Effective math instruction begins when educators have high expectations of students and believe that all students have the potential to learn and do math. It uses culturally relevant practices and differentiated learning experiences to meet individual students’ learning needs. It focuses on the development of conceptual understanding and procedural fluency, skill development, communication, and problem-solving skills. And it involves educators choosing from and using a variety of high-impact instructional practices (Hattie, 2009; National Council of Teachers of Mathematics, 2014).
To learn more about these High Impact Instructional Practices, check out this resource that is included in the new Mathematical curriculum.
Direct instruction is a concise, intentional form of instruction. It uses clearly communicated learning goals, introduces models and representations in context, and incorporates questioning and brief activities. It verbalizes thought processes, defines and uses math vocabulary, and makes key concepts and connections explicit. Direct instruction checks for understanding, summarizes the experience, and provides feedback. It can involve the whole class, small flexible groups, or individual students. Effective direct instruction is not a lecture. It is not didactic, educator-led talking from the front of the classroom (Hattie, 2009).
Practice is a necessary component of an effective math program. Practice is best when it is deliberate, purposeful, and spaced, and it can take many forms – math games, math stations, and paper-and-pencil tasks – any of which can be done independently or with a partner. Regardless of the form of practice, ongoing feedback is crucial, so that students know that they are practicing correctly and that they have practiced sufficiently. This ensures that practice is as effective as possible.