Fusion (Whole Number Foundations Level 1)
Study: Clarke et al. (2013)

Summary

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.

Target Grades:
1
Target Populations:
  • Any student at risk for academic failure
Area(s) of Focus:
  • Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
Where to Obtain:
Baker, Clarke, Doabler, Fien & Jungjohann
mathctl@uoregon.edu
Initial Cost:
Contact vendor for pricing details.
Replacement Cost:
Contact vendor for pricing details.

N/A based on print costs

Staff Qualified to Administer Include:
  • Special Education Teacher
  • General Education Teacher
  • Reading Specialist
  • Math Specialist
  • EL Specialist
  • Interventionist
  • Student Support Services Personnel (e.g., counselor, social worker, school psychologist, etc.)
  • Paraprofessional
  • Other:
Training Requirements:
1-4 hours of training

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.


Training materials were developed and field-tested over a three year period. Materials and manuals were modified after years 1 and 2 of training and implemented in year 3. Year 3 results are presented in this report.

Access to Technical Support:
email contact for information: mathctl@uoregon.edu
Recommended Administration Formats Include:
  • Small group of students
Minimum Number of Minutes Per Session:
30
Minimum Number of Sessions Per Week:
3
Minimum Number of Weeks:
20
Detailed Implementation Manual or Instructions Available:
Yes
Is Technology Required?
No technology is required.

Program Information

Descriptive Information

Please provide a description of program, including intended use:

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.

The program is intended for use in the following age(s) and/or grade(s).

not selected Age 0-3
not selected Age 3-5
not selected Kindergarten
selected First grade
not selected Second grade
not selected Third grade
not selected Fourth grade
not selected Fifth grade
not selected Sixth grade
not selected Seventh grade
not selected Eighth grade
not selected Ninth grade
not selected Tenth grade
not selected Eleventh grade
not selected Twelth grade


The program is intended for use with the following groups.

not selected Students with disabilities only
not selected Students with learning disabilities
not selected Students with intellectual disabilities
not selected Students with emotional or behavioral disabilities
not selected English language learners
selected Any student at risk for academic failure
not selected Any student at risk for emotional and/or behavioral difficulties
not selected Other
If other, please describe:

ACADEMIC INTERVENTION: Please indicate the academic area of focus.

Early Literacy

not selected Print knowledge/awareness
not selected Alphabet knowledge
not selected Phonological awareness
not selected Phonological awarenessEarly writing
not selected Early decoding abilities
not selected Other

If other, please describe:

Language

not selected Expressive and receptive vocabulary
not selected Grammar
not selected Syntax
not selected Listening comprehension
not selected Other
If other, please describe:

Reading

not selected Phonological awareness
not selected Phonics/word study
not selected Comprehension
not selected Fluency
not selected Vocabulary
not selected Spelling
not selected Other
If other, please describe:

Mathematics

not selected Computation
not selected Concepts and/or word problems
not selected Whole number arithmetic
selected Comprehensive: Includes computation/procedures, problem solving, and mathematical concepts
not selected Algebra
not selected Fractions, decimals (rational number)
not selected Geometry and measurement
not selected Other
If other, please describe:

Writing

not selected Handwriting
not selected Spelling
not selected Sentence construction
not selected Planning and revising
not selected Other
If other, please describe:

BEHAVIORAL INTERVENTION: Please indicate the behavior area of focus.

