Incremental Rehearsal

Study: Burns (2005)

Burns, M. K. (2005). Using Incremental Rehearsal to Increase Fluency of Single-Digit Multiplication Facts with Children Identified as Learning Disabled in Mathematics Computation Education and Treatment of Children, 237-249.

Descriptive Information


Acquisition and Cost

Program Specifications and Requirements


A student is presented with flashcards containing unknown items added in to a group of known items. Presenting known information along with unknown can increase retention of the newly learned items, behavioral momentum and resulting time on task. Research shows that this technique can be used with sight/vocabulary words, simple math facts, letter names, and survival words/signs.

Incremental Rehearsal is intended for use in Kindergarten through eighth grade. The program is intended for use with students with disabilities (including learning disabilities and intellectual disabilities), and any student at risk of academic failure. The academic area of focus is early literacy (alphabet knowledge), reading (fluency), and mathematics (computation).

Where to Obtain: 
The intervention is an instructional technique that is available to anyone.

The intervention is listed on several websites including: and

Cost: Incremental Rehearsal is a non-commercial intervention and, therefore, does not have a formal pricing plan.

It is recommended that Incremental Rehearsal is used with individual students 10-15 minutes per session, three to four days a week, for 10-15 weeks.

The program does not include a highly specified teacher’s manual.

Incremental Rehearsal does not require technology.

Training is not required for the instructor.

The minimum qualifications of instructors are that they must be paraprofessionals. The program does not assume that the instructor has expertise in a given area. 

Training manuals and materials are available. The technique is described in two places. There is an unpublished document (Tucker, 1988) that is available for free from the author and is included in this application. It is also described in Tucker & Burns (2016), which is available for free to members of the National Association of School Psychologists and is included in this application. The technique has also been described in the dozens of articles that have been published about it.


Participants: Convincing Evidence

Sample size: Three children identified with a learning disability (LD) in mathematics computations, according to Michigan special education regulations, were randomly selected for participation in the study. Each student received mathematics instruction in a special education resource room within the same district in central Michigan, but within three different elementary schools. All children identified as LD in mathematics computation in these three resource rooms were identified as potential participants. Next, the three special education teachers identified those students labeled as LD in mathematics who lacked adequate fluency with single-digit multiplication facts to the degree that interfered with computation of double-digit problems. Finally, one name was selected from each of the lists generated by the three teachers by assigning a number to the students and selecting a number from a random number table.

Risk Status: Each student was identified as LD in mathematics and as lacking fluency of single-digit multiplication facts. Student scores from the most recent multi-disciplinary evaluation team assessment found Wechsler Intelligence Scale full-scale intelligence quotients that fell within the average range (age-based standard scores between 90 and 110), and the students' age-based mathematics computation standard scores on the Woodcock-Johnson Test of Achievement fell between 75 and 85.






Socioeconomic Status

Disability Status

ELL Status

Other Relevant Descriptive Characteristics

Case 1: Student 1




Not Reported


English Speaker

Student 1 was an 8-year old third grade student. The median baseline score was 3 digits correct per minute on a single-digit multiplication probe.

Case 2: Student 2




Not Reported


English Speaker

Student 2 was an 8-year old third grade student. His median baseline score was 8 digits correct per minute on a single-digit multiplication probe.

Case 3: Student 3




Not Reported


English Speaker

Student 3 was an 8-year old third grade student. Her median baseline score was 11 digits correct per minute on a single-digit multiplication probe.

Training of Instructors: Student researchers were white female undergraduate special education teacher candidates participating in an undergraduate assessment course taught by the author. Before beginning the project, each student researcher participated in 2 hours of training regarding intervention procedures and research, and 2 hours of instruction in conducting CBM for different academic areas including mathematics. Next, each student researcher was observed by the author within the first week of being placed within the special education classrooms to assess the fidelity of implementation and deliver guided practice.

Design: Partially Convincing Evidence

Does the study include three data points or sufficient number to document a stable performance within that phase?: Yes

Is there opportunity for at least three demonstrations of experimental control?: No

If the study is an alternating treatment design, are there five repetitions of the alternating sequence?: N/A

If the study is a multiple baseline, is it concurrent?: Yes

Fidelity of Implementation: Partially Convincing Evidence

Describe when and how fidelity of treatment information was obtained: A second observation by the author occurred during the 13th week to again assess the fidelity of implementation. A checklist containing 16 items was used to assess implementation fidelity during the second observation. Items on the checklist addressed fidelity of treatment condition procedures and conducting the mathematics fluency probes.

