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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 ...
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.
They also demonstrated that when students practice classifying algebraic transformations using PLMs, the results show remarkable improvements in fluency at algebra problem solving. [57] [74] [75] These results suggests that perceptual learning can offer a needed complement to conceptual and procedural instructions in the classroom.
A classroom in Norway. Learning theory describes how students receive, process, and retain knowledge during learning. Cognitive, emotional, and environmental influences, as well as prior experience, all play a part in how understanding, or a worldview, is acquired or changed and knowledge and skills retained. [1] [2]
[a] More simply put, concepts are the mental categories that help us classify objects, events, or ideas, building on the understanding that each object, event, or idea has a set of common relevant features. Thus, concept learning is a strategy which requires a learner to compare and contrast groups or categories that contain concept-relevant ...
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]
"In-depth understanding requires detailed knowledge of the facts within a domain. The key attribute of expertise is a detailed and organized understanding of the important facts within a specific domain." Thus, the debate within education between advocates of deep conceptual understanding and advocates of broad factual understanding misses the ...