age of increasingly diverse classrooms, the challenges increase to ensure that math “makes sense” for all students. Vastly differing backgrounds, knowledge, experience and learning styles require us, as educators, to become more flexible—shifting both the “what” AND the “how” of our math instruction.
Creative Professional Learning
Over the next few months we will explore ways you can design your professional learning program in order to realize the aspirational goals of the Common Core to help your students “Make Sense of Math.” Our design for this series of articles and ideas is based on the ancient Chinese Tangram—a puzzle of geometric pieces that can be combined to form an almost endless variety of shapes. We consider the Tangram a perfect metaphor not only for the individual ways we (and your students) each “Make Sense of Math” but it is also an ideal metaphor for our commitment to helping you design a unique professional learning solution tailored to your district, your school and your students.
Drawing upon academic work and our own classroom-grounded research and experience, Math Solutions has identified the following four instructional needs as absolutely essential to improving instruction and student outcomes:
• Robust Content Knowledge
• Understanding of How Students Learn
• Insight into Individual Learners through Formative Assessment
• Effective Instructional Strategies
These four instructional needs drive the design of all Math Solutions courses, consulting and coaching. We consider them our guiding principles and strive to ensure that all educators:
Know the math they need to teach—know it deeply and flexibly enough to understand various solution paths and students’ reasoning.
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Understand the conditions necessary for learning, what they need to provide, and what students must make sense of for themselves.
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Recognize each student’s strengths and weaknesses, content knowledge, reasoning strategies, and misconceptions.
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Have the expertise to make math accessible for all students, to ask
questions that reveal and build understanding, and help students make sense
of and solve problems.
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