Incremental Cost Effectiveness Ratios (ICERs) are the most rigorous way to evaluate costs and benefits in education. ICERs are reported as the cost in dollars for one standard deviation of gain in the intervention group; thus, lower ICERs are better, indicating greater efficiency. Because the metric is a ratio, there are two ways to attain a lower ICER: lower the cost to implement and/or improve the effect given implementation. Readers should question cost-benefit analyses that are computed in the absence of a randomized controlled trial. Barrett and VanDerHeyden (2020) reported ICERs for classwide math intervention in SpringMath from a randomized controlled trial. Barrett and VanDerHeyden computed ICERs three ways across many outcome measures, including year-end state test scores and more proximal outcomes, such as CBM screening scores. Specifically, they calculated costs in increasing degrees of comprehensiveness. First, they calculated the costs needed to implement, including the training, ongoing coaching and support, including salary costs for an RTI coach and school principal, and program costs and materials. Second, they calculated costs, adding personnel costs required for teachers, RTI coach, and school principal to attend the trainings. Third, they calculated the cost adding teacher salaries for the time spent delivering the intervention each day. Among fourth-graders, incremental cost-effectiveness ratios ranged from $74.01 to $362.39, depending on which ingredients were included for CBM measures, and from $57.73 to $862.24, depending on which ingredients were included and level of prior risk for state assessment outcomes. Among fifth-graders, incremental cost-effectiveness ratios ranged from $96.95 to $540.21, depending on which ingredients were included for CBM measures. Among all students receiving treatment with SpringMath, it cost $296.10 to prevent one student from failing the state assessment. SpringMath was most cost effective for students who were already at high risk for poor educational outcomes because of the smaller number needed to be treated among those subpopulations. Specifically, the cost was $126.90 to prevent failure on the state assessment for one fourth-grade student receiving special education services or for one student who scored below the 25th percentile on the prior year's state assessment. SpringMath ICERs were very strong and superior to changing curricula in math. 

Screening occurs three times per year. The first two screenings (fall and winter) are primarily the basis for identifying classes in need of classwide intervention and/or students in need of individual intervention. The spring screening is primarily used for program evaluation (along with the fall and winter screening data). Generally, students who require intervention are identified by the fall and winter screenings, and the only “new” cases detected at spring screening are students who did not participate in previous screenings and did not participate in classwide intervention. For classes routed into classwide intervention, the classwide intervention data are used to identify students for more intensive intervention.

The SpringMath screening measures are intentionally efficient. They are group administered and take about 15 minutes each season. If your class is recommended for classwide intervention, 15-20 minutes per day is sufficient to complete classwide intervention, and the recommended dosage is a minimum of four days per week. Day 5 can fall on any day of the week. Individual interventions (which can be recommended from classwide intervention or directly from screening when there is not a classwide learning problem), require 15-20 minutes per day. If students are recommended for individual intervention, recommendations will be made for small groups from week to week, which allows for a single investment of 20 minutes to deliver intervention to several students at the same time. We recommend that teachers and data team members (e.g., principals, RTI coaches, math coaches) log in to the SpringMath coach dashboard each week to identify what actions are underway and where assistance is needed to improve results. The coach dashboard makes specific recommendations about which teachers require assistance; summarizes learning gains at the grade, teacher, and student level; allows for coaches to share data with parents; and provides an ideal tool to facilitate data team meetings in the school. 

One of the lessons from MTSS research is that supplemental interventions can be much shorter than 45 minutes, but sessions need to occur more often than twice per week. In fact, exciting contemporary dosage research is finding in rigorous experimental studies that briefer, more frequent intervention sessions (i.e., micro-dosing) produce stronger and more enduring learning gains (Duhon et al., 2020; Schutte et al., 2015; Solomon et al., 2020). Codding et al. (2016) directly examined this question for SpringMath intervention in a randomized, controlled trial and found that given the same weekly investment of minutes allocated to intervention, the condition that offered the greatest number of sessions per week (with shorter sessions) produced about twice the effect of the twice weekly condition, which was about twice the effect of the weekly condition, which was no different from students who received no intervention (i.e., control).  

