Response to intervention in mathematics: Critical elements

What Works Clearinghouse, 2009

to bring the best available evidence and expertise to bear on the types of systemic challenges that cannot currently be addressed by single interventions or programs. Authors of practice guides seldom conduct the types of systematic literature searches that are the backbone of a meta-analysis, although they take advantage of such work when it is already published. Instead, authors use their expertise to identify the most important research with respect to their recommendations, augmented by a search of recent publications to ensure that research citations are up-to-date.

2016

The purpose of this thesis is to examine the impact of response to intervention (RTI) in a high school mathematics setting. A major concern in the literature related to the fact that majority of RTI research focused on students at the elementary level and in reading. Therefore in this study RTI was implemented in a high school mathematics classroom and the effects were analyzed. This study is focused on a sample of ninth and tenth grade students from two classes and taught by one teacher in the same high school in an action research setting. Quantitative and qualitative methods of data were collected using documents/artifacts, observations, surveys and interviews. The data was analyzed using both descriptive statistics and the constant comparative method. Validating the results of this study included member checking, pilot testing and triangulation. Over a six-week data collection period, themes were noted that included how Tier 2 interventions are implemented in a high school mathe...

Learning Disabilities Research & Practice, 2007

Responsiveness to intervention (RTI) is an innovative approach to the identification of learning disabilities (LD). The central assumption is that RTI can differentiate between two explanations for low achievement: poor instruction versus disability. If the child responds poorly to validated instruction, then the assessment eliminates instructional quality as a viable explanation for poor academic growth and instead provides evidence of a disability. For children who do respond nicely, RTI serves a critical prevention function. Most of RTI research has been focused on early reading. In this article, we describe two ongoing programs of research on RTI in the area of mathematics: one on a comprehensive mathematics curriculum at first grade and the other focused on word problems at third grade. For each research program, we describe the sample, explain how students are identified as at risk for mathematics disability, provide an overview of the interventions to which responsiveness is gauged, and describe some results to date.

Response to intervention (RTI) is a framework in which interventions are implemented mostly in general education classes to resolve academic difficulties and help to mitigate contextual variables (i.e., lack of instruction, socio economic status, cultural differences, etc.) as an explanation for academic failure. The implementation of evidence-based interventions is very important to the RTI framework. There is limited research regarding RTI and evidence-based interventions in mathematics and young students. For math interventions to be successful in an RTI framework, comprehensive math interventions have to incorporate computation fluency, problem solving, and the use of visual representational simultaneously. Moreover, early instruction in math skills sets the foundation for developing higher order math skills. Therefore, this manuscript reviews the literature regarding math interventions that would apply to early childhood students and are conducive to the RTI model.

Center on Instruction, 2009

… , US Department of …, 2009

Laurel Marsh HOWARD COUNTY PUBLIC SCHOOL SYSTEM ... Joseph Dimino Madhavi Jayanthi Rebecca Newman-Gonchar INSTRUCTIONAL RESEARCH GROUP ... Shannon Monahan Libby Scott MATHEMATICA POLICY RESEARCH ... Recommendation 3. Instruction during the ...

Psychology and Education: A Multidisciplinary Journal , 2022

This study aimed to determine the intervention strategies used by elementary Mathematics teachers and their effectiveness in enhancing learners' performance. Employing a descriptive-correlational research design, the study described the demographic profile of the respondents and the intervention strategies utilized by the teachers and their effectiveness in terms of fundamental, computational and word problem-solving skills. It also determined the significant difference in the intervention strategies utilized by the teachers when grouped according to their demographic profile and the significant relationship between the intervention strategies and their extent of effectiveness in enhancing their learner's performance. Findings revealed that the teachers strongly agreed that they used Repetition in helping their pupils learn better. A significant difference was also noted in the use of Repetition and Timed-testing as intervention strategies specifically in terms of sex. Meanwhile, Male and female teachers differ in their use of two strategies although there was no significant difference in all other strategies under study. Moreover, the teachers did not exhibit any significant difference on the perceived level of effectiveness of the intervention strategies based on the selected demographic profile. Also, significant relationship between the intervention strategies and their perceived level of effectiveness in enhancing learners' performance was evident in the study. Finally, the study concluded that teachers perceived the intervention strategies as effective in enhancing their learners' performance.

