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[20] The Panel effectively called for an end to the Math Wars, concluding that research showed "conceptual understanding, computational and procedural fluency, and problem-solving skills are equally important and mutually reinforce each other. Debates regarding the relative importance of each of these components of mathematics are misguided."
The Common Core Standards, which have been adopted by most states since 2011, adopt such a mediating position for curricula, requiring students to achieve both procedural fluency and conceptual understanding. The Common Core does not endorse any particular teaching method, but does suggest students solve word problems using a variety of ...
Conceptual and procedural knowledge develop iteratively, but the conceptual knowledge may have a greater influence on procedural knowledge than the reverse. [41] [42] Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual ...
Another thing to address is the importance of teaching and promoting multiple solution processes. Procedural fluency is often times taught without an emphasis on conceptual and applicable comprehension. This leaves students with a gap between their mathematical understanding and their realistic problem solving skills.
Rigor: Pursue conceptual understanding, procedural skills and fluency, and application with equal intensity; As an example, here is the description of one of the key shifts, a greater focus on fewer topics: [40] The Common Core calls for greater focus in mathematics.
Findings suggest that regardless of perceptual or conceptual factors, distinctiveness of processing at encoding is what affects remembering, and fluency of processing is what affects knowing. [2] Remembering is associated with distinctiveness because it is seen as an effortful, consciously controlled process. [2]
This emphasis by no means excludes the learning of number facts; indeed, a major goal of early mathematical education is procedural fluency. The NCTM in recent revisions has made more explicit this need for learning of basic math facts and correct, efficient methods. Many new editions of standards-based texts do present standard methods and ...
Declarative knowledge arises in many forms. It is possible to distinguish between them based on the type of content of what is known. For example, empirical knowledge is knowledge of observable facts while conceptual knowledge is an understanding of general categorizations and theories as well as the relations between them.