There’s a common myth surrounding students who struggle with math. This is that students learn at different rates, so those who are behind will catch up later.
While catch-up growth is achievable, it is not possible without providing students with targeted and personalized math intervention activities that grow their knowledge and skills to close the achievement gap.
In this webinar, learn the importance of meeting the academic and behavior needs of students from a systems level with math intervention strategies built into your Multi-Tiered Systems of Support (MTSS) framework. Also walk through advice for providing students with effective response to intervention (RtI) in math, effective strategies for teaching students with difficulties in math, and specific strategies for building mathematical fluency and building conceptual understanding in math.
MTSS and RtI greatly impact the success of math fluency intervention for struggling students. Watch the webinar to review some of the elements necessary for a successful MTSS program. These include:
Also learn the four main steps for building an effective and sustainable MTSS framework for supporting students who are struggling with math. Walk through each of the following tasks in detail:
After discussing the role of MTSS, the webinar reviews the specific questions to address in order to build a strong framework to support students struggling with math, specifically:
Students who enter a classroom lacking a basic understanding of math facts and fluency in core mathematical procedures need more than practice. Students receiving interventions rarely require extra support simply because they have not memorized their math facts. They need to master mathematical concepts, procedures and problem-solving strategies, too.
Review effective teaching techniques and math fluency strategies for struggling students. Specifically, receive advice for building mathematical fluency and building conceptual understanding in math by making math connections more explicit. It is important for students to be able to see connections between and within mathematical ideas. This conceptual understanding is the foundation for fact and procedural fluency, and fluency forms the foundation for continued learning and math ideas. Students in interventions often struggle to see mathematical connections on their own. Learn specific and explicit ways you can teach to strengthen these connections.
Dean Ballard: The first myth was a prevalent belief for many decades, but has been soundly disproven by research. Myth number one, students learn at different rates so they will catch up later.
Dean Ballard: While it’s true that not all students are alike and there are variations in learning rates, what is perhaps more true or more important to understand, is that students who fall behind are likely to stay behind if they’re not provided support. The earlier the support to catch up, the better. The further behind a student is, the more intensive the support needs to be. Benchmarks for reaching and math are set at levels that all students (except possibly those with learning disabilities) can and should attain.
Dean Ballard: There’s ample research to back this up, such as studies from ACT, Geary, Hoard, Nugent, and Bailey, Shaywitz , and others. Keep in mind, kindergarten and first grade are not too early to identify and address learning deficits.
Dean Ballard: Because identifying and addressing learning needs at all grade levels is important, I want to briefly call attention to practices of multi-tiered systems of support in response to intervention. According to McIntosh and Goodman, MTSS is a coherent, strategically combined system, meant to address multiple domains or content areas in education. MTSS is important as a systems focus within a district or a school on meeting the academic and behavioral needs of all students. I’m not going to delve deeply into MTSS since that’s not the focus of this webinar, however, it’s good to recognize that what we’re talking about in this webinar is part of MTSS and RTI.
Dean Ballard: It’s worth just taking a moment to review key components of RTI, because these heavily impact the success of math support for struggling math students or in math interventions. Leadership and a team that plans, monitors, and drives an intervention system are critical for school-wide and district-wide success. One of my colleagues at CORE was just telling me about two different schools she was working with, and how the leadership at one school was focused and drove an emphasis on supporting struggling learners in both math and reading, versus another school in the same district with leadership that, at most, provided suggestions to staff on interventions.
Dean Ballard: The results have been very clear. The school with the focused support on addressing learning gaps is far out performing the school that was driven by suggestions for interventions. Additionally, research has proven the schools that succeed with RTI have leadership RTI teams that monitor and manage intervention systems within the school, and use data to drive decision making with generally three tiers of instructional support.
Dean Ballard: Those three tiers of instructional support include Tier 1, which is the core instruction itself, which can include some differentiated support within the core instruction to address immediate or emerging gaps and misconceptions. Tier 2, which is small group instruction, is instruction designed to address more persistent gaps, very weak or missing important prior knowledge, or continued and deepening struggles with understanding core instruction. Tier 2 can take place within core classrooms or it can be additional time in a support class.
Dean Ballard: Tier 3 addresses severe learning needs, typically students who are two or more years behind in key areas in mathematical understandings or skills. Tier three requires working with students outside the core instruction, and in extreme cases may even replace the core instruction with what is called an intervention core class.
Dean Ballard: My final words on RTI itself are to mention the four main steps in the RTI process. The MTS/RTI team may first explore and identify as a school-wide needs, resources, and personnel that are likely to be part of the system [practicum 00:07:00] and support. Then a plan is put together for how to identify and place students, along with what assessment systems and data will be collected, how it’ll be used. The plan includes what interventions to be put in place, what content will be taught, who will the teachers be, and how students and programs will be assessed.
Dean Ballard: Additionally, the plan includes how interventions will be implemented, such as you might just do one or two classes to start with, and then expand from there, or the whole school will implement it incrementally. Then the plan is implemented. Finally, interventions much be sustained with on-going support and be monitored. Part of sustaining a system is to continually monitor its effectiveness. We want to know where the interventions, where they’re working and where they’re not working, so we can see how to improve them. We should monitor if students are closing gaps and if they are able to progress out of the interventions, or if at best, students are just treading water and not actually catching up to grade level proficiency.
Dean Ballard: Those important components of a RTI process bring us to the key areas I’m going to address throughout the rest of this webinar, as they relate to providing support for struggling students in math. I’ll talk about who are the students that need and will receive added support. How do we decide on what to teach? What is the content focus for added support or intervention? When to teach? Where is the time in the schedule for providing added support? How to teach? What are the basic instructional techniques to use for different levels of support? Who are the teachers that will provide the added support? When should we use a publisher intervention curriculum program? When that should be used versus other resources? When are the best intervention materials to use in different situations? Why we need to assess, review, and revise intervention programs.
Dean Ballard: Next, let’s look at effective teaching techniques and how these are similar to and different from the techniques that may be used for core instruction. One common complaint from teachers is that students come into their math classes unprepared, because students don’t know their math facts and are not fluent in basic procedures. This often leads to a common refrain we hear, and this learns to our myth number seven. Students just need lots and lots of practice with math facts. Well, of course it is true. Students do need plenty of practice, both immediate and distributed. This is even more true for students struggling in math. As we’ve seen in intervention, what we have them practice on is a subset of earlier math concepts, the key concepts that are most meaningful for helping these students move forward.
Dean Ballard: However, it is just as important to recognize that students rarely need extra support simply because they don’t have all their math facts memorized. As described in research and by math experts, these students still need understanding of concepts, fluency with math, and ability to apply the math. The key difference is in how we narrow that focus on specific concepts for these students.
Dean Ballard: Additionally, with more focus for struggling students, we need to make math connections very explicit. Take a moment here to read this statement from Marilyn Burns.
Emily: Students who need intervention instruction typically fail to look for relationships or make connections among mathematical ideas on their own. They need help building new learning on what they already know.
Dean Ballard: Thanks again, Emily, for reading that. So, it’s important for students to see connections between and within mathematical ideas. Conceptual understanding is the foundation for fact and procedural fluency, just as fluency is part of a foundation for continued learning and math ideas. However, students in interventions struggle to see those connections on their own or on their first pass through a concept. Therefore, we as teachers need to provide more explicit direct instruction that attends to these connections.
Dean Ballard: We still need to require students to think and reason about math and make some connections, but as teachers, we’ll do more of the heavy lifting than we typically do with a Tier 1 instruction. For example, suppose students are making a common error when adding fractions with unlike denominators, such as one half plus one fourth. They incorrectly add the numerators and the denominators to get the wrong answer of two sixths, rather than three fourths. To address this misconception about adding fractions, rather than simply reviewing the correct procedure again and again, which students in intervention will have likely seen multiple times already, a better approach is to return to the conceptual level and the important maths concepts this is built on.
Dean Ballard: Use a number line to start with, to visually show adding one fourth and one half. Provide a number line, such as this shown on the slides, and have students label the parts on the number line. Then have students justify the placement of one fourth and one third and one half. Make this clear for all the students, where those go and why they go where they go. Provide bars to visualize the size of the fractions on the number line. Show students how to make the drawing on their own number line that illustrate one fourth plus one half, then have them determine the value of these two bars when they’re put together, where they end up on the number line.
Dean Ballard: Have students locate their answer of two sixths on the number line and compare this to the visual of three fourths. We do that because this helps convince students that their answer … Hmm, maybe it really is wrong. Because they see that the answer should be three fourths. This provides a nice visual proof for that. Misconceptions can be like weeds. They’re very hard to get rid of. So, you really have to take the extra step to help students see that, “Oh! That answer was wrong. It’s not just because I have a procedure that gets a different answer. It’s because it really doesn’t look right. I mean, there’s a reason for it.”
Dean Ballard: So, we want to convince students about that. And next, remind students about adding whole numbers, and how fractions are like adding whole numbers. We add like units together. We add the ones to the ones, the tens to the tens, the hundreds to hundreds. Then we explain that one fourth and one half are not like units. They’re not ones ….. They have different denominators. You have to make them like first. So, in order to add them together you have to get them to be the same unit, just like we do with whole numbers. So, first we change one or both fractions so they have the same denominator, because the denominator is the unit of the fraction.
Dean Ballard: Now we move to the procedure for adding the fractions. We changed one half to two fourths, and then we add one fourth and two fourths to get three fourths. Have students identify this on the number line and compare it to the visual model. This kind of explicit instruction combined with student interactions around the connections within the math, allows students to see why a common error is wrong and why the correct procedure makes sense.
Dean Ballard: Next we would model and provide guided practice on a couple more like problems, and then have students practice this skill. Practice should include having students illustrate on number lines a couple of problems on their own to solidify the connections between the procedure and the concepts, in their minds. Then students can practice the procedures many times to build fluency with it.
Dean Ballard: So, you see from this, we include some student thinking and reasoning into this sequence of instruction by doing things like, we provide a number line without numbers and have students fill those in. Have students think about where those numbers are. Have them justify the placement of the numbers, one fourth and one half and one third on the number line. We ask them to figure out where the two sixths goes on the number line. Compare that to the answer of three fourths. We have students make a drawing of their own, of these. Let them see and make that illustration to show what the value of the fractions are and what they are when they’re put together.
Dean Ballard: So, we can be very explicit about the math. We can scaffold the problem to give access to all students and ask targeted questioned within the framework, that ask students to do some thinking that lays the foundation for the mathematical connections. The math connections that are going to be made clear, most likely by us. By connecting visual models to math ideas, we help students see and understand concepts, and see the sense in those give procedures. Connecting to prior knowledge, such as connecting fractions, operations to whole numbers, also reinforces the consistent and connected nature of mathematics.