Designing a Math Classroom that Returns on Investments
Peter Drucker, the well know management consultant, educator and author is famous for saying, “What gets measured, gets managed,” reflecting his core belief that taking action without thinking is the cause of every failure. As educators, we clearly understand this idea relative to student performance—by evaluating what students know and understand we can better provide the support they need to be successful. However, to create a truly effective, uniquely targeted improvement strategy, it is important to understand not just what students need but to have a clear understanding of what support teachers need to create a successful classroom experience.
The best way to do this is to understand and benchmark your mathematics classrooms on key success indicators relative to the learning environment, reasoning & sense making, focus & coherence, and formative assessment. By understanding what you do well and critical challenges that need immediate attention, you will be in an excellent position to prioritize key challenges and develop a strategic professional learning plan with clearly defined milestones and metrics that promotes instructional strategies that lead to student achievement.
Common Core Connections
Learning Environment: The Common Core Standards of Mathematical Practice call upon students to speculate, reason, defend and debate their thinking an solve problems in more ways than one. These eight practices, which span all grades—Kindergarten through grade 12—reflect the most advanced and innovative thinking on how students interact with math content to master essential skills and their underlying concepts. At its most fundamental, an effective learning environment is one in which students are expected and feel safe to take risks, share their ideas and learn from their classmates—to develop the “processes and proficiencies” necessary to make math make sense.
Reasoning & Sense Making: Among the highest priorities of the Common Core is for students to build a deep understanding of mathematics and use that understanding to reason about problems, make sense of new learning, and communicate their thinking to others. They are expected not only to have knowledge of procedures—when and how to perform them (doing so flexibly, accurately and efficiently)—but they should also understand the underlying concepts—developing the skill, fluency, conceptual understanding and perseverance required for college and career.
Focus & Coherence:
The Common Core Mathematical 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 dynamic process of ongoing assessment through listening, observation, examination and guided questioning allows teachers to determine their students’ comprehension of rigorous content and ideas. This understanding enables teachers to adjust—real-time—their presentation of the material, responding to different approaches and learning styles thereby making the math accessible for all of their students.
Cathy Seeley, Past President of NCTM and author of the 2009 AEP award-winning book Faster Isn’t Smarter: Messages About Math, Teaching, and Learning in the 21st Century recommends two key ideas for creating rich learning environments: Upside-Down Teaching and Constructive Struggle.
Dr. Seeley explains that one of the key differences between math classes in the U.S. and high-performing Japan is how the information is presented in a typical class flow. In the U.S. we tend to demonstrate a procedure, assign similar problems for exercise and then assign homework to reinforce the idea whereas in Japan, teachers take a different approach. They present a problem without demonstrating how to solve it, they facilitate individual or group problem solving, they compare and discuss multiple solution strategies and then summarize and assign homework.
Dr. Seeley further notes that the problems presented are often tough, stretch goals for the students enabling them to “constructively struggle” which is a good thing:
When we introduce complexity in the problems we ask students to solve and challenge them beyond what they think they can do, we give them the opportunity to struggle a bit—an opportunity that many students never experience in mathematics from elementary school through high school. A look at those American classrooms where teachers and students invite complexity shows that the kind of mathematics problems students can really sink their teeth into (and consequently might struggle with) are often more interesting and engaging than the problems we have traditionally provided in math classrooms. It turns out that offering students a chance to struggle may go hand in hand with motivating them, if we do it right.
into your classroom by doing the following:
- Start with a rich problem that has multiple entry points
and allows a variety of strategies
- Engage students in dealing with the problem
- Discuss, compare, interact ensuring a supportive
environment that encourages respect
- Help students connect and notice what they’ve learned
- Assign exercises & homework
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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