In addition to conceptual knowledge, students need to develop procedural fluency in mathematics. Providing students with practice activities that build fluency is essential. Opportunities to work through multi-step problems allow students to develop the higher-level thinking skills they need in order to progress to more complicated math concepts. Students need effective strategies and ample practice to increase their fluency in basic mathematics skills such as operational facts. The only way to truly increase fluency is to combine timed activities with additional practice opportunities (Raghubar et al., 2010; Woodward, 2006).
When students become more fluent in mathematics skills, their motivation and confidence often increase. To heighten motivation, students should self-correct whenever possible for immediate feedback and then graph the results. Instructors also can integrate goal setting to further motivate and increase student self-regulation (Burns et al., 2010; Codding et al., 2009; Montague, 2007; Rock, 2005). Following is a list of suggested activities that instructors may use for fluency building practice. Many of these activities can be incorporated into peer tutoring activities.
Another benefit of fluency can be enhanced motivation. When students become more fluent in mathematics skills, their motivation and confidence often increase. To heighten motivation, students should self-correct whenever possible for immediate feedback and then graph the results. Instructors also can integrate goal setting to further motivate and increase student self-regulation (Burns et al., 2010; Codding et al., 2009; Montague, 2007; Rock, 2005). Following is a list of suggested activities that instructors may use for fluency building practice. Many of these activities can be incorporated into peer tutoring activities.
1. Timed Activities: The use of timed activities to increase fluency in demonstrating knowledge of basic facts is a mainstay of mathematics education. The purpose of timed tests is to motivate students to increase their speed and to surpass their previous scores. Although timed activities are an effective tool for building fluency, they should not be the sole mode of instruction. Instructors should explicitly teach strategies that aid students in demonstrating their knowledge of mathematical facts. It is important to note that timed activities are not a motivator for all students; the focus, therefore, should be on answering correctly as well as quickly answering questions related to mathematical facts.
*Timed activities are not appropriate for all students. Jo Boaler, Professor of Mathematics Education, Standford University.
Research suggests times tests cause math anxiety2. Flash Cards: Flash cards are often used to improve fluency in demonstrating knowledge of basic facts. They also can be used in activities such as identifying coins and their values, reading clocks, identifying fractions, and performing other mathematical tasks. Flash cards can be used with students and instructors or with peer tutors. Answers are provided on the backs of the cards so that the flash cards can be worked through quickly. Peer tutors should be taught how to correct answers so that neither peer is practicing the wrong answer during flash card activities. Students should record items scored as “incorrect” so that they can further practice the specific skills associated with these items. Students can graph the total number of flash cards answered correctly under timed conditions. This graphing can be done in tandem with goal setting to motivate the development of fact fluency.
3. Computer Software: Computer software activities, when paired with explicit teaching, can be highly engaging for students. Computer software programs provide the additional practice that struggling students need to increase mathematics fluency and accuracy. Instructors should evaluate software programs to ensure that they meet the needs of students and that they require students to actively solve problems. Effective computer software will contain clear directions and will provide students with positive and corrective feedback immediately after they have answered questions (i.e., worked through problems). Computer programs should complement, rather than replace, instructor-led learning.
4. Instructional Games: Games provide students with fun, stimulating ways to practice skills that they have already been taught. Instructional games, including board games, have been found to increase skills in estimation, magnitude comparison, identification of numbers, and counting (Ramani, Hitti, & Siegler, 2012; Ramani & Siegler, 2008; Siegler & Ramani, 2008). The games should include mathematical components and foundational skills that correlate to the state standards. Following are some common games that can be adapted for teaching most mathematical concepts:
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- Bingo: The instructor draws a card and reads the number, basic facts, fraction, or other item. Students mark the number or solution on their bingo cards. The first student who completes a row or column wins only if he or she can read all the numbers or answer all the problems in the row or column.
- Concentration/Memory: Students play the game as they would with cards; however, before students can pick up a match, they must read the numbers or solve the problem.
- Dominoes: Students play the game as they would regular dominoes by matching numbers with objects, math facts, fraction names with pictures of fractions, and so forth. Students must be able to answer the problem before they place their dominoes.
- Board games: Using commercially produced board games can assist students in counting, estimation, and understanding real-world applications of money. Board games also tend to be linear and link to understanding of measurement and fractions in later grades.
- have _____; who has _______? This game can be used to practice a variety of mathematical skills. The sentence structure “I have _____; who has _____?” is written on each card. The cards are evenly distributed among students. One card has the word Start written on it.
“I have 5; who has 6 more?”
“I have 11; who has 2 less?”
“I have 9; who has its double?”
“I have 18; who has 7 less?”
The game continues until all cards have been used. This game can be used to practice knowledge of basic facts or more advanced skills such as adding and subtracting fractions with unlike denominators.