Given recent experimental findings related to dosage, it is becoming clear that daily dosing of intervention or at least four days per week is likely ideal, not just for SpringMath, but for all supplemental and intensive academic interventions, as measured by producing strong learning gains. That said, schools that are trying to implement within a schedule that has already been set can find ways to approximate more effective dosing schedules. For example, if students are available twice per week, teachers might try running two consecutive sessions each time. Teachers might find a way to add a third session during the week either via creative scheduling or working with the core classroom teacher to deliver classwide intervention to the entire class as part of the day’s fluency-building routine in the classroom. We recommend that schools use their planning for year 2 implementation to build schedules that are consistent with optimal dosing in MTSS, which means four or five days per week of shorter supplementation blocks (e.g., 20 minutes).

This question is often a sign to our teams that the instructional expectations, sequencing, and pacing of math learning in a system may be out of sync with best practices. The SpringMath measures have been designed to reflect current learning expectations and when systems report that such content has not yet been taught, this is often a sign that the pacing of instruction in a system may be off track. Let’s answer this question in three parts: screening, classwide intervention, and individual intervention. For part one, let’s focus on screening. Screening skills have been selected for maximal detection of risk. These skills are those that are expected to have been recently taught, that students must be able to do accurately and independently to benefit from the upcoming grade-level instruction. High-leverage skills are emphasized, and mastery is not expected. Screening skills are rigorous, and we expect that more learning will occur with those skills. Our instructional target used at screening reflects successful skill acquisition. There is flexibility for schools to choose when to screen, and this allows some flexibility if you know you have not yet taught a skill that will be assessed but anticipate teaching that skill in the next week or two. It is fine to delay winter and spring screening for a few weeks into each screening window. 

Now for part two to this answer: Let’s focus on classwide intervention. There is a set sequence of skills unique to each grade level that classes must progress through. The sequence is intentionally designed to begin with below-grade-level foundation skills and to increase incrementally in difficulty such that mastery on skills that appear early in the sequence prepares students for mastery on the later skills. This sequencing is used because classwide math intervention is, by design, a fluency-building intervention. You might have noticed (or will notice) that when the median score in classwide intervention is below the instructional target, which we call the frustrational range, a whole-class acquisition lesson is provided so that the teacher can easily pause and reteach that skill before proceeding with the classwide fluency-building intervention. There is flexibility here in that teachers can enter classwide intervention at any time during the year (following fall or winter screening) and can enter scores daily until the class median is below mastery. When the class median is below mastery, that is the sweet spot within which to begin classwide math intervention for maximal efficacy and efficiency. 

Part three of this answer is about individual intervention. SpringMath screenings are the dropping-in points to intervention. Screening skills reflect rigorous, grade-level content. When a student is recommended for individual assessment and intervention, the assessment will begin from the first screening skill and sample back through incrementally prerequisite skills to find the skill gap or gaps that must be targeted to bring the student to mastery on the grade-level skill (which is the screening skill). There is a science to this process, and the skill that should be targeted is based on student assessment data. There is flexibility for teachers in that they might use the instructional calendars in Support as a model of pacing and a logical organizer to locate acquisition lessons, practice sheets, games, and word problems, which are available for all 145 skills in SpringMath. For convenience, we have also recommended booster lessons and activities in Support for teachers who wish to do more than just classwide math intervention. In other words, teachers can always do more, but it is sufficient to simply do what is recommended within the teacher and coach dashboards. 

SpringMath is a comprehensive multi-tiered system of support (MTSS). MTSS begins with universal screening to identify instructional need. These needs can range from an individual to a schoolwide level. If a curricular gap is identified, classwide intervention is the most efficient level at which to address these needs. Thus, all students need to be included in SpringMath. The screening data are used to summarize learning gains within and across classes and grades and to identify areas of need at the school level via automated program evaluation. These important actions of SpringMath and MTSS are not possible when all students are not included in the implementation. Many systems wonder if they can use an existing screening tool to identify students for intervention and then just use SpringMath to deliver intervention. This is a costly mistake because SpringMath continually harvests data to make more accurate decisions about who requires intervention and what kind of intervention they require based on the foundation of universal data collected three times per year. 

