4. Teaching Strategies That Raise Performance in Mathematics to Close the Achievement Gap

Mathematics matters. So does having access to strategies used by expert learners in mathematical thinking. We know that mathematical power derives from deep understanding of mathematical concepts, as well as the ability to use those concepts to translate real-world phenomena into mathematical models described in multiple symbol systems. Successful learners master concepts and relationships, then skills. Different Ways of Knowing’s coaching support and tools help teachers close the gap between developing and successful learners.

• Understanding and applying mathematical thinking to make students better problem solvers by emphasizing

— Precision: Students ask and precisely answer questions of “how many” and “how much.”
— Representation: Students represent concepts, quantities, relationships, and characteristics in models, numbers, tables, graphs, diagrams, and equations, as well as through the arts.
— Justification: Students and teachers explain their thinking and using deductive and inductive reasoning to extend and connect knowledge.
— Organization: Students organize mathematical data to recognize patterns and solve problems.

• Understanding and applying strategies for student engagement and expression focused on

  — Comprehension: Students gain a thorough understanding of mathematical vocabulary and concepts, and they know that the first step to solving any problem is to completely understand the statement of the problem.
  — Connection: Students relate mathematics concepts and skills to other mathematics concepts and skills, and to their applications in other subjects and the world.
  — Communication: Students and teachers are speaking, listening, viewing, thinking, reading, and writing with the purpose of mastering and assessing mathematical concepts, understandings, and skills.
  — Computation: Students complete mathematical operations rapidly, accurately, and with an understanding of their rationale.