Assisting Students Struggling with Math: RTI

Another great resource that I feel is worthy of saving is the What Works Clearinghouse’s “Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools,” available at

The fact that this guide is from 2009 makes it somewhat outdated, however, the information is still fairly sound and can be applied to most settings, especially as interventions for mathematics are notoriously difficult. If an RtI Framework is mostly nonexistent in my future setting, I think the best bet for moving forward is the explicit recommendations and checklists in this document. It goes step-by-step, recommendation-by-recommendation, explaining potential roadblocks (e.g. questions from teachers, misidentification, etc.) and how to move forward.

The recommendations are:

  1. Screen all students to identify those at risks, and then provide interventions. (Moderate)
  2. Materials should be mostly in-depth on whole numbers in K-5, and rational numbers in 4-8. (Low)
  3. Instruction should be explicit and systematic (e.g. problem solving models, guided practice, feedback, review) (Strong)
  4. Interventions should include instruction on solving word problems that is based on common underlying structures (Strong)
  5. Intervention materials include opportunities to work with visuals (Strong)
  6. Interventions should include fluency retrieval of basic math facts (Moderate)
  7. Progress monitoring is helpful (Low)
  8. Include motivational strategies (e.g. verbal praise, completion-contingent rewards) (Low)

These recommendations may seem like common sense, but it is moreso the plethora of evidence cited under each recommendation and the steps to overcoming roadblocks that is helpful with this resource. I believe this is a different type of valuable than the other review posted to this site, which examines specific interventions that schools may or may not have the resources to provide, or may not have the buy-in to support. These recommendations can be applied to any curriculum.


Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle Schools. NCEE 2009-4060. What Works Clearinghouse.


Best Practices in Math Intervention – Resources

One great resource I found when looking for Mathematics interventions was Hanover Research’s 2014 Best Practices in Math Intervention research summary. This summary can be found at:

“Hanover Research identified seven mathematics intervention programs with broad support from the research community. Credible authorities suggest the following programs are likely to significantly improve students’ mathematics abilities:

  • Fraction Face-Off!
  • Hot Math Tutoring
  • Number Worlds
  • I CAN Learn Pre-Algebra and Algebra
  • DreamBox Learning
  • enVisionMATH
  • Do The Math

Three crucial practices should be applied to all mathematics interventions: universal screening, explicit and systematic instructional methods, and data‐based decision making (p.3).”

Additionally, they suggested that fluency practice is crucial, role play and technology are typically helpful, and that early intervention is key, as we know.

Overall, this document is a helpful resource if looking for a scripted intervention program to implement in your school, as it reviews research and looks into a variety of interventions.

Great Number-Line Race! – Numeracy Game

More information about this intervention can be found at:

This intervention is essentially a simple number board game that helps students with early number sense, typically students in pre-school or similar age programs. Complete steps, as well as a game board, can be found at the aforementioned link at InterventionCentral. This game takes 12-15 minutes per individual player and is very simple to implement with the instructions at the above link. The below resource, with a link to access to actual research, goes into the development of the game and how it can be effective for low-SES preschool students, who may have had only limited exposure to mathematics or math intervention and have thus not developed an early number sense. For these students, even a simple intervention such as this can have large effects that will help reduce the risk of later difficulties in math.

Siegler, R. S. (2009). Improving the numerical understanding of children from low-income families. Child Development Perspectives, 3(2), 118-124. Retrieved from

Custom Math Self-Monitoring Checklists

More information about this intervention can be found at:

This intervention essentially involves a teacher creating a list of errors that a student commonly makes in their classroom and then creating a checklist for the student to eventually self-monitor for their own mistakes. This list can be developed based on a review of data or previous assessments with the student. For example, if a student commonly mistakes addition for subtraction on a mixed-problems worksheet, or mistakenly is off by one digit. This checklist is best if it is short, e.g. 4-5 items. This checklist is introduced and then eventually faded out once the student’s error rate decreases (e.g. 90% success rate). Reinforcement, praise, and encouragement is always helpful and can be built-in to this intervention.

Sample checklists can be found at the aforementioned link. This intervention is backed by self-monitoring research and has been specifically conducted for students with learning disabilities.

  • Dunlap, L. K., & Dunlap, G. (1989). A self-monitoring package for teaching subtraction with regrouping to students with learning disabilities. Journal of Applied Behavior Analysis, 229, 309-314.
  • Uberti, H. Z., Mastropieri, M. A., & Scruggs, T. E. (2004). Check it off: Individualizing a math algorithm for students with disabilities via self-monitoring checklists.Intervention in School and Clinic, 39(5), 269-275.

