U. Of Oregon

Whole Number Foundations (Roots/ Fusion)

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Grade Levels Group Size Tutor Type Qualifying Studies Average Effect Size
K-12-5Teachers, Para-professionals, and Part-time tutors3+0.18

Contact Info


Groups Studied
Asian American
English Learners
Free and Reduced Lunch

Communities Studied

Program Description

Whole Number Foundations Level K (Roots) and Level 1 (Fusion) create a continuum of Tier 2 small group support specifically designed to meet the needs of students at-risk in mathematics. Both levels, developed through grants from the US Department of Education, Institutute of Education Sciences, are comprised of three main components: development of conceptual understanding, procedural fluency and automaticity, and the use of of mathematics vocabulary and discourse. WNF Level K and WNF Level 1 have been developed in both English and Spanish.


Tutors have successfully included certified classroom teachers, para-professionals, and part-time tutors. Regardless of the tutor’s amount of experience, high-quality interactions with students are supported through intentionally designed lessons that are explicit and systematic. These lessons provide detailed descriptions of each lesson activity, appropriate wording to emphasize important mathematics vocabulary and definitions, and frequent opportunities for students to respond.


WNF Levels K and 1 draw from the critical foundational content areas of Kindergarten and First Grade Common Core State Standards.  Students in grades K-1 that are at-risk in mathematics are placed into either program based on their achievement on program assessments. If needed, both levels can be successfully completed in a single school year for which WNF K would build a strong foundation for WNF 1.


Technology is not necessary for implementation, however, Whole Number Foundations Level K lessons have been adapted for online instruction, if necessary.


The primary aim of the fifty, 20-minute lessons in WNF Level K is the mastery of number concepts and skills through the number 20. While the sixty, 30-minute lessons in WNF Level 1 emphasizes place value and base ten concepts with numbers to 120, number properties, number combinations, addition and subtraction of 2-digit numbers without renaming, and word problem solving. Each lesson also includes a “Note Home” in both English and Spanish that summarizes the mathematical concepts and skills from the daily lessons.



Regular in-program assessments help to guide instruction. Assessments are to be individually administered and results recorded on the group summary form. Specific supports for interpreting data and strategies to enhance learning are suggested to tutors and lead tutors during professional development. Data is shared with lead tutors, and CTL trainers. These data are used in regular coaching conversations or observation visits to help make sure that all students are on track to success.

Program Operation

Lessons are designed to be completed in a single session.  Ideally, groups would meet daily with the same tutor.  Tutor will need to prepare for each lessons by prereading the lesson and gathering manipulatives (approximately 15 min.).  Lessons can be taught wherever small group lessons are typically delivered in your building and should be taught in addition to grade level core math instruction.

Professional Development, Progress Monitoring, and Follow-up

Experienced trainers through the University of Oregon, Center on Teaching and Learning, provide in-person or online professional development and support. Professional development is negotiated based on district needs and may include training for leadership, lead tutors (coaches), as well as follow-up coaching. The following is suggested for consideration:

  • Leadership
    • Four-hour institute to learn how to support implementation and requirements necessary for success
  • Lead Tutors/Coaches (each district or region, hired by local districts)
    • Trained to do regular coaching visits to observe tutors in action (6 Hours)
    • Provide ongoing support and evaluation of coaches (6 Hours quarterly)
  • Tutors
    • Provide initial training/Book 1 tutors (6 Hours)
    • Provide initial training/Book 2 (6 Hours)
    • Provide refined training for returning tutors (4 Hours)
  • Ongoing coaching support


WNF Levels K and 1 can be purchased directly from CTL or through a licensing agreement. Visit the CTL Marketplace for curriculum samplers and more information!

See website for specific details. Information below is for one intervention kit in either pdf (to be printed by purchaser) or one pre-printed/assembled. Professional development and training costs are negotiated based on your needs.

Intervention Kit – PDF

Includes Teacher Book 1 and Teacher Book 2 (license for 1 copy); Math Practice worksheets (1 worksheet per lesson and 3 additional Math Check Points, license for 5 copies); Reproducible Program Support Materials; manipulative list (manipulatives not included with purchase). Downloadable PDF. Prices do not include printing.

Price: $250.00


Intervention Kit – Book

Includes Teacher Book 1 and Teacher Book 2; Math Practice worksheets (1 worksheet per lesson and 3 additional Math Check Points, 5 copies); Program Support Materials; manipulative list (manipulatives not included with purchase).

Research on Program Outcomes

Randomized control trials indicate that Whole Number Foundations Level K (Roots) and Level 1 (Fusion) have positive impacts on student achievement. A multi-year, multi-site efficacy project occurred across 3 school years with over 1,200 Kindergarten students randomly assigned to one of three conditions: 2:1 ROOTS, 5:1 ROOTS, and a no-treatment control condition. Participating schools were located in a mix of rural, suburban, and urban Oregon school districts, as well as in two urban Massachusetts school districts, all with high levels of eligibility for free and reduced-price lunch. The student population was 64% White, 24% Hispanic, and 5% Black. On standardized, norm-referenced measures, students in the Whole Number Foundation conditions significantly outperformed students in the control condition (effect size = +0.23). Similarly strong outcomes were found for English Learners (Doabler et al., 2018) and even stronger outcomes for students with the most severe skill deficits at the start of the intervention (Clarke et al., 2019). Two additional studies investigated the impact of WNF-1 (Fusion). The first was a small pilot study with 78 first-grade students from schools in two suburban districts in the Pacific Northwest that showed WNF students scoring non-significantly higher on the SAT-10 (effect size = +0.11). The second evaluation involved 450 first graders from 9 elementary schools in three Oregon school districts. 17% of students received special education services, 14% were English learners, 65% were white, and 21% Hispanic. WNF students scored non-significantly higher on the TEMA-3 (effect size = +0.07), with students in the two student group per interventionist (vs the five student group) demonstrating stronger results (effect size = +0.21).  Averaging across the three studies, weighting by sample size, the mean effect size is +0.18.

Key Studies

  • Clarke, B., Doabler, C. T., Turtura, J., Smolkowski, K., Kosty, D., Sutherland, M., Kurtz Nelson, E., Fien, H., & Baker, S. K. (2020). Examining the efficacy of a kindergarten mathematics intervention by group size and initial skill: Implications for practice and policy. The Elementary School Journal, 121(1), 125–153. doi: 10.1086/710041
  • Clarke, B., Doabler, C. T., Smolkowski, K., Turtura, J., Kosty, D., Kurtz Nelson, E., Fien, H., & Baker, S. K. (2019). Exploring the relationship between initial mathematics skill and the impact of a kindergarten mathematics intervention on student mathematics outcomes. Exceptional Children, 85(2), 129–146. doi: 10.1177/0014402918799503
  • Doabler, C. T., Clarke, B., Kosty, D., Kurtz-Nelson, E., Fien, H., Smolkowski, K., & Baker, S. K. (2019). Examining the impact of group size on the treatment intensity of a Tier 2 mathematics intervention within a systematic framework of replication. Journal of Learning Disabilities, 52(2), 168–180. doi: 10.1177/0022219418789376
  • Doabler, C. T., Clarke, B., Kosty, D., Smolkowski, K., Kurtz-Nelson, E., Fien, H., & Baker, S. K. (2019). Building number sense among english learners: A multisite randomized controlled trial of a Tier 2 kindergarten mathematics intervention. Early Childhood Research Quarterly, 47, 432–444. doi: https://doi.org/10.1016/j.ecresq.2018.08.004
  • Clarke, B., Doabler, C., Smolkowski, K., Kurtz Nelson, E., Fien, H., Baker, S. K., & Kosty, D. (2016). Testing the immediate and long-term efficacy of a Tier 2 kindergarten mathematics intervention. Journal of Research on Educational Effectiveness, 9, 607–634. doi: 10.1080/19345747.2015.1116034
  • Clarke, B., Doabler, C. T., Smolkowski, K., Baker, S. K., Fien, H., & Strand Cary, M. (2016). Examining the efficacy of a Tier 2 kindergarten mathematics intervention. Journal of Learning Disabilities, 49, 152–165. doi: 10.1177/0022219414538514
  • Clarke, B., Doabler, C. T., Strand Cary, M., Kosty, D. B., Baker, S. K., Fien, H., & Smolkowski, K. (2014). Preliminary evaluation of a tier-2 mathematics intervention for first grade students: Utilizing a theory of change to guide formative evaluation activities. School Psychology Review, 43, 160–177.
  • Clarke, B., Doabler, C. T., Sutherland, M., Kosty, D., Turtura, J., & Smolkowski, K. (2021). Examining the Impact of a First Grade Whole Number Intervention by Group Size [Manuscript submitted for publication]. University of Oregon, Center on Teaching and Learning. 

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