Doing Math Assessment and Intervention Smarter: Why Spring Math

By Dr. Amanda VanDerHeyden

Why Spring Math?

Teachers often express less enthusiasm for teaching math compared to teaching other topics like language arts. Schools often have not allocated systematic supports for math achievement schoolwide. And there are not many evidence-based tools that teachers can use to help students who struggle in math. It turns out math proficiency is one of the best gifts you can give your student, whatever your student’s future career might be. Early numeracy skills predict a child’s academic success not just in math, but also in reading and other areas (Duncan et al., 2007). Math proficiency during K-12 forecasts not only enrollment in, but also completion of, a 2- or 4-year college degree in any academic major (Lee, 2012; Porter & Polikoff, 2012). Teaching students to think mathematically is a skill that benefits them throughout life and the stark line between reading success and math success is artificial.


Reading/writing proficiency and mathematical proficiency are integrated life skills. The mathematical counterparts to reading fluency, text analysis, vocabulary acquisition, and writing include understanding the four basic operations, mathematical laws, quantity representations and conversions, and understanding linear relationships. Mathematics is just another language by which students can characterize relationships between observed or hypothetical events, summarize findings, and pose new questions. Making a logical argument with words is very similar to making a logical argument with numbers. When you make sure your student is proficient in math, you open doors for your student for the rest of his or her life.


However, growing math proficiency is not easy. For example, existing standards, such as the Common Core State Standards, offer a clear sequence of expected learning outcomes from kindergarten through grade 8 that represent useful assessment targets by which teachers can verify that students are mastering key concepts and skills as instruction unfolds. Embedding skill assessments into the lesson plan to inform instruction (commonly called “formative assessment) is a logical part of effective mathematics instruction for all students, is commonly recommended in policy documents concerning evidence-based mathematics instruction (National Math Panel, 2008; VanDerHeyden & Allsopp, 2014), and garners one of the strongest effect sizes on student achievement among the variables considered by Hattie (2009) (d = .90). Formative assessment is effective because it allows the teacher to make mid-stream adjustments to instructional strategy and task difficulty as student learning progresses. However, formative assessment requires resources of teacher time, teacher skill in conducting the “right” assessment and correctly interpreting the data, and locating the necessary materials to assess and organize the data. Thus, as a matter of practicality, high-quality formative assessment often does not occur routinely in classrooms.


Technological tools in education have created opportunities for rapid integration of assessments of student learning with instructional programming and delivery (Twyman & Sota, 2016). Examples of web-based student assessment systems abound and are commonplace in most schools (e.g., Aimsweb, iSteep). These tools reduce the burden on the teacher in locating the assessments and organizing/interpreting data from screening. What existing screening tools do not provide is the direct link to intervention tactic and implementation materials based upon student assessment. Similarly, online and print-based math intervention tools (e.g., ixl, Accelerated Math) provide excellent skill practice, but no real link to student skill and capacity to benefit from practicing a particular skill. Spring Math provides both, linking student assessment data directly to the right intervention tactic and providing all needed materials to use the intervention for maximal gains.


What is Spring Math and how does it work?

Spring Math is a web-based comprehensive response to intervention system for mathematics for students in grades K-8. It can be used to direct remedial instruction for students in grades 9-12. Spring Math guides the teacher through screening, intervention, progress monitoring, and data interpretation.


 Screening. Screening assessments within Spring Math require less than five-minutes and are group administered. Spring Math summarizes the results of screening in a dashboard format unique to the teacher, principal and/or coach. Spring Math tells the teacher which students are on track, which students are potentially at risk, and whether there is a need for classwide intervention. Assessments were built using the science of curriculum-based assessment. Measures were constructed to sample specific skills, yield reliable (r = .67 to above r = .90; Foegen, Jiban, & Deno, 2007) and valid scores (r = .3 to r = .6; Foegen et al., 2007), and to allow for brief, repeated assessment to model progress over time and in response to instructional changes. Three to five screening measures are provided at fall, winter, and spring at each grade level. Screenings are group administered and timed to minimize loss of instructional time. Screening requires less than 20 minutes and meets the highest standards for screening adequacy.


Data summary and interpretation. Following screening, Spring Math graphs and interprets data by classroom within the teacher dashboard. The teacher can see which students are on track and which students are at risk. Spring Math indicates whether the class as a whole needs classwide intervention. If no classwide intervention is needed, Spring Math indicates which students need intervention and prompts the teacher to select 1-2 students to get started. At each “decision point,” a help section of the site is available to explain the decision rules if the teacher desires more information. When individual intervention is needed, Spring Math’s decision trees will provide the follow-up assessment and data interpretation to select the right intervention for the student. Once intervention is underway, Spring Math tracks the student’s progress and adjusts the intervention weekly, providing summary reports that the teacher can use to communicate and share progress with data teams, parents, and students.