HELPS – Reading Fluency

More information about this intervention can be found at:

HELPS, which stands for Helping Early Literacy with Practice Strategies, is a free, one-on-one intervention that is quick to implement (10-15 minutes a day, 2-3 times a week) and has a significant amount of evidence basis. A variety of information about HELPS can be found at their website,, including training materials and the HELPS One-on-One Program Teacher’s Manual. The aforementioned teacher’s manual goes into great detail about how this intervention can be used in an RTI system at all three tiers of intervention, and also discusses the types of readers who may benefit from this intervention (including ELLs). HELPS has not been studied by the What Works Clearinghouse or the Best Evidence Encyclopedia, at least not that I could find. However, I was able to access Begeny et al. (2010), which was the initial evaluation of the HELPS curriculum. This study found that HELPS had a medium-to-large effect size on several measures of reading fluency (the TOWRE, R-CBM, GORT, WJ-III Ach, and MAZE). The intervention involves timed readings, recall checks, feedback and goal-setting/achievement, practice with incorrect words, repeated reading, modeling, and a reward procedure – essentially, many of the elements of best practice in reading instruction all in one efficient intervention.

I truly believe that every school with available intervention specialists, especially if they have Title teachers, would benefit from implementing HELPS, as the fact that it is quick, free, and research-based is essentially my personal trifecta of a solid intervention. This intervention is designed to help with reading fluency, which tends to have a subsequent impact on reading comprehension as fluency improves.

Begeny, J. C., Laugle, K. M., Krouse, H. E., Lynn, A. E., Tayrose, M. P., & Stage, S. A. (2010). A Control-Group Comparison of Two Reading Fluency Programs: The Helping Early Literacy with Practice Strategies (HELPS) Program and the Great Leaps K-2 Reading Program. School Psychology Review, 39(1), 137-155.

Folding-In – Math

More information about this intervention can be found at:

A previous post described the merits of using “Folding-In” as an intervention related to reading. This general concept of creating known and unknown flashcards and sorting them until mastery can also be applied to mathematics. Specifically, Self-Administered Folding-In is a common intervention script that can assist students in developing their fluency in basic math facts. For this intervention, flash cards are made with the math fact to be practiced on the front, and the answer on the back. Similar to in reading, these cards are sorted into “known” and “unknown” piles in accordance with a baseline procedure or with a prior assessment of knowledge. As in the reading version, the student creates a pile of 7 known and 3 unknown facts, and writes the answer on a dry erase board. If the answer is given within 3 seconds, it is considered known. Students repeat this process with all 10 cards until mastery. This is a brief summary of this intervention, but more detailed instructions are available at the link at the top of this page, including a checklist of the intervention’s steps for students, as well as a log of their mastered facts. This intervention is also a result of the Shapiro “Academic Skills Workbook” (cited below) and can be easily adapted to use with a tutor or instructor if the student is unable to self-manage their own work. Another example of an intervention script, for use with peers, can be found at:


Shapiro, E. S. (2004). Academic skills problems: Direct assessment and intervention (3rd ed.). New York: Guilford Press.



More information about Folding-In can be found at a variety of websites, including:

Folding in is a very simple intervention that can be used with many different types of students, including students who are struggling with sight words/letters (depending on grade), vocabulary, or general reading fluency in need of additional support, or even in different categories (see the separate post “Folding In – Math” for an example in mathematics). This additional intervention is easily adaptable and can be used at all intervention tiers depending on resources. The intervention could also include direct instruction on errors and use a variety of error correction procedures. 

This intervention involves creation of a master deck of flash cards in the area of need (e.g. sight words, vocabulary, letter names) and a baseline assessment of known vs. unknown cards, with known indicating that the student can correctly respond in less than 3 seconds (automatic). The cards are sorted following this baseline, and in future sessions, the tutor creates a deck of 10 cards, 7 known and 3 unknown. The card is shown, and if the student gets the card right, the tutor repeats the correct answer back, while if they get it wrong, the tutor corrects the student and asks them to repeat the correct answer. This process is repeated until the student can get the daily deck correct 3 times in a row, and then can be repeated again by removing 3 cards from the daily deck and adding 3 new unknowns.

This intervention is valuable because it is quick, extremely flexible to student need, and can be implemented for as much or as little time is available with the tutor. Folding in is considered an “incremental rehearsal” intervention, and appears to result from Shapiro’s (2004) Academic Skills Problems Workbook. In the Best Practices for Reading Problems chapter of the Best Practices book, Joseph (2008) states that this technique “has been supported in several investigations for teaching reading words as a whole and teaching vocabulary” (p. 1171), helping students acquire fluency and also maintain these words over time. 

Joseph, L. M. (2008). Best practices on interventions for students with reading problems. Best practices in school psychology, 4, 1163-1180.

Shapiro, E. S. (2004). Academic skills problems: Direct assessment and intervention (3rd ed.). New York: Guilford Press.