Classwide intervention is a very powerful tactic when it is needed. It is an inefficient tactic when it is not needed. With SpringMath, you are not buying classwide math intervention. Rather, you are buying a comprehensive MTSS system that seamlessly links instructional intensifications to assessment data using automated data interpretation and summary reports and guides your MTSS implementation step by step. All students must be included in the assessments at routine timepoints to verify core program effectiveness, to detect students who are lagging behind expectations in a highly sensitive way, and to guide effective reparation of learning gaps. When classwide intervention is not recommended, that is because it is not needed as a second screening gate, nor as a mechanism to reduce overall risk (because risk is low). Using the automated summary reports and data interpretation, SpringMath will then very accurately recommend students for small-group or individual intervention. The summary reports, including the coach and administrator dashboard, harvest data from all students to allow for progress monitoring of math learning at the system level. This is not possible when SpringMath is not used universally. It is also not possible to use other screening measures to determine who should get intervention in SpringMath because other measures are not as sensitive as those used in SpringMath. Further, SpringMath screening measures are the “dropping-in” points for diagnostic assessment to provide the right interventions for students who need them. Summary reports will show you the growth of all students across screening measures over the course of the school year and gains for students receiving tier 2 or 3 interventions relative to the performance of classroom peers on the same measures. Again, this is not possible when not all students are included in the assessments. SpringMath assessment and expert layered decision rules recommend — and then provide — precisely what is needed, ensuring the correct stewardship of limited resources and the best return on investment for the effort. 

If your class has already started classwide intervention based upon the results of a prior screening you will be allowed to continue classwide intervention if you choose, even if your class scores above the criterion for recommending classwide intervention on subsequent screenings.  

Teachers often express this concern. The short answer is “No, it’s not a waste of time for high-performing students to participate in classwide math intervention.” Classwide intervention requires only about 15-20 minutes per day, and children in all performance ranges tend to grow well. If many children score in the frustrational range, an acquisition lesson will be recommended (and provided) right in the classwide intervention teacher dashboard. Students in the instructional and mastery range show strong upward growth given well-implemented classwide intervention. When the median reaches mastery, the entire class is moved up to the next skill, which ensures that students who are already in the mastery range do not remain on that skill for very long. Additionally, for higher-performing students, classwide intervention is a useful cumulative review tactic that has been associated with long-term skill retention and robust, flexible skill use. Thus, it has been demonstrated that even higher-performing students grow well with classwide math intervention, both in SpringMath and in other peer-mediated learning systems. 

The decision rule to move children to the next skill is written such that most of your remaining students should be above the instructional target (meaning they have acquired the skill but have not yet reached the level of proficiency that forecasts generalized, flexible use of that skill). Because the skills often overlap within a grade level and across grade levels in increasing increments of difficulty, it is a low-stakes event to move students forward who are in the instructional range as they are likely to experience continued skill development support and to demonstrate growth and even future skill mastery on subsequent skills. In contrast, children who remain in the frustrational range when the class has moved on to a new skill are highly likely to be recommended for individual intervention. That decision occurs in the background and has a very high degree of accuracy, such that children who require individual intervention are not missed (we call this “sensitivity”). Thus, when SpringMath recommends that you move on to a new skill, you should feel confident moving your class on to the next skill. SpringMath continues to track individual student progress and will recommend intervention for any child who really requires additional support to succeed in grade-level content. That said, when considering student progress, users should pay particular attention to the metric on the dashboard called “Scores Increasing.” You should aim to move this value greater than 80% each week as it reflects the overall growth of all your students from week to week and reflects that even your lowest-performing student beat his or her score from the preceding week. If you have an additional 15-20 minutes to supplement students and/or a teacher or coach to help you differentiate during core instruction, you can provide additional instruction via acquisition lessons, games, and practice materials. These materials are available in the support portal and can be used with students who were most recently not at mastery when the class moved on to a subsequent skill. Again, working with students who did not attain mastery in this way is not technically necessary since SpringMath will recommend individual intervention and deliver the right protocol for you when it’s truly necessary for individual students. 

