Examples of Effective RtI Use and Decision Making: Part 3 - Mathematics

We conclude our three-part series of articles with case examples in mathematics to show how Response to Intervention (RtI) decisions are reached in real-world scenarios. For each case example, we’ll guide you through a series of three questions that should be asked:

  1. Is there a gradewide learning problem? If yes, what is causing the problem?
  2. Is there a classwide or individual learning problem? If yes, what is causing the problem?
  3. Did intervention successfully resolve the problem?


Is There a Gradewide Learning Problem? Are There Individual Learning Problems?

Note: graph created on iSTEEP.

Computation probes work well for universal screening in mathematics. In this 4th grade class, multiplication facts 0 to 9 was administered at fall screening. Multiplication facts are a prerequisite skill, taught in 3rd grade, and required for a child to be successful in most 4th grade mathematics curricula. Children who cannot compute basic multiplication facts at the beginning of 4th grade are at pronounced risk for failure in mathematics because expectations for learning in math at 4th grade emphasize proportional reasoning (computations and problem solving with fractions, percentages, and decimals).

In this case, more than half the class is performing in the frustrational range and only nine students are in the instructional range. No student in this class has mastered this prerequisite skill. In this case, there is a classwide learning problem in mathematics, or stated another way, this entire class is at risk for mathematics failure. The next step is to determine whether this class is the only class at 4th grade at risk or whether many classes are at risk for failure, reflecting a gradewide learning problem. Where there is a gradewide learning problem, it is not possible to determine accurately whether individual learning problems exist.

Note: graph created on iSTEEP..

The graph above shows all classes in 4th grade at this school. These data show us that the majority of students in 4th grade are performing in the risk range on this particular skill, forecasting that most students in 4th grade are currently at risk in mathematics. Because many students are at risk at this grade level, implementers must troubleshoot core instructional programming to identify and repair the instructional problems that are causing so many students to perform below expectations. It is also necessary to implement supplemental intervention to “catch students up.” Corrective efforts can be planned and implemented immediately. Routine screening data can be used to evaluate whether corrective efforts are paying off or not.

Note: graph created on iSTEEP..

In this case, efforts to repair the gradewide learning problem in mathematics seem to be working. Each class has shown a dramatic reduction in the number of students at risk in each class in only a short period of time. Because this measure reflects only one skill, it is important to examine other sources of information to verify that improvements are detected more broadly (across a number of mathematical skills). Examining the percentage increase in students meeting the proficiency criterion on the year-end accountability measure in mathematics would provide important corroboration that the interventions are working as intended to reduce mathematical risk at 4th grade. Additionally, districts and schools can examine intervention progress across classes, grades, and schools to verify that interventions are working as planned. These data can be used to identify classes that are lagging behind, and coaches can go into those classrooms and provide assistance to catch lagging classes up as shown below.


TIP: A coach can be someone at the school who has experience running classwide intervention. The coach should watch the teacher conduct the intervention and provide assistance to improve intervention delivery. The coach should be looking for high rates of student responding, high accuracy of student responding, frequent corrective feedback, use of goals and incentives to maximize student motivation, and correct completion of all the steps listed in the intervention protocol. An incorrectly implemented intervention does not yield data that can be used for RtI decision making.

Note: graph created in Microsoft Excel™

The graph above shows the progress of each class at mastering the skills that are being targeted during gradewide intervention. The classes that are lagging behind (the top four classes) are those classes where implementation coaches should spend time troubleshooting intervention and supporting improvements to instructional efficacy.

As classes show improvement, individual students who lag behind their peers can readily be identified for individual intervention. Student A in the graph below remains in the frustration range when the class median has reached mastery. Student A should proceed for individual assessment and intervention.


TIP: Long delays between decisions in RtI often are signs of poor implementation. Long delays between decisions signify misuse rather than correct use of RtI

Note: graph created in Microsoft Excel™

What if a Classwide Problem is Not Detected? Who as at Risk in This Class?

Note: graph created on iSTEEP.

In this case, there is no classwide learning problem because most of the scores in the class are above the risk range. Four students in the class are performing below criterion on the screening. These four students participate in a brief follow-up assessment, in exchange for a small reward, to determine whether their scores improve. Three of the four students improve their scores to the instructional range and get a small reward. Student 3 remains in the risk range. Student 3 is the student who should proceed for further individualized assessment and intervention.

What is Causing the Problem?

Note: graph created in Microsoft Excel™

In this case, the student’s performance is unimproved when incentives are offered. Dropping down a level of difficulty and adding error correction as an instructional technique caused an immediate improvement. When these instructional supports were withdrawn, performance decreased to baseline levels. When the instructional supports were reinstated, performance again improved. This assessment required about 30 minutes and in effect provided a “road test” of the intervention, showing it would work if properly used in the classroom. The last phase shows that the intervention works for this student.

Note: graph created in Microsoft Excel™

Over 2 weeks of individual intervention, the student’s performance improves and the student’s score no longer falls in the risk range on an expected, grade-level mixed computations probe. This intervention is successful.

One of the best contributions of RtI is that it focuses decision makers on student learning outcomes. An RtI implementation is working only when we see upward growth or improvements in student learning. It is hard to beat as an educational investment because by its very definition, its use must return results (or it’s not being used correctly). However, to attain the expected effects, implementers must attend to the small details and work each step with great fidelity. RtI implementation has been compared to going on a diet. Ultimately the weight loss will come, but it follows careful and consistent monitoring of caloric intake and exercise. Short bursts of exercise on an inconsistent schedule will not work. One can do most everything right, but have periodic calorie splurges that ultimately cost the dieter his or her results. In RtI, the decisions made at each step of decision making are only as solid as the data upon which they are based. Yet, the process is not all that complicated, as the examples in this three-part article series show. If users take care to ensure that they conduct each step with accuracy and efficiency, then decision errors will be minimized and learning outcomes will be enhanced. One of the great characteristics of RtI as a system improvement strategy is that any idea set forth by a leadership team is a hypothesis that can be tested with routine, high-quality student performance data. This series articles has provided an overview of RtI decision making as well as examples of decision making in reading and mathematics to help implementers identify where RTI implementation efforts can be tightened up for more accurate decision making and stronger learning effects.

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