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THE VALUE OF BUILDING FLUENCY ON INDIVIDUALLY-DETERMINED ERROR SETS
IN THE TEACHING OF BASIC MATH FACTS

Angela Galvin, Michelle I. Harrington, Edward Langford, and Matthew L. Israel, Ph.D.

Judge Rotenberg Educational Center
Canton, MA USA 

The Judge Rotenberg Educational Center (www.judgerc.org) operates day and residential programs for children and adults with behavior problems, including conduct disorders, emotional problems, brain injury or psychosis, autism, and developmental disabilities. The fundamental approach taken at JRC is the use of behavioral psychology and its various technological applications, including behavioral education, programmed instruction, precision teaching, behavior modification, behavior therapy, behavioral counseling, self-management of behavior, and chart-sharing.

At the Judge Rotenberg Center the implementation of a large portion of the basic math curriculum is based on the principles of Precision Teaching. This includes conducting multiple assessment timings with participants on basic facts until they reach a high rate-per-minute correct and a low rate-per-minute incorrect within each of the curriculum steps.

Subjects worked through a curriculum of basic math facts that was presented on a computer using the see/type learning channel. The curriculum was modeled after the principles of Precision Teaching. Materials were presented in small increments. Each lesson was presented until a high rate of fluency was achieved and data were plotted on the Standard Celeration Chart (Lindsley, 1992a,). Subjects went through the addition and subtraction curriculum, or the addition and multiplication curriculum, with and without building fluency on individually-determined sets of errors that the student has made in the previous chapter. This option was automatically activated if the student answered any problem(s) incorrectly. The software presented the incorrect problem(s) and prompted the student to complete as many 20 second timings as necessary until the student made no errors. We examined how this option affected retention and if it had an effect on the amount of time it took a student to master the curriculum.

Methods

Participants and Setting

Participants in this study included 2 males, both of whom were enrolled at JRC as full-time students in the residential program. Participant 1 was aged 16 years, 3 months with a Full Sale IQ of 42. His previous diagnoses included impulse control disorder NOS, personality disorder, Hirschprung’s Disease, MR and conduct disorder. When tested in July of 2005 with the Woodcock Johnson III Test of Achievement, his Math Fluency was a 1.7GE. This placed him far below his same-aged peers whose average grade equivalence would be a 10.0GE. Participant 2 aged was 19 years, 11 months with a Full Scale IQ of 66. His previous diagnoses included cognitive DO/NOS (reported h/o), MR, Cannabis Abuse, r/o Dysthymic D/O, deficits in speech and language and sequential thinking and perceptual organizational skills. When tested in August of 2005 with the Woodcock Johnson III Test of Achievement, his Math Fluency was a 2.3GE. This placed him far below his same-aged peers whose average grade equivalence would be a 12GE.

These participants were chosen because they tested far below grade level in the area of math fluency. The participants were in the same classroom during the academic day, which was from 9AM to 3PM, Monday through Friday. Each participant used a computer that was individually configured to meet both their behavioral and academic needs. Both participants lived in JRC group homes and attended school at JRC’s main school building.

Measures and Instruction

The participants worked through a curriculum of basic math facts that was presented on a computer using the see/type learning channel. Both participants completed at least 5 timings per day. The curriculum, which was presented in small increments, was modeled after the principles of Precision Teaching. All lessons were worked on until a high rate of fluency was achieved and data was plotted on the Standard Celeration Chart (Lindsley, 1992a). The participants were presented with a math problem and typed the answer. The participants were required to answer problems at a pre-determined rate correct to move from one lesson to the next. Participants received immediate feedback for correct and incorrect responses.

Participant 1 went through the addition and subtraction curriculum. Participant 2 went through the addition and multiplication curriculum. Both participants went through the addition lessons without building fluency on individually-determined sets of errors that the student has made in the previous chapter. Participant 1 went through the subtraction lessons by building fluency on individually-determined sets of errors that he had made in the previous chapter. Participant 2 went through the multiplication lessons by building fluency on individually-determined sets of errors that he had made in the previous chapter. This option was automatically activated if the student got any problem(s) incorrect. The software presented the incorrect problem(s) and prompted the student to complete as many 20 second timings as necessary until the student made no errors.

Results

Participant 1 completed 1101 timings in fourteen addition lessons and 386 timings in fourteen subtraction lessons. Participant 1 had higher celeration rates in the lessons which required him to build fluency in individually-determined sets of errors; 10 of the 14 lessons had higher celeration. Celerations were determined using the successive timings chart. When tested in May of 2006 with the Woodcock Johnson III Test of Achievement, his Math Fluency increased to 2.9GE from 1.7GE. Participant 2 completed 445 timings in twelve addition lessons and 119 timings in twelve multiplication lessons. Participant 2 had higher celeration rates in the lessons which required him to build fluency in individually-determined sets of errors; 7 of the 12 lessons had higher celeration. Celerations were determined using the successive timings chart. When tested in May of 2006 with the Woodcock Johnson III Test of Achievement, his Math Fluency increased to 2.9GE from 2.3GE.

Participant 1

Daily, Best per day, Addition chart

Daily, Best per day, Subtraction chart

Daily, Best per day, Subtraction chart (cont)

Participant 2

Daily, Best per day, Addition chart

Daily, Best per day, Addition chart (cont)

Daily, Best per day, Multiplication chart

Discussion

There was a difference in the participants’ progress in lessons with and without building fluency on individually-determined sets of errors. The participants completed fewer timings and had a higher celeration by building fluency on individually-determined sets of errors as well as increasing their math fluency. Further study can examine the effects of building fluency on individually-determined sets of errors on other math operations or other academic areas that are too difficult for the student.

References

Lindsley, O. R. (1992a). Precision teaching: Discoveries and effects. Journal of Applied Behavior Analysis, 25, 51-57.

McDermott, P., & Watkins, M. (1983). Computerized vs. conventional remedial instruction for learning disabled pupils. The Journal of Special Education, 17(1), 81-88.

Chiang, B. (1986). Initial learning and transfer effects of microcomputer drills on LD Participants' multiplication skills. Learning Disability Quarterly, 9(2), 118-123.