942203 research-article2020 ISCXXX10.1177/1053451220942203Intervention in School and ClinicJohnson et al. Feature Intervention in School and Clinic 2021, Vol. 56(3) 163­–171 © Hammill Institute on Disabilities 2020 Article reuse guidelines: sagepub.com/journals-permissions https://doi.org/10.1177/1053451220942203 DOI: 10.1177/1053451220942203 isc.sagepub.com A Self-Regulated Learner Framework for Students With Learning Disabilities and Math Anxiety Evelyn S. Johnson, EdD1, Anne B. Clohessy, PhD2, and Pragnyaa Chakravarthy, MEd2 Abstract Students with math learning disabilities have been shown to experience math anxiety at rates nearly double those of their typical peers. Anxiety about math is thought to disrupt learning by co-opting attentional resources that could be used in problem-solving and may be caused by the way in which students interpret their math-related experiences. This article describes a math intervention designed through a framework of self-regulated learning that defines self-regulated learners as students who are connected, self-aware, self-determined, strategic, and resilient. Specifically described is an intervention that helps students regulate anxiety, initiate a problem-solving strategy, and advocate as needed to use approaches they find effective. Keywords math anxiety, math learning disability, self-regulation, emotion regulation, cognitive flexibility Math anxiety is a state of discomfort caused by performing math-related tasks (Ma & Xu, 2004) and has been associated with physiological outcomes similar to those when experiencing pain (Lyons & Beilock, 2012), and high levels of extreme stress (Pizzi & Kraemer, 2017). Students with math-related learning disabilities (LDs) tend to have deficits in working memory (Johnson et al., 2010), which makes math challenging. Students with LD in mathematics have also been found to experience math anxiety at nearly twice the rate as that of their typically developing peers (Devine et al., 2018). Anxiety triggers negative thoughts and emotions that co-opt the working memory needed to solve math problems (Ashcraft & Kirk, 2001). Put simply, math anxiety contributes to poor math performance. Students with LD in mathematics tend to struggle with self-regulated learning, or the ability to select and use appropriate strategies to achieve learning goals, and this leads to math anxiety (Duncan & McKeachie, 2005; Jain & Dowson, 2009; Kramarski et al., 2010), and low math achievement (Ramirez et al., 2018). When a student does not have the strategies to approach a math task, their stress levels can spike, and this further compromises their ability to perform math tasks. Finally, math anxiety may also be caused by a student’s negative appraisal of their math learning experiences (Ramirez et al., 2018). When students evaluate their math learning experiences as negative, they can begin to adopt a “failure as debilitating” mindset (Ramirez et al., 2018). This thought process creates a negative cycle of failure–stress–failure that can cause a student to become highly anxious about math, and significantly compromise a student’s ability to self-regulate and compromise their math performance. Taken together, these findings suggest that intervention approaches for students with LD in mathematics should include techniques to manage anxiety, to positively appraise their math learning experiences, and to develop their strategic thinking in math. This article describes the components of a multidimensional math and self-regulated intervention developed to address these issues. The intervention described 1 Boise State University, Boise, ID, USA Lee Pesky Learning Center, Boise, ID, USA 2 Corresponding Author: Evelyn S. Johnson, Boise State University, MS 1725, 1910 University Dr., Boise, ID 83725-1725, USA. Email: evelynjohnson@boisestate.edu 164 is grounded in two frameworks, one focused on self-regulated learning and the other on math intervention, integrated to support students with math anxiety and LD in mathematics (Johnson, Clohessy, & Chakravarthy, 2018; Johnson, Clohessy, Meek, & Spears, 2018). Overview of the Frameworks Because students face different challenges, an understanding of these frameworks provides practitioners a way to tailor specific components as needed to respond to the unique needs of their learners. For example, the student (i.e., D) highlighted in the vignette in this article was identified as having a specific LD that impacted her math performance and experienced high levels of math anxiety that often prevented her from getting started with a math task. She also had compromised working memory, low competence with self-regulated learning strategies, low confidence levels, and was struggling with long division in her fifth-grade math class (see Note 1). Through the use of the two frameworks to guide intervention design, the specific strategies can be adapted to support each student’s unique needs. For example, the math strategy will vary depending on the math concept to be taught, or the technique to support math anxiety may differ depending on how anxiety manifests for the student. Self-Regulated Learner Framework Self-regulated learning is the ability to regulate one’s thinking, behavior, and emotions in pursuit of a learning goal. Self-regulation has been strongly linked to successful learning outcomes and it is critical for success in school (Durlak et al., 2011; Zimmerman & Schunk, 2008). Self-regulation is a multifaceted, dynamic construct. This means that students may be able to demonstrate some aspects of self-regulation but not others; it also means that students may be able to selfregulate in some contexts but not others. To reflect this complexity, self-regulated learners are defined as students who are connected, self-aware, self-determined, strategic, and resilient (Johnson, Clohessy, & Chakravarthy, 2018). Connected learners feel safe, trust their teachers, and tend to be more engaged during the learning process, which can lead to higher academic achievement (Leighton & Bustos Gómez, 2018). Self-aware students understand their strengths and needs as learners, and they understand which learning approaches