Provide documentation (i.e., in terms of numbers) of fidelity of treatment implementation: On average, the student researchers correctly completed 96%, with a range of 94% to 100%, of the necessary steps for implementation on both the treatment and assessment probes.

Measures Targeted: Convincing Evidence

Measures Broader: Data Unavailable

Targeted  Measure

Reliability Statistics

Relevance to Program Instructional Content

Exposure to Related Content Among Control Group

Single-Digit Multiplication Probes

Interrater = 0.99 (and 98.8% agreement).

Alternate form = 0.89, interrater = 0.99, and reliability of slope = 0.75 for third-grade students on computation probes (NCII Academic Progress Monitoring Tools Chart for math computation with 3rd grade students).

The measure was based on all possible single-digit multiplication combinations because the study taught unknown multiplication facts.

No other rehearsal of single-digit multiplication facts occurred during the baseline phase, but each student was taught multi-digit multiplication with base-ten blocks and rehearsed single- and double-digit problems with untimed worksheets.



Broader  Measure

Reliability Statistics

Relevance to Program Instructional Content

Exposure to Related Content Among Control Group






Number of Outcome Measures: 1 Math

Mean ES - Targeted: Data Unavailable

Mean ES - Broader: Data Unavailable

Effect Size:

Visual Analysis (Single Subject Design): Convincing Evidence

Description of the method of analyses used to determine whether the intervention condition improved relative to baseline phase (e.g. visual analysis, computation of change score, mean difference): The study reported visual analysis and a percentage of nonoverlapping data.

Results in terms of within and between phase patterns: There was an immediate and positive change in level for each student and all three sets of data resulted in 100% nonoverlap between baseline and intervention. Moreover, baseline data were stable with a flat trend, but the intervention data for all three students had an upward trend.

Disaggregated Data for Demographic Subgroups: No

Disaggregated Data for <20th Percentile: No

Administration Group Size: Individual

Duration of Intervention: 10-15 minutes, 3-4 times a week, 10-15 weeks

Minimum Interventionist Requirements: Paraprofessional, Training is not required

Reviewed by WWC or E-ESSA: No

What Works Clearinghouse Review

This program was not reviewed by What Works Clearinghouse.


Evidence for ESSA

This program was not reviewed by Evidence for ESSA.

Other Research: Potentially Eligible for NCII Review: 9 studies

Bunn, R., Burns, M. K., Hoffman, H. H. & Newman, C. J. (2005). Using Incremental Rehearsal to Teach Letter Identification with a Preschool-Aged Child. Journal of Evidence-Based Practice for Schools, 6, 124-134.

Burns, M. K. (2007). Comparison of Opportunities to Respond within a Drill Model when Rehearsing Sight Words with a Child with Mental Retardation. School Psychology Quarterly22, 250-263.

Burns, M. K., Dean, V. J., & Foley, S. (2004). Preteaching Unknown Key Words with Incremental Rehearsal to Improve Reading Fluency and Comprehension with Children Identified as Reading Disabled. Journal of School Psychology, 42, 303-314.

DuBois, M. R., Volpe, R. J., & Hemphill, E. M. (2014). A randomized trial of a computer-assisted tutoring program targeting letter-sound expression. School Psychology Review, 43, 210-221.

DuBois, M. R., Volpe, R. J., Burns, M. K., & Hoffman, J. A. (2016). Parent-administered computer-assisted tutoring targeting letter-sound knowledge: Evaluation via multiple-baseline across three preschool students. Journal of School Psychology, 59, 39-53.

Klingbeil, D. A., Moeyaert, M., Archer, C. T., Chimboza, T. M., & Zwolski Jr, S. A. (2017). Efficacy of peer-mediated incremental rehearsal for English language learners. School Psychology Review, 46, 122-140.

Kwong, E., & Burns, M. K. (in press). Preliminary study of the effect of incremental rehearsal with a morphological component for teaching Chinese character recognition. School Psychology International.

Malloy, K. J., Gilbertson, D., & Maxfiled, J. (2007). Using brief experimental analysis for selecting reading interventions for English language learners. School Psychology Review, 36, 291 – 310.

Rahn, N. L., Wilson, J., Egan, A., Brandes, D., Kunkel, A., Peterson, M., & McComas, J. (2015). Using incremental rehearsal to teach letter sounds to English language learners. Education and Treatment of Children, 38, 71-91.