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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 ...
[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."
[19] [20] Baroody proposed an iterative view of conceptual and procedural development view—a middle ground perspective between the skills-first view and the some-concepts-first view. [ 21 ] [ 22 ] According to the iterative view, children gradually construct an understanding of small numbers by seeing examples of a number labeled with a ...
Conceptual understanding precedes procedural skill. [38] Instruction about concepts as well as procedures can lead to increased procedural skill. [39] And increasing conceptual knowledge leads to procedure generation. [40] [41] However, this relationship is not unidirectional. Conceptual and procedural knowledge develop iteratively, but the ...
Curricula that support starting from conceptual understanding, then developing procedural fluency, for example, AIMS Foundation Activities, [6] frequently use multiple representations. Supporting student use of multiple representations may lead to more open-ended problems, or at least accepting multiple methods of solutions and forms of answers.
There is an ongoing discussion of relationships between memory, procedural fluency with algorithms, and conceptual understanding of elementary mathematics. Sharing songs, rhymes, visuals and other mnemonics is popular in teacher social networks.
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.
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]