Externalizing Behavior

not selected Physical Aggression
not selected Verbal Threats
not selected Property Destruction
not selected Noncompliance
not selected High Levels of Disengagement
not selected Disruptive Behavior
not selected Social Behavior (e.g., Peer interactions, Adult interactions)
not selected Other
If other, please describe:

Internalizing Behavior

not selected Depression
not selected Anxiety
not selected Social Difficulties (e.g., withdrawal)
not selected School Phobia
not selected Other
If other, please describe:

Acquisition and cost information

Where to obtain:

Address
Phone Number
Website
mathctl@uoregon.edu

Initial cost for implementing program:

Cost
Unit of cost

Replacement cost per unit for subsequent use:

Cost
Unit of cost
Duration of license

Additional cost information:

Describe basic pricing plan and structure of the program. Also, provide information on what is included in the published program, as well as what is not included but required for implementation (e.g., computer and/or internet access)

N/A based on print costs

Program Specifications

Setting for which the program is designed.

not selected Individual students
selected Small group of students
not selected BI ONLY: A classroom of students

If group-delivered, how many students compose a small group?

   3-5

Program administration time

Minimum number of minutes per session
30
Minimum number of sessions per week
3
Minimum number of weeks
20
not selected N/A (implemented until effective)

If intervention program is intended to occur over less frequently than 60 minutes a week for approximately 8 weeks, justify the level of intensity:

Does the program include highly specified teacher manuals or step by step instructions for implementation?
Yes

BEHAVIORAL INTERVENTION: Is the program affiliated with a broad school- or class-wide management program?

If yes, please identify and describe the broader school- or class-wide management program:

Does the program require technology?
No

If yes, what technology is required to implement your program?
not selected Computer or tablet
not selected Internet connection
not selected Other technology (please specify)

If your program requires additional technology not listed above, please describe the required technology and the extent to which it is combined with teacher small-group instruction/intervention:

Training

How many people are needed to implement the program ?

Is training for the instructor or interventionist required?
Yes
If yes, is the necessary training free or at-cost?

Describe the time required for instructor or interventionist training:
1-4 hours of training

Describe the format and content of the instructor or interventionist training:
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.

What types or professionals are qualified to administer your program?

selected Special Education Teacher
selected General Education Teacher
selected Reading Specialist
selected Math Specialist
selected EL Specialist
selected Interventionist
selected Student Support Services Personnel (e.g., counselor, social worker, school psychologist, etc.)
not selected Applied Behavior Analysis (ABA) Therapist or Board Certified Behavior Analyst (BCBA)
selected Paraprofessional
not selected Other

If other, please describe:

Does the program assume that the instructor or interventionist has expertise in a given area?
No   

If yes, please describe: 


Are training manuals and materials available?
Yes

Describe how the training manuals or materials were field-tested with the target population of instructors or interventionist and students:
Training materials were developed and field-tested over a three year period. Materials and manuals were modified after years 1 and 2 of training and implemented in year 3. Year 3 results are presented in this report.

Do you provide fidelity of implementation guidance such as a checklist for implementation in your manual?

Can practitioners obtain ongoing professional and technical support?
Yes

If yes, please specify where/how practitioners can obtain support:

email contact for information: mathctl@uoregon.edu

Summary of Evidence Base

Please identify, to the best of your knowledge, all the research studies that have been conducted to date supporting the efficacy of your program, including studies currently or previously submitted to NCII for review. Please provide citations only (in APA format); do not include any descriptive information on these studies. NCII staff will also conduct a search to confirm that the list you provide is accurate.

Clarke, B., Doabler, Cl, Strand Cary, M., Kosty, D., Baker, S., Fien, H. & Smolkowsi, K. (2013). Examining the efficacy of a tier 2 first grade mathematics intervention program (Technical Report 1302). Eugene, OR: University of Oregon.

Study Information

Study Citations

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 matheamtics intervention program. Eugene, OR:

Participants Full Bobble

Describe how students were selected to participate in the study:
Eligible students were from all first grade classrooms within schools participating in the project.

Describe how students were identified as being at risk for academic failure (AI) or as having emotional or behavioral difficulties (BI):
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.

