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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.
Basic research on processing fluency has been applied to marketing, [29] to business names, and to finance. For example, psychologists have determined that, during the week following their IPO, stocks perform better when their names are fluent/easy to pronounce and when their ticker symbols are pronounceable (e.g., KAG) vs. unpronounceable (e.g., KGH).
The largest supporter of reform in the US has been the National Council of Teachers of Mathematics. [4]One aspect of the debate is over how explicitly children must be taught skills based on formulas or algorithms (fixed, step-by-step procedures for solving math problems) versus a more inquiry-based approach in which students are exposed to real-world problems that help them develop fluency in ...
Procedural memory is affected by Broca's aphasia. Agrammatism is apparent in Broca's aphasia patients, where a lack of fluency and omission of morphology and function words occur. While those with Broca's aphasia are still able to understand or comprehend speech, they have difficulty producing it.
The second example can only be solved using geometric knowledge, specifically that of the formula for the volume of a cylinder with a given radius and height, and requires an understanding of the concept of "rate". There are numerous skills that can be developed to increase a students' understanding and fluency in solving word problems.
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 ...
Referential questions are employed at higher rates when brainstorming a topic and gathering responses. [9] As there is no one fixed answer to referential questions, they can be used to instigate genuine communication, thereby facilitating less restricted discourse and promoting greater creativity in the classroom.
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.