What is high-quality mathematics instruction and why is it important?
Page 4: Evidence-Based Mathematics Practices
Once they have adopted a standards-based curriculum, teachers can begin to help their students learn the identified concepts and procedures. The most effective way to teach concepts and procedures is to implement evidence-based practices (EBPs)—techniques and strategies that have been shown through research to be effective for teaching mathematical concepts and procedures. When teachers implement EBPs along with a standards-based curriculum, they are providing high-quality mathematics instruction.
For Your Information
Though the terms evidence-based practices and evidence-based programs are often used interchangeably, experts and practitioners now recognize the importance of differentiating between them. The definitions below reflect the distinct characteristics of each.
Evidence-based practice: A technique or strategy that has been shown to be effective through multiple high-quality experimental research studies or large-scale research field studies; the criteria for identification of this practice vary by organization or agency.
Evidence-based program: A collection of practices that, when used together, has been shown to be effective through experimental research studies or large-scale research field studies.
Why Should Teachers Use Evidence-Based Practices (EBPs)?
Educators often shape their instruction around practices and methods that they have grown accustomed to. These might be commonly used practices or ones that they have noticed colleagues using in classrooms. They might even be practices or strategies that educators learned from their own teachers during school. Unfortunately, many of these methods have been shown to be ineffective or have no data to support their effectiveness. Moreover, educators who rely only on personal experiences might miss out on strategies that research has shown to be effective. The solution, then, is for teachers to verify that they are using EBPs in their classroom instruction. There are good reasons for doing so. From a practical standpoint, the use of EBPs is mandated by the Every Student Succeeds Act (ESSA) and the Individuals with Disabilities Education Act (IDEA). These federal laws require teachers to use, to the greatest extent possible, academic and behavioral practices and programs grounded in scientifically based research.
Every Student Succeeds Act (ESSA)
glossary
Individuals with Disabilities Education Act (IDEA)
glossary
scientifically based research
glossary
Beyond the issue of legal obligation, however, is the fact that EBPs significantly increase the prospects of student achievement and learning. The benefits of using EBPs include:
- Increased likelihood of being responsive to learners’ needs
- Increased likelihood of positive student mathematics outcomes
- Increased accountability because data back the selection of a practice or program, which in turn facilitates support from administrators, parents, and others
- Less wasted time and fewer wasted resources because educators start off with an effective practice or program, rather than attempting to select one through trial and error
- Higher probability of convincing students to try a practice or program because there is evidence that it works
Now that we have discussed why educators should use EBPs in their classrooms, let’s turn to how they can select and implement EBPs with fidelity.
Identifying and Selecting EBPs
When trying to identify EBPs in mathematics, educators will not only locate general overviews of EBPs but research findings and effectiveness ratings. Attention to this information is important. Not every EBP is appropriate for every situation or setting. In general, the closer a given practice or program matches student needs, the greater the likelihood it will lead to a desired outcome. For example, a third-grade teacher with a classroom containing a large proportion of ELs should look for a mathematics program that has been shown to be effective with all students, including those who are learning English.
Implementing EBPs with Fidelity
Once an EBP is chosen, the practice or program must be implemented with fidelity, or in the manner intended by its researchers or developers. Research indicates that improper EBP implementation is one of the most common reasons educators fail to get the results they anticipate. To implement an EBP with fidelity, a teacher generally should:
fidelity (of implementation)
glossary
- Adhere to the procedures of the instructional practice or program (e.g., implement with groups of the correct size)
- Implement the practice or program with recommended frequency (e.g., daily, three times per week)
- Implement the practice or program for the recommended duration (e.g., one semester, one academic year)
- Skillfully implement the instructional procedures
- Seek training and ongoing support
Though correct implementation of an EBP increases the likelihood of improved performance, there will nevertheless typically be a small percentage of students who do not respond to it. For this reason, educators should collect data on each student’s response to determine whether the practice or program is beneficial for each student.
Sarah Powell, a researcher in the area of mathematics strategies, discusses why educators should implement EBPs and the importance of doing so with fidelity (time: 2:20).
Sarah Powell, PhD
Professor, Department of Special Education
The University of Texas at Austin
Transcript: Sarah Powell, PhD
It’s really important to use evidence-based practices in mathematics so that we are not wasting the time of students. We need to be very efficient with the instruction that we provide to students. And that’s not only true for students with learning difficulties, but that’s true for every student in the mathematics classroom. We only have 180 days in a school year with these students. Many times, it’s less when we put in field trips and absences and things like that. And there’s a lot of mathematics that needs to be taught in any school year. So the importance of evidence-based practices is to get right at the heart of how to teach mathematics and how students learn mathematics. And we also have to rely on the research over the last 10, 20, 30 years. It’s nice to try out new things, but we’re not always sure if those are working, and we don’t want to waste teachers’ time, and we don’t want to waste students’ time.
There are quite a few resources out there that help us identify evidence-based practices. We can go to the original sources, which would be research journals or practitioner journals, but most people don’t access those because they’re long and hard reads. So there’s some really good websites that we can use that synthesize evidence-based practices in mathematics. Once you choose an evidence-based program or an evidence-based strategy to implement, we need to make sure that the teacher or you implement it as it was designed. And usually in the research world, we say that you need to be implementing about 90% of the parts or components of an intervention to be implementing that intervention with fidelity. If you don’t implement it in such a way, then you can’t really expect the same results that came from the original research study or the original research studies.
There are always going to be a few students that are what we call non-responders to a specific intervention or a specific strategy, and that’s okay. Then we have to fine-tune what we’re doing or go a different direction and find what works for those students. We need to think of students as individuals, and what works for most may not work for one. And then we have to figure out what works for that one student. The nice thing about evidence-based practices is that we know that they do work for most, so it’s a really good starting point.
EBPs for Mathematics
moderate evidence
glossary
strong evidence
glossary
High-Leverage Practices
High-leverage practices (HLPs), developed by CEEDAR and the Council for Exceptional Children (CEC), are essential special education techniques that all teachers of students with disabilities should master for use across a variety of classroom contexts. As each of the EBPs (listed on the left) are described on the following pages, we will connect them to the relevant HLPs when applicable.
Research on effective instructional practices in mathematics is ongoing. As more research is conducted, new practices deemed effective for teaching mathematical skills and concepts will most likely emerge. This module will highlight four broad instructional practices that show moderate evidence to strong evidence for improving student outcomes in mathematics.
- Explicit instruction
- Visual representations
- Schema instruction
- Metacognitive strategies
As you read about these four practices, you will notice some overlap. For instance, explicit instruction is a particularly effective method of teaching mathematics procedures. But it is also a key component of teaching students how to use visual representations and schema instruction.
For additional information about content discussed on this page, review the following IRIS resources. Please note that these resources are not required readings to complete this module. Links to these resources can be found in the Additional Resources tab on the References, Additional Resources, and Credits page.
To learn more about identifying EBPs, implementing them with fidelity, and evaluating whether they are beneficial for individual students, review the following IRIS Modules:
Best Evidence EncyclopediaThis online resource offers information on the researched evaluations of numerous educational programs in a coherently arranged and easy-to-navigate format. Center on InstructionExplore this website to find “a cutting-edge collection of scientifically based research and information on K–12 instruction in reading, math, science, and special education.” On hand are links to resources for struggling readers, literary resources for adolescents, an introduction to progress monitoring in math, and many others. National Center on Intensive InterventionThe National Center on Intensive Intervention hosts and provides links to resources on an incredible number of academic topics and instructional practices. Among their offerings related to mathematics are sample lessons and activities, a wide variety of instructional videos, diagnostic assessments, and resources for intensive interventions, among much more. What Works ClearinghouseThis U.S. Department of Education site offers a variety of mathematics-related resources, such as the following practice guides (listed in order by publication date):
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