Leveled Literacy Intervention

Information about LLI can be found at: (Heinemann/Fountas & Pinnell/Houghton Mifflin Harcourt)

Leveled Literacy Intervention (LLI) is designed as a small group daily intervention for students who are having difficulties with phonics, fluency, or vocabulary. The curriculum, outlined in a highly specific manual (often overly specific, according to the instructor), includes specific enjoyable activities (e.g. acting in a play or debate), a significant amount of modeling and direct instruction in phonics rules, group discussions as reinforcement and further learning, and “word work” in a writing journal. According to the National Center on Intensive Intervention (n.d.), this intervention was developed by Fountas & Pinnell and is designed for groups of 3 students in 30 minute sessions, 4-5 times a week for 14-18 weeks. 

The What Works Clearinghouse has not published a review of LLI at this time that I was able to find. However, as mentioned previously, the National Center of Intensive Intervention outlined one study on LLI that indicates some moderate student gains (Ransford-Kaldon et al., 2010). The effect sizes they found, based on the Fountas and Pinnell Benchmark Assessment Systems for grades K-2, were .76 (Kindergarten), .81 (1st grade), and .39 (2nd grade), and also found some effects based on DIBELS assessments, ranging from small to large depending on measure. Heinemann, owner of the assessment, further outlines this and another independent study on  their website (, which indicate significant success in helping students catch up to grade level in both rural and suburban settings (Ransford-Kaldon et al., 2010) and urban settings (Ransford-Kaldon et al., 2013). Overall, this evidence seems to indicate that LLI is successful in enhancing student outcomes of reaching grade level in reading, though more research would be helpful. The somewhat rigid curriculum may be an area of concern for implementers, but these lessons can be supplemented with other materials if students have specific needs. 

National Center on Intensive Intervention (n.d.). Leveled Literacy Intervention System. American Institutes for Research. Retrieved from

Ransford-Kaldon, C. R., Flynt, E. S., Ross, C. L., Franceschini, L., Zoblotsky, T., Huang, Y., & Gallagher, B. (2010). Implementation of Effective Intervention: An Empirical Study to Evaluate the Efficacy of Fountas & Pinnell’s Leveled Literacy Intervention System (LLI). Center for Research in Educational Policy (CREP). Retrieved from

Ransford-Kaldon, C.R., Ross, C.L., Lee, C.C., Flynt, E.S., Franceschini, L.A., & Zoblotsky, T.A. (2013). Efficacy of the Leveled Literacy Intervention System for K–2 Urban Students: An Empirical Evaluation of LLI in Denver Public Schools. Center for Research in Educational Policy (CREP). Retrieved from


Fast ForWord

More information on Fast ForWord can be found at: (The Scientific Learning Corporation)

Fast ForWord is a computer-based reading program that is intended to help students strengthen their cognitive skills necessary for later success in reading and math (U.S. Dept. of Education (DOE), 2013). This intervention is intended to be part of a daily routine for students, for at least 30 minutes over 4-16 weeks. At my site in Milford, only a few students receive this intervention, as part of Tier 3 services, and they go to a separate classroom during their “differentiation” time block in order to do so.  I was able to observe two students independently working on the Fast ForWord to Reading program under supervision of an intervention specialist, which is one of the series available under the Fast ForWord name, in one of the first days at my practicum site. This specific series focuses on “reading skills such as sound-letter associations, phonological awareness, word recognition, knowledge of English-language conventions, vocabulary, and comprehension” and is highly adaptable based on student responses (U.S. DOE, 2013, p.1). 

In terms of evidence base, the What Works Clearinghouse’s assessment of Fast ForWord is that it has positive (medium-to-large) effects on alphabetics, minimal positive impact on reading fluency (small), and mixed effects on comprehension (medium-to-large). One major potential flaw of this intervention is its cost for these somewhat mixed effects. Each license for the reading program costs upwards of $500, meaning that this is a significant investment in the program for the school. This cost is a significant assessment for mixed results and should be used with caution, especially if the product is being shopped by a publisher who may over-emphasize its effects on working memory. 

U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2013, Mar.). Intervention Report: Fast ForWord. Retrieved from


Reading Mastery

Information about Reading Mastery can be found at: (McGraw-Hill Education)

According to the What Works Clearinghouse Intervention Report (2006), RM has potentially positive effects for both English Language Learners and English speaking students, though only one study met their standards, with a 28 point percentile gain for an average student in the study they include. RM is a direct instruction method that uses a special type of font in its book to help students identify the sound a letter makes in that particular word. These lessons are scripted for the instructor, including modeling, scaffolded practice (individual and guided), and direct instruction in many of the rules of reading and pronunciation. The lesson began with a review of some specific sounds (e.g. /x/, or ȳ) and letter combinations (e.g. vowel combinations, “the first one does the talking”, or the two possible “oo” sounds), and eventually sounding out full words until mastery (the “fast way”). Lessons also involve choral reads of text together with the instructor, practice reading individual sentences and challenge words, and repeated readings.

U.S. Department of Education, Institute of Education Sciences, What Works Clearinghouse. (2006, Sept.). Intervention Report: Reading Mastery/SRA/McGraw-Hill. Retrieved from