All students at times and especially students who experience mathematics difficulties may also have difficulties with attention, motivation, self-regulation, and working memory (Compton, Fuchs, Fuchs, Lambert, & Hamlett, 2012). Unfortunately, executive-function-focused interventions have not been shown to improve achievement. Yet, supporting executive-function difficulties within academic interventions can enable more successful academic intervention. For example, Burns, et al. (2019) found that intervention based on student assessment produced strong effects on multiplication learning gains that were independent of working memory, whereas simple flashcard practice did not. Thus, ideally, intensive interventions provide math instruction in ways that support self-regulation and reinforcement strategies, minimize cognitive load on working memory, minimize excessive language load by incorporating visual representations, and provide fluency practice (Fuchs, Fuchs, & Malone, 2018; Powell & Fuchs, 2015). 

In SpringMath, diagnostic assessment is used to verify mastery of prerequisite understandings and determine the need for acquisition support versus fluency-building support so that a student is placed into the correctly aligned intervention skill (task difficulty) and receives the aligned instructional support according to their needs. Concrete-representational-abstract sequencing is used within and across intervention protocols, and students are provided with multiple response formats (e.g., oral, written, completing statements and equations to make them true, finding and correcting errors). Tasks are broken down into manageable chunks and new understandings are introduced using skills students have already mastered. Fluency of prerequisite skills is verified and, if needed, developed to ease learning of more complex content. Weekly progress monitoring and data-driven intervention adjustments ensure that the intervention content and tactic remain well aligned with the student’s needs. Intervention scripts provide goals to students and emphasize growth and beating the last best score. Self-monitoring charts are used for classwide and individual intervention, and rewarding gains is recommended. Sessions are brief but occur daily for optimal growth (Codding et al., 2016). These features make the learning experience productive, engaging, and rewarding to the student. The coach dashboard tracks intervention use and effects throughout the school. When needed, SpringMath alerts the coach to visit the classroom for in-class coaching support to facilitate correct intervention to promote student learning gains and student motivation for continued growth. Several accommodations are permitted, including adjusting response formats, reading problems to students, and repeating assessments. 

(My students have processing disorders so they will never reach mastery if I don’t extend their time.) 

We understand the pressure teachers feel to move through content quickly, but moving students on to the next skill before they have attained mastery on the prerequisite skill will lessen their chances of mastering future content. In one district, in classes in which students moved on without having reached the mastery criterion, the probability of mastering any additional content plummeted to 35%. In classes that required students to reach mastery before moving on, probability of future skill mastery was 100%. Further, classes that took the time to make sure students attained mastery actually covered more content because they were able to reach mastery much more quickly on later skills.  
Thus, we strongly recommend that you make the investment to bring as many students to mastery as possible during classwide intervention. It is possible. Students will get there. And the investment will pay off for you with better learning and more content coverage in the long run.  
 
It is not true that students with processing disorders cannot attain instructional and mastery criteria. One or two low-performing students will not prevent your class from moving forward, and these one or two students would certainly be recommended for individual intervention, which arguably is the correct level of support for such students. Individual intervention is customized to a specific student’s learning needs via diagnostic assessment, and often, such students require acquisition and fluency building for prerequisite skills to enable success in grade-level content. In fact, we recommend that students who receive individual intervention be allowed to continue in classwide intervention if possible because at some point their skill gap will close sufficiently that they will derive greater benefit from classwide intervention. 
 
We recommend focusing on improving your Scores Increasing metric in your dashboard, which is an indicator of overall growth during classwide intervention. We have many resources in Support to help teachers attain upward growth in classwide intervention.