Mathematics

There are 5 elements of math proficiency

National Academies report Adding It Up (2001b, p. 107)

Conceptual Understanding

Comprehension of mathematical concepts, operations, and relationships

Procedural Fluency

Skill in choosing the best method to do operations and in doing them correctly

Strategic Competence

Ability to figure out how to turn problems into a solvable form and then solve them

Adaptive Reasoning

Ability to think logically and explain arguments

Productive Disposition

Tendency to see math as useful and worth learning

Traditionally, math classes have focused almost exclusively on procedural fluency, but all five elements depend on each other to create real proficiency.

THEREFORE

Math education requires more time spent on discussion, practice with feedback, and understanding key ideas and strategies.

AND

Those discussions need to focus on the interconnectedness of mathematical concepts and how mathematical argument works.