ACADEMIC INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:
  • below the 30th percentile on local or national norm, or
  • identified disability related to the focus of the intervention?
%

BEHAVIORAL INTERVENTION: What percentage of participants were at risk, as measured by one or more of the following criteria:
  • emotional disability label,
  • placed in an alternative school/classroom,
  • non-responsive to Tiers 1 and 2, or
  • designation of severe problem behaviors on a validated scale or through observation?
%

Specify which condition is the submitted intervention:
Fusion

Specify which condition is the control condition:
Only one control condition

If you have a third, competing condition, in addition to your control and intervention condition, identify what the competing condition is (data from this competing condition will not be used):
NA

Using the tables that follow, provide data demonstrating comparability of the program group and control group in terms of demographics.

Grade Level

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Age less than 1
Age 1
Age 2
Age 3
Age 4
Age 5
Kindergarten
Grade 1 44 45 Invalid
Grade 2
Grade 3
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8
Grade 9
Grade 10
Grade 11
Grade 12

Race–Ethnicity

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
African American
American Indian
Asian/Pacific Islander
Hispanic 6 12 0.50
White
Other 4 9 0.56

Socioeconomic Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Subsidized Lunch 31 31 0.00
No Subsidized Lunch 13 14 0.06

Disability Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Speech-Language Impairments
Learning Disabilities
Behavior Disorders
Emotional Disturbance
Intellectual Disabilities
Other
Not Identified With a Disability 31 34 0.22

ELL Status

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
English Language Learner 6 10 0.37
Not English Language Learner 38 35 0.26

Gender

Demographic Program
Number
Control
Number
Effect Size: Cox Index
for Binary Differences
Female 23 16 0.40
Male 21 29 0.45

Mean Effect Size

0.18

For any substantively (e.g., effect size ≥ 0.25 for pretest or demographic differences) or statistically significant (e.g., p < 0.05) pretest differences between groups in the descriptions below, please describe the extent to which these differences are related to the impact of the treatment. For example, if analyses were conducted to determine that outcomes from this study are due to the intervention and not demographic characteristics, please describe the results of those analyses here.

NA

Design Full Bobble

What method was used to determine students' placement in treatment/control groups?
Random
Please describe the assignment method or the process for defining treatment/comparison groups.
The study design was a randomized control trial, with students randomly assigned to condition blocking on school. The study took place in 9 schools with approximately 10 eligible students per school, based on screening scores and teacher recommendation, selected to be in the study. The research team randomly assigned these10 students to intervention (Fusion instruction) or control (standard district practice). The final sample included 89 students, 44 intervention and 45 control, within nine schools.

What was the unit of assignment?
Students
If other, please specify:

Please describe the unit of assignment:

What unit(s) were used for primary data analysis?
not selected Schools
not selected Teachers
selected Students
not selected Classes
not selected Other
If other, please specify:

Please describe the unit(s) used for primary data analysis:

Fidelity of Implementation Full Bobble

How was the program delivered?
not selected Individually
selected Small Group
not selected Classroom

If small group, answer the following:

Average group size
5
Minimum group size
4
Maximum group size
5

What was the duration of the intervention (If duration differed across participants, settings, or behaviors, describe for each.)?

Weeks
20.00
Sessions per week
3.00
Duration of sessions in minutes
30.00
What were the background, experience, training, and ongoing support of the instructors or interventionists?
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.

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.

What were the results on the fidelity-of-treatment implementation measure?
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.

Was the fidelity measure also used in control classrooms?
No

Measures and Results

Measures Targeted : Half Bobble
Measures Broader : Full Bobble

Study measures are classified as targeted, broader, or administrative data according to the following definitions:

  • Targeted measures
    Assess outcomes, such as competencies or skills that the program was directly targeted to improve.
    • In the academic domain, targeted measures typically are not the very items taught but rather novel items structured similarly to the content addressed in the program. For example, if a program taught word-attack skills, a targeted measure would be decoding of pseudo words. If a program taught comprehension of cause-effect passages, a targeted measure would be answering questions about cause-effect passages structured similarly to those used during intervention, but not including the very passages used for intervention.
    • In the behavioral domain, targeted measures evaluate aspects of external or internal behavior the program was directly targeted to improve and are operationally defined.
  • Broader measures
    Assess outcomes that are related to the competencies or skills targeted by the program but not directly taught in the program.
    • In the academic domain, if a program taught word-level reading skill, a broader measure would be answering questions about passages the student reads. If a program taught calculation skill, a broader measure would be solving word problems that require the same kinds of calculation skill taught in the program.
    • In the behavioral domain, if a program taught a specific skill like on-task behavior in one classroom, a broader measure would be academic performance in that setting or on-task behavior in another setting.
  • Administrative data measures apply only to behavioral intervention tools and are measures such as office discipline referrals (ODRs) and graduation rates which do not have psychometric properties as do other, more traditional targeted or broader measures.

Click here for more information on effect size.


What populations are you submitting outcome data for?
selected Full sample
not selected Students at or below the 20th percentile
not selected English language learners
not selected Racial/ethnic subgroups
not selected Economically disadvantaged students (low socioeconomic status)
Targeted Measure Reverse Coded? Reliability Relevance Exposure
Broader Measure Reverse Coded? Reliability Relevance Exposure
Administrative Data Measure Reverse Coded? Relevance

Posttest Data

Targeted Measures (Full Sample)

Measure Sample Type Effect Size P

Broader Measures (Full Sample)

Measure Sample Type Effect Size P

Administrative Measures (Full Sample)

Measure Sample Type Effect Size P

Targeted Measures (Subgroups)

Measure Sample Type Effect Size P

Broader Measures (Subgroups)

Measure Sample Type Effect Size P

Administrative Measures (Subgroups)

Measure Sample Type Effect Size P
For any substantively (e.g., effect size ≥ 0.25 for pretest or demographic differences) or statistically significant (e.g., p < 0.05) pretest differences, please describe the extent to which these differences are related to the impact of the treatment. For example, if analyses were conducted to determine that outcomes from this study are due to the intervention and not pretest characteristics, please describe the results of those analyses here.
Please explain any missing data or instances of measures with incomplete pre- or post-test data.
If you have excluded a variable or data that are reported in the study being submitted, explain the rationale for exclusion:
Describe the analyses used to determine whether the intervention produced changes in student outcomes:
A series of random effects models were estimated using SPSS MIXED procedure to compare gains in ProFusion, EN-CBM, and SAT-10 outcomes between the treatment and control conditions. The random effects models nested pretest and posttest assessments within students and students within instructional groups. The models included the effects of time (coded 0 = pretest, 1 = posttest), condition of instructional group (coded 0 = control and 1 = treatment), and the condition by time interaction. The condition by time interaction represents the difference in gains in outcomes between the two groups. Hedges’ g was reported as a metric of intervention effect size for each outcome (What Works Clearinghouse, 2008; .2, .5, and .8 are considered small, medium, and large effects). As recommended by Feingold (2009), Hedges’ g was computed as the condition by time interaction effect divided by the posttest pooled standard deviation of the outcome. In accordance with an intent-to-treat approach, maximum likelihood estimation was used to obtain model parameters and standard errors using all cases available, which results in less bias in parameter estimates and standard errors than other methods of handling missing data (e.g., listwise deletion; Schafer & Graham, 2002).

Additional Research

Is the program reviewed by WWC or E-ESSA?
WWC
Summary of WWC / E-ESSA Findings :

What Works Clearinghouse Review

 

WWC only reviewed the report “Examining the efficacy of a Tier 2 kindergarten mathematics intervention.” The findings from this review do not reflect the full body of research evidence on Fusion (Whole Number Foundations Level 1).

 

WWC Rating: Does not meet WWC standards because the intervention and comparison groups are not shown to be equivalent at baseline.


Full Report

 

Evidence for ESSA

This program was not reviewed by Evidence for ESSA.

How many additional research studies are potentially eligible for NCII review?
0
Citations for Additional Research Studies :

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