Academic journal article The Journal of Early and Intensive Behavioral Intervention

Learning Channel Intervention to Develop and Generalize Fluency in Multiplication Facts

Academic journal article The Journal of Early and Intensive Behavioral Intervention

Learning Channel Intervention to Develop and Generalize Fluency in Multiplication Facts

Article excerpt


This study demonstrates that the learning channel intervention, utilizing a continuous assessment system, enabled 3 students with special needs to build and generalize fluency in multiplication facts. This study contrasts generalization of 2 learning channels- "see-say" and "hear-say"- to see if either of the 2 channels has an advantage over the other. The data from this study suggests that the particular learning channel was influential in generalization to application. The findings of this study indicate the "hear-say" learning channel has an advantage in the generalization of learning over the "see-say" learning channel. However, this preliminary finding suggests further studies employing a design in which two intervention modes can be alternated in 2 groups of participants.

KEYWORDS: learning channels, fluency, generalization, continuous assessment, multiplication facts, SAFMEDS.


Many students lack fluency in basic math skills, thus their performance requiring applications of those skills become slow, tedious, and erroneous. Dysfluent basic math skills may even limit and prevent acquisition of advanced math skills that depend on those skills (Binder, 1996; Haughton, 1972; Starlin, 1972). For example, those students not fluent in the multiplication tables will have recurring failures with multiplication and division facts.

Fluency can be defined as the ability to perform skills and demonstrate knowledge both accurately and speedily without hesitation (Binder, 1990, 1996; Haughton, 1980). Skinner (1986) indicated the school, especially at the elementary level, has some responsibility for developing fluency in the basic skills that students will need for more complex learning at later levels. The National Council of Teachers of Mathematics (NCTM, 2000, p.32) also signifies the importance of fluency in its standards, "understanding number and operations, developing number sense, and gaining fluency in arithmetic computation form the core of mathematics education for the elementary grades."

In a typical education system, however, mastery is measured in terms of accuracy rate and students move to a next level when they acquire a certain rate of accuracy (e.g., 80%) without ensuring a fluency level. In this situation, students are usually not challenged to learn mental calculation but to be dependent on less efficient calculation methods. Particularly students with mild disabilities are often found using counting strategies (e.g., finger counting) to solve basic math facts (Casey, McLaughlin, Weber, & Everson, 2003; Skinner, Turco, Beatty, & Rasavage, 1989). NCTM (2000, p.32) recommends that mental computation in basic number skills be fluent to enhance the problem-solving process. While collecting data, it was observed that most students, who were severed in a pull-out special education program, depended on their finger-counting strategy to solve multiplication facts.

Students with disabilities, especially those with mental retardation and learning disabilities, have difficulty generalizing their learning to settings or situations that differ from the context in which they first learned those skills (Heward, 2006, p.147; Binder, 1996; DuVall, McLaughlin, & Sederstrom, 2003). Lin and Kubina (2004) described a particular problem related with learning channel where a student learned to answer addition problems visually, a "see-write" channel, but when teacher asked the student to answer orally, a "hear-say" channel, the student could not respond correctly. Such transfer or generalization of learning can be improved with a specific intervention involving ongoing measurements monitoring how students are making progress in one channel and how they transfer the learning to other learning channels.

A learning channel represents the "input" sensory modality involved with a stimulus and the "output" sensory modality or behavior contained in the response (Haughton, 1980; Lindsley, 1998, p. …

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