Mathematical Practices

  • Winnetka students learn to approach problems in a variety of different ways, make conjectures and generalize, construct convincing arguments, defend their ideas orally and in writing, use precise language, determine the reasonableness of answers, and critique the arguments of others. Fluency in skills is still critical for success and learned with equal emphasis on conceptual ideas and application of those skills. These Habits of Mind, which span grade levels and ages, are part of the Common Core Math Practice Standards. They are acknowledgement of what mathematicians and math educators have long recognized: "...it is not possible to be knowledgeable about mathematics if all a person knows is mathematical content. The essential partner to mathematical content is a set of mathematical ways of thinking and reasoning that can equip a person to navigate through hard or known mathematical territory.” (Smarter Than We Think; More Messages about Math, Teaching, and Learning in the 21st Century, Cathy Seeley, 2014). They are derived from the National Research Council’s Adding It Up (2001) document which describes the five strands of mathematical proficiency (conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) as well as NCTM’s Process Standards (problem solving, reasoning and proof, communication, connections, representation) from the 1989 Curriculum and Evaluation Standards for School Mathematics and 2000 Principles and Standards for School Mathematics. You can access the Standards for Mathematical Practice by clicking here.