Intervention. When classwide intervention is needed, Spring Math delivers all materials needed to use the intervention each week, summarizes student and classwide intervention progress, adjusts the skill difficulty, and shares progress with the school’s coach or principal. Classwide intervention requires 12-15 minutes per day and is one of the most powerful math improvement tactics a teacher can use. In one randomized controlled trial, researchers found that providing classwide math intervention prevented math failure for one of every two at-risk children who were exposed to classwide math intervention (VanDerHeyden & Codding, 2015).


Individual intervention is recommended when there is not a classwide problem at screening or after four weeks of classwide intervention has occurred and a decision rule can be applied to identify individual students who are not benefiting from classwide intervention. Individual intervention is more intensive. It provides skill acquisition and fluency building support along with scripted explicit instruction guides to build conceptual understanding related to the target skill. Individual intervention requires 15-20 minutes each day.

When individual children need intervention, Spring Math directs the follow-up assessment providing each assessment to identify the right intervention for the student. Spring Math delivers the right intervention packet for the student(s). Each packet contains scripted instructions for the intervention. The words in bold-faced print are the words that the teacher can say when delivering the intervention, offered as a guide to simplify intervention delivery. The packet also includes a troubleshooting section, and scripted, specific activities to build conceptual understanding for the particular skill. These activities connect the skill performance to the “big ideas,” past understandings and future understandings in math using explicit instruction techniques that are scripted for the teacher for ease of use. Next, the packet contains the actual practice materials that the student will use each day during the intervention. The packet ends with two brief timed assessments, administered at the end of the week: a target skill assessment and a generalization skill assessment. At the end of the week, the teacher enters the assessment scores and Spring Math summarizes weekly progress and adjusts the intervention each week (increasing difficulty or changing intervention tactic) based on student performance.

Importantly, Spring Math assessment and intervention materials are generated on demand when needed and the content is controlled to provide technically equivalent (but not identical) assessment forms and to provide the right practice opportunities within intervention sessions that differ across days (so the child can’t just memorize the answers).

Intervention features have been designed based upon best-available research evidence from the research community and these include: aligning intervention tactic and skill difficulty with student proficiency via assessment, decision rules to determine intervention tactic that will produce maximal growth, the sequence of intervention moving from prerequisite to goal skills, specific intervention tactics including modeling, guided practice, immediate versus delayed corrective feedback, verbal rehearsal strategies and “think aloud” problem solving, and scripted conceptual understanding tactics specific to each skill. All interventions were designed to maximize probability of correct use including: minimizing intervention complexity, providing all materials needed to implement the intervention, and a state-of-the-art user interface that prompts, supports, and rewards teacher use of the intervention over time.

 Implementation support. The principal and coach dashboard does the work of supporting screening completion; interpreting screening data at the school, grade, and class level; tracking risk reduction over time for the school; tracking the growth of students receiving classwide and individual intervention; and directing attention to students who could benefit from additional support to improve growth. Guided by implementation science (Fixsen & Blasé, 1993) Spring Math measures intervention consistency within and across classrooms, rate of improvement for at-risk students, and recommends specific actions to improve student growth each week.

Spring Math decision rules are grounded in the instructional hierarchy and learning trajectories theories (Harniss, Stein, & Carnine, 2002) and are designed to increase alignment between learner proficiencies, task content, and instructional strategy. The theory of change is that the automated use of student assessment data to select the intervention skill and instructional strategy and generate the intervention packet as occurs within Spring Math will (1) Increase alignment between student proficiency, task, and instructional strategy; (2) Increase correct intervention use, and that these effects will increase mathematics achievement. Intervention and generalization skill assessments are embedded to reflect learning gains each week. The model has been tested with especially promising results for students who were at risk for mathematics failure (e.g., effect size = .66 for students performing in the risk range on the preceding year’s state test; VanDerHeyden, McLauglin, Algina, & Snyder, 2012). A randomized controlled pilot study of Spring Math (formally referred to as Intervention Advisor) has also been conducted in the Boston public schools to examine the effect of Spring Math on intervention skill and strategy alignment, intervention use, and mathematics learning gains. At-risk students in grades 1-5 (N = 39) were randomly assigned to the web-based intervention system or a teacher-selected intervention for four weeks. Brief skill assessments were administered each week following standard curriculum-based measurement procedures to track growth of students assigned to each group. Growth was computed as answers correct per two minutes per week on the intervention skill and the generalization skill. Integrity was estimated by permanent product as days per week of intervention use. Intervention skill and strategy alignment were superior in the web-based intervention condition with alignment approximating the base rate (or accuracy based upon chance alone) in the Teacher Choice condition. Statistically significant differences were detected on all outcome measures with effect sizes partial η2 ranging from .14 to .67 for integrity, partial η2 = .13 for intervention skill gains.


Spring Math provides a comprehensive Response to Intervention (RtI) that helps teachers by providing screening, interventions and progress monitoring for individuals or classrooms. Spring Math is unique in how it uses individual student data to create customized class-wide and individual intervention plans that are delivered by teachers to students. Implementation is simple and aided through the use of clear intervention plans, easy to understand graphs and reports back to teachers through a user-friendly dashboard.


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