2021

Recent intervention research has demonstrated success in raising the achievement level of students who are struggling with mathematics. This practice guide, developed by the What Works Clearinghouse™ (WWC) in conjunction with an expert panel, distills this contemporary mathematics intervention research into easily comprehensible and practical recommendations for teachers to use when teaching elementary students in intervention settings. Two federal laws, the Elementary and Secondary Education Act (ESEA) 2 and Individuals with Disabilities Education Act (IDEA), require use of instructional practices supported by evidence. The recommendations presented in the guide address these laws by translating the body of high-quality evidence into actionable practices for teachers to use with their students. Although this guide is an update of the 2009 guide, Assisting Students Struggling with Mathematics: Response to Intervention (RtI) for Elementary and Middle School, 3 it is narrower in scope, focusing only on practices and principles underlying effective small-group interventions in grades K-6. In contrast, the earlier guide was a broad overview of multi-tiered systems of support (MTSS) in mathematics-then typically referred to as RtI-a data-driven, systemic, problem-solving framework that helps educators provide core instruction, screening, intervention, progress monitoring, and support for students with various need. It also included grades 7 and 8. See the Glossary for a full list of key terms used in this guide and their definitions. These terms are underlined and hyperlinked to the glossary when first introduced in the guide. Minimal: Evidence may not meet standards or may exhibit inconsistencies, but the panel determined that the recommendation must be included because the intervention is based on strong theory, is new and has not yet been studied, or is difficult to study with a rigorous research design. More detailed information can be found in Appendix A and Appendix C. The recommendations and the panel's strength of evidence assessment are shown in Table . The panel suggests that the practices recommended in this guide be used in combination to help students achieve the strongest outcomes. Users of this guide are encouraged to use the advice provided in ways that best fit the varied lessons and contexts in which they work. For each of the six recommendations, we include the following: • Recommendation: Each recommendation includes details about the recommended practice and a summary of the evidence. Appendix C contains a detailed rationale for the Level of Evidence with supporting details from individual studies. • How to carry out the recommendation: The "how-to steps" include the bulk of the guidance for teachers and other educators on • Potential obstacles/roadblocks: The panel offers guidance for addressing potential challenges to implementation. WWC 2021006 Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades | Recommendation 1 | 5 Provide systematic instruction during intervention to develop student understanding of mathematical ideas. How to carry out the recommendation 1. Review and integrate previously learned content throughout intervention to ensure that students maintain understanding of concepts and procedures. WWC 2021006 Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades | Recommendation 2 | 11 Recommendation 2: Mathematical Language Teach clear and concise mathematical language and support students' use of the language to help students effectively communicate their understanding of mathematical concepts. Exercise 30 minutes 8 min bike 2 min push-ups Ratio 8 min 2 min 10 min Exercise 30 minutes 8 min bike 2 min push-ups Ratio a word problem. Her ongoing and repetitive use of the term helps reinforce the meaning of a ratio and how the ratio in the problem provided critical information for solving the problem. Example 2.6. Teacher prompts students to use mathematical terminology in their explanations. Kerry: I noticed that 8 is bigger than 7. Teacher: You first compared the digits in the ones place? Did you mean 8 is greater than 7? Remember, when a number is "bigger" or "larger" than another number we say greater than. Kerry: Yes, I started with the ones place, 7 and 8. 8 was larger, so I needed to cross out the 2 and make it 1. That made 17. Teacher: Because 8 was greater than 7, you regrouped. You took 10 from the 20 in 327 and added it to the 7 ones to get 17. Then you changed the 2 in the tens place to a 1 in the tens place. The teacher points to the numeral 2 in the tens place. Kerry: Yes, because there were 2 tens, I used one of them to make 17. Then I subtracted the 8 and got 9 ones. Next, I looked over and the 4 was greater than the 1. So, I had to change it again. Teacher: You are describing how you knew to regroup the ones and then needed to use that approach again for the tens place. When you regrouped, you used what you knew about place value. Kerry: So then, I regrouped from the hundreds because there were 3 hundreds in 327. I could break apart 300 into 200 and 100. I added 100 to the 1 ten in the tens column, and now I can subtract 40 from 110! That gave me a 7 in the tens place for the answer. That's 7 tens. Teacher: So, your answer for the difference is 79 so far? Kerry: Yes, and then I just had to subtract the hundreds. I did not need to regroup. 200 minus 100 equals 100. The difference is 179! Use a well-chosen set of concrete and semi-concrete representations to support students' learning of mathematical concepts and procedures. 5 Recommendation 3: Representations WWC 2021006 Assisting Students Struggling with Mathematics: Intervention in the Elementary Grades | Recommendation 3 | 22 Recommendation 3 • Semi-concrete representations are two-dimensional (2D) visual depictions such as strip diagrams, simple drawings, tables, arrays, graphs, and number lines that may help students organize information. They can be used in conjunction with concrete representations to transition to more abstract representations. For example, students who struggle with addition, subtraction, multiplication, or division may find it useful to represent quantities with tick marks or by drawing dots. Because the number line is an essential semi-concrete representation in many interventions and standards, we devote a separate recommendation to using the number line effectively (see Recommendation 4). Pictures of concrete and semi-concrete representations described above are sometimes presented virtually on a computer or tablet screen. • Abstract representations are mathematical notations that can include numbers, equations, operations, relational symbols, and expressions (such as 4, 16, multiplication and equal signs, greater than or less than signs, as well as equations such as 4 x 4 = 16). How to carry out the recommendation Use the number line to facilitate the learning of mathematical concepts and procedures, build understanding of grade-level material, and prepare students for advanced mathematics.

Reading Teacher, 2008