Fusion (Whole Number Foundations Level 1)

Study: Clarke, Doabler, Strand Cary, Kosty, Baker, et al. (2013) Technical Report

Clarke B., Doabler, C., Strand Cary, M., Kosty, D., Baker, S., Fien, H. & Smolkowski, K. (2013). Examining the efficacy of a tier 2 first grade mathematics intervention program (Technical Report 1302). Eugene, OR: University of Oregon.
Descriptive Information Usage Acquisition and Cost Program Specifications and Requirements Training

The Fusion curriculum is a Grade 1 mathematics intervention designed for students at risk in whole number concepts and skills. Students are taught in small groups for 60, 30-minute lessons. Each lesson includes the explicit introduction of new content and systematic practice and review in 4-to-5 brief, scripted mathematics activities. Lessons utilize a variety of math models and contain teacher modeling, scaffolded instructional examples, and opportunities for academic feedback. Two mathematical domains in the first grade Common Core State Standards -- Operations and Algebraic Thinking and Number and Operations in Base Ten form the basis of Fusion content. The first half of the curriculum emphasizes number sense, basic number combinations, and place value concepts. During the second half of the curriculum students encounter multi-digit computation without regrouping and word problem solving.

Fusion is intended for use in first grade. It is designed for use with any student at risk of academic failure. The academic area of focus is math (comprehensive: includes computation/procedures, problem solving, and mathematical concepts).

Fusion has been used in both Oregon and Hawaii. Eight Oregon schools and ten Hawaii schools participated in the field development and testing of the Fusion program. Schools worked closely with the authoring and research teams to implement Fusion in their first grade classrooms. Data from the Oregon field test are contained in this report. Data from the Hawaii field test are undergoing analysis.

Where to obtain: UO CTL Marketplace website

Available as: Whole Number Foundations Level 1

Website: https://dibels.uoregon.edu/market/movingup/firstfoundation

Email: support@dibels.uoregon.edu

Phone: 1-888-497-4290

Cost: See website for details.

Fusion is designed for use with small groups of three to five students.

Fusion takes 30 minutes per session with a recommended 4-5 sessions per week for 12-15 weeks.

The program includes a highly specified teacher’s manual. No technology is required.

The minimum qualifications for FUSION instructors are that they be instructional assistants and/or paraprofessionals. The program does not assume that the instructor has expertise in a given area.

Two half-day trainings and regular on-going support were provided to instructors implementing the program in the research study. Coaching support was provided to facilitate high levels of implementation fidelity.

The first half-day workshop introduced the instructor to the FUSION program, instructional practices that have been empirically validated to increase student math achievement, and effective small-group management techniques. Program training focused on teaching place value concepts and instruction on number combinations covered in the first 30 lessons. Lesson practice accompanied by coaching support and feedback was also provided.

In the second half-day workshop, interventionists shared progress data as well as any difficulties encountered in delivering the lessons. The workshop facilitator and other interventionists shared strategies for overcoming problems encountered. Program training focused on teaching multi-digit addition and subtraction strategies, and problem solving strategies. Lesson practice accompanied by coaching support and feedback was also provided.

Practitioners may obtain ongoing professional/technical support by contacting:

Email: support@dibels.uoregon.edu

Phone: 1-888-497-4290


Participants: Convincing Evidence

Sample size: 81 (40 program, 41 control)

Risk Status: All first-grade students completed the Group Curriculum Based Measure (Group CBM) screening assessment. This was a modified version of the Early Numeracy Curriculum Based Measures (Author, 2004). Eligible students were the 10 lowest students on the screener per school who could count and identify numbers from 1 to 10. We excluded students who had received special education services or had severely limited English proficiency.





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Socioeconomic status

  Subsidized lunch






  No subsidized lunch






Disability status

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  Not identified with a disability






ELL status

  English language learner






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Training of Instructors:  Nine district-employed instructional aides (i.e., “interventionists”), all female, each taught one small FUSION group. Aides were included in the study based on time and schedule availability. Six had masters degrees, two had bachelors degrees, and one was a high school graduate. On average, they had 8.7 years teaching experience (range 3-25 years), 7.4 years experience teaching math (range 4-25 years), and 7.7 years teaching first grade (range 4-20 years). Interventionists participated in two, 3-hour professional development workshops led by the authoring and research team. Workshops were intended to deepen interventionists’ content knowledge for teaching mathematics, pedagogical knowledge, and comfort teaching Fusion lessons. Workshops provided time for interventionists to practice teaching Fusion lessons and receive feedback from their peers and the curriculum’s authors. The first workshop occurred in October, prior to Fusion instruction. Content included an overview of the study design and their role, an overview of the Fusion intervention and its underlying principles and content, lesson demonstrations, group management tips, and practice opportunities. The second training occurred in February, after interventionists had implemented a portion of Fusion lessons. During this training, interventionists had the opportunity to ask questions about the first half of the curriculum and were introduced to concepts in the second half of the curriculum.  

Design: Convincing Evidence

Did the study use random assignment?: Yes

If not, was it a tenable quasi-experiment?: N/A

If the study used random assignment, at pretreatment, were the program and control groups not statistically significantly different and had a mean standardized difference that fell within 0.25 SD on measures used as covariates or on pretest measures also used as outcomes?: Yes

If not, at pretreatment, were the program and control groups not statistically significantly different and had a mean standardized difference that fell within 0.25 SD on measures central to the study (i.e., pretest measures also used as outcomes), and outcomes were analyzed to adjust for pretreatment differences?: N/A

Were the program and control groups demographically comparable at pretreatment?: Yes

Was there attrition bias1?: No

Did the unit of analysis match the unit for random assignment (for randomized studies) or the assignment strategy (for quasi-experiments)?: Yes

1 NCII follows guidance from the What Works Clearinghouse (WWC) in determining attrition bias. The WWC model for determining bias based on a combination of differential and overall attrition rates can be found on pages 13-14 of this document: http://ies.ed.gov/ncee/wwc/pdf/reference_resources/wwc_procedures_v2_1_standards_handbook.pdf


Fidelity of Implementation: Convincing Evidence

Describe when and how fidelity of treatment information was obtained: Trained project staff observed each group’s Fusion instruction three times (i.e., once during the beginning, middle, and end of the curriculum). Observers rated implementation fidelity for each primary activity in a FUSION lesson (Activities 1 through 3), using a 0-1 scale (0 = not taught, 0.5 = partial implementation, and 1 = full implementation). A fidelity score for each observation was calculated by averaging ratings across Activities 1 through 3. Each interventionist’s fidelity scores were averaged across the three observation occasions. Observers also provided a holistic rating of overall level of implementation on a 7-point scale with a score of “1” representing low implementation and “7” representing high implementation. Interobserver reliability was conducted on 20% of all observations and was 95% and 86% for the activity-based and the holistic rating, respectively. 

Provide documentation (i.e., in terms of numbers) of fidelity of treatment implementation:  Results on specific components of fidelity ranged from 0.90-0.93 with a standard deviation range of 0.07 to 0.17. Overall fidelity was rated as 5.2 with a standard deviation of 1.1.  

Measures Targeted: Partially Convincing Evidence

Measures Broader: Convincing Evidence

Targeted  Measure Reliability Statistics Relevance to Program Instructional Content Exposure to Related Content Among Control Group


Criterion validity (r = 0.56-0.68); Inter-correlations (r=0.40-0.82)


Exposure through core instruction


Broader Measure Reliability Statistics Relevance to Program Instructional Content Exposure to Related Content Among Control Group


Criterion validity 0.46-0.72; Inter-rater 0.98-.099; test-retest 0.76-0.86; alternate form 0.79-0.93


Exposure through core instruction

SAT 10

Criterion validity 0.67; Reliability 0.93


Exposure through core instruction


Number of Outcome Measures: 3 Math

Mean ES - Targeted: 0.84*

Mean ES - Broader: 0.13

Effect Size:

Targeted Measures

Construct Measure Effect Size
Math ProFusion 0.84***

 Broader Measures

Construct Measure Effect Size
Math EN-CBM 0.12
Math SAT 10 0.15


*       p ≤ 0.05
**     p ≤ 0.01
***   p ≤ 0.001
–      Developer was unable to provide necessary data for NCRTI to calculate effect sizes
u      Effect size is based on unadjusted means
†      Effect size based on unadjusted means not reported due to lack of pretest group equivalency, and effect size based on adjusted means is not available


Visual Analysis (Single Subject Design): N/A

Disaggregated Data for Demographic Subgroups: No

Disaggregated Data for <20th Percentile: No

Administration Group Size: Small Group, (n=3-5)

Duration of Intervention: 30 minutes, 3 times a week, 20 weeks

Minimum Interventionist Requirements: Paraprofessional, 1-4 hours of training

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: 0 studies