Procedural Fluency According to the National Research Council (NCR) (2001), the term mathematical proficiency comprises five interwoven strands consisting of conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. To assist educators, NCTM provided an explanation in Principles and Standards for School Mathematics (2000) that suggested students will reach specific levels of conceptual understanding and procedural fluency each year (p. 7) rather than every topic every year. The aim of this paper is to provide research on the process of developing procedural fluency in students, the strategies that promote procedural fluency in the classroom, and the methods for assessing procedural
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Unfortunately, many educators struggle to define fluently as only the measure of speed. King and Bay-Williams (2015) applied Baroody’s (2006) three developmental phases of basic fact mastery to describe the process that students must go through to master multiplication facts. Phase 1 consisted of the use of counting strategies, either with fingers, blocks, or marks, or verbal counting. Phase 2 included reasoning strategies to determine the answer of an unknown combination logically. Finally, Phase 3 was considered mastery as it produced practical answers. King and Bay-Williams (2015) suggested that students should be given multiple opportunities for meaningful practice to learn multiplication facts. The described meaningful practice to include the use of games to provide students with meaning and enjoyment without the use of timed tests. Games included Strive to Derive, a game involving array cards and dice, in which students roll dice to show decomposed arrays of multiplication facts. Cover It was a game in which students play together. Player 1 selected an array while Player 2 found two arrays that would completely cover the array from Player 1. Multiplication Tetris used the familiar game of Tetris so that students practiced creating arrays of multiplication facts to cover a gridded paper. The student’s goal is to stay in the game the longest. Through the use of understanding fluency, thoughtful sequencing strategies, and meaningful strategies, students can learn multiplication facts fluently (King and Bay-Williams,
Unfortunately, many educators struggle to define fluently as only the measure of speed. King and Bay-Williams (2015) applied Baroody’s (2006) three developmental phases of basic fact mastery to describe the process that students must go through to master multiplication facts. Phase 1 consisted of the use of counting strategies, either with fingers, blocks, or marks, or verbal counting. Phase 2 included reasoning strategies to determine the answer of an unknown combination logically. Finally, Phase 3 was considered mastery as it produced practical answers. King and Bay-Williams (2015) suggested that students should be given multiple opportunities for meaningful practice to learn multiplication facts. The described meaningful practice to include the use of games to provide students with meaning and enjoyment without the use of timed tests. Games included Strive to Derive, a game involving array cards and dice, in which students roll dice to show decomposed arrays of multiplication facts. Cover It was a game in which students play together. Player 1 selected an array while Player 2 found two arrays that would completely cover the array from Player 1. Multiplication Tetris used the familiar game of Tetris so that students practiced creating arrays of multiplication facts to cover a gridded paper. The student’s goal is to stay in the game the longest. Through the use of understanding fluency, thoughtful sequencing strategies, and meaningful strategies, students can learn multiplication facts fluently (King and Bay-Williams,