are most effective for them. Selfdetermined learners are able to set goals, make plans, and monitor their progress to reach their goals. Strategic learners are able to select and effectively use an appropriate strategy to reach their learning goal (Karlen, 2016). Resilient learners are able to use strategies to recover from setbacks and are able to adapt to stress or adversity. Cognitive flexibility, the ability to approach a problem in a different way, Intervention in School and Clinic 56(3) and emotion regulation are important in developing resilience (Zolkoski & Bullock, 2012). A key principle of the self-regulated learner framework is teachers’ flexibility for adapting strategies to meet the specific needs of their individual students in the moment. Table 1 includes a definition of each component and the general approaches to develop students’ self-regulation skills within the classroom. Math Intervention Framework The math intervention framework includes teaching for conceptual and procedural understanding, developing students’ mathematical reasoning ability, and the ability to make connections across concepts. The intersection of these aspects of math is strategic competence with problem-solving, demonstrated when a student can independently identify and apply an effective and efficient approach to solving a given mathematics problem. Conceptual understanding is defined as the understanding of the principles that govern a math domain (Rittle-Johnson & Schneider, 2015). Procedural understanding is the knowledge of action sequences for solving problems (RittleJohnson & Schneider, 2015). Mathematical reasoning is the ability to develop and evaluate math arguments (Liu & Xin, 2017). Mathematical connections are a cognitive process in which students relate ideas, concepts, procedures, or representations (García-García & Dolores-Flores, 2018). The math instructional framework is not a sequential instructional preference (Rittle-Johnson & Schneider, 2015). Rather, the goal is to ensure that an intervention is designed to support students’ math ability through these four areas. An extensive research base identifies a number of instructional practices aligned with elements of this framework that are effective for students with LD to develop strong competency in math, which include the following: 1. 2. 3. 4. 5. Explicit instruction of math concepts and procedures (Doabler et al., 2015); Visual representations to support conceptual understanding and the ability to connect the math concept to the math procedures (Gersten et al., 2009); Cognitive strategy instruction to learn to identify and solve a variety of problem types (Griffin & Jitendra, 2009); Explicit inquiry routines to support students’ strategic competence (Impecoven-Lind & Foegen, 2010; Scheuermann et al., 2009); Teaching students to verbalize their math reasoning and use math vocabulary (Gersten et al., 2009). These evidence-based practices form the basis for the instructional approaches used in the integrated self-regulation and math intervention. Johnson et al. 165 Table 1. Self-Regulated Learner Framework: Components, Definitions, and Strategy Approaches. Component Definition Connected Connected is when learners: 1. Feel safe and that they belong; 2. Feels supported to be themselves and are socially aware; 3. Can take the perspective of others; 4. Can develop, manage, and maintain relationships that are healthy and helpful. Self-aware students: 1. Understand their strengths and needs as learners; 2. Can self-monitor during the learning task; 3. Understand how their emotions and actions affect themselves and those around them; Self-determined learners: 1. Are self-directed; 2. Make plans and commit to reaching goals; 3. Monitor their progress toward goals; 4. Understand the relationship between short-term and long-term goals. Strategic learners: 1. Know how to select and effectively use the appropriate strategies to reach their learning goals; 2. Create an environment that helps them accomplish their goals. Self-aware Self-determined Strategic Resilient Resilient learners: 1. Are able to recover from disappointment; 2. Can adapt to sources of stress or adversity; 3. Persevere through challenges and setbacks. An Integrated Intervention In this section, the application of the self-regulated learner framework within the math instructional environment is explained. The goal is to create an intervention designed to (a) reduce math anxiety and build student confidence, (b) teach a strategy that promotes flexibility in solving problems, and (c) support students’ ability to better appraise stressful situations, and to adopt a “failure as enhancing learning” mindset. Figure 1 includes a completed intervention template. Each part of the template is described below to facilitate application to students with different presenting concerns. Although the example provided in this article highlights the application of the framework to a single student, this approach can be used with small groups. Step 1: Connection The first part of the intervention design involves creating a safe and positive learning environment for students. Students with LD and attention deficits have more distant, more conflictual, and more dependent relationships with their teachers (Demirkaya & Bakkaloglu, 2015). Establishing a positive rapport and a strong connection supports student well-being because it can make them feel more understood and less vulnerable about having a disability (Mason et al., 2013). Positive Strategy approaches • • • • • Intentional planned feedback Building in interests Communicate routines/expectations Responsive to student needs Frequent opportunities to respond • • • • • • • • Rating scales Tools to explain emotions Video self-reflection Models of proficient performance Noticing feedback Goal setting/tracking tools Choice-making opportunities Promoting advocacy • Word problem solving strategies (schema instruction) • Use of manipulatives to support problem-solving • Step-by-step guides to monitor work • If-then planning • Positive emotion building • Opportunities for success • Celebratory feedback emotions and connections have been