Whole Number Foundations

D. Maximizing State Level Funds to Support Students

The Department recognizes that States have an extraordinary opportunity to address the disproportionate impact of the COVID-19 pandemic on underserved students through the ARP Act’s required State set-asides to address the academic impact of lost instructional time, provide summer learning and enrichment programs, and provide comprehensive afterschool programs. In this section, SEAs will describe their evidence-based strategies for these resources.

Academic Impact of Lost Instructional Time: Describe how the SEA will use the funds it reserves under section 2001(f)(1) of the ARP Act (totaling not less than 5 percent of the State’s total allocation of ARP ESSER funds) on evidence-based interventions to address the academic impact of lost instructional time by supporting the implementation of evidence-based interventions, such as summer learning or summer enrichment, extended day, comprehensive afterschool programs, or extended school year programs, and ensure that such interventions respond to students’ academic, social, emotional, and mental health needs. The description must include:

i. A description of the evidence-based interventions (e.g., providing intensive or high-dosage tutoring, accelerating learning) the SEA has selected, and the extent to which the SEA will evaluate the impact of those interventions on an ongoing basis to understand if they are working;

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.

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.


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 student to respond.


WNF Level K and 1 draw from the critical foundational content areas of Kindergarten and First Grade Common Core State Standards.  Students in grades K-2 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.

Assessments to Monitor Progress

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.

Insert specific state test or assessment approach.

  1. How the evidence-based interventions will specifically address the disproportionate impact of COVID-19 on certain groups of students, including each of the student groups listed in question A.3.i.-viii. When possible, please indicate which data sources the SEA will use to determine the impact of lost instructional time; and

How the evidence-based interventions will specifically address the disproportionate impact of COVID-19 on certain groups of students

Strong evidence exists that WNF will specifically address the impact of COVID-19 across a range of student groups. 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 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 school 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.

Data sources the SEA will use to determine the impact of lost instructional time

INSERT STATE’S PLANS TO EVALUATE ALL STUDENTS WHEN THEY RETURN, IF ANY. Within WNF, ongoing assessments will provide in real time feedback to teachers on student skill acquisition. Performance on these assessments have been linked to performance on broader measures of achievement similar to state tests (Shanley et al., 2020). The State will use a standardized measure, the XXX, to evaluate program impact on a large scale in the spring.

  1. The extent to which the SEA will use funds it reserves to identify and engage 1) students who have missed the most in-person instruction during the 2019-2020 and 2020-2021 school years; and 2) students who did not consistently participate in remote instruction when offered during school building closures.


Amplify Education (2021). COVID-19 means more students not learning to read. Author.

Gersten, R., Haymond, K., Newman-Gonchar, R., Dimino, J., & Jayanthi, M. (2020). Meta-analysis of the impact of reading interventions for students in the primary grades. Journal of Research on Educational Effectiveness, 13(2), 401–427.

Madden, N. A., & Slavin, R. E. (2017). Evaluations of technology-assisted small group tutoring for struggling readers. Reading & Writing Quarterly, 1-8.

Neitzel, A., Lake, C., Pellegrini, M., & Slavin, R. (2021). A synthesis of quantitative research on programs for struggling readers in elementary schools. Reading Research Quarterly. doi:10.1002/rrq.379

Nickow, A, Oreopoulos, P., & Quan, V. (2020). The impressive effects of tutoring on preK-12 learning: A systematic review and meta-analysis of the experimental evidence. National Bureau of Economic Research.

Pellegrini, M., Neitzel, A., Lake, C., & Slavin, R. (2021). Effective programs in elementary mathematics: A best-evidence synthesis. AERA Open, 7 (1), 1-29.

Ross, S. N., Laurenzano, M., & Madden, N. A. (2017). An evaluation of the Lightning Squad computer-assisted small group tutoring program in the reading achievement of disadvantaged students in grades 1-3 (tech rep). Baltimore: Johns Hopkins University, Center for Research and Reform in Education.

Wanzek, J., Vaughn, S., Scammacca, N., Gatlin, B., Walker, M. A., & Capin, P. (2016). Meta-analyses of the effects of tier 2 type reading interventions in grades K-3. Educational Psychology Review, 28(3), 551–576. doi:10.1007/s10648-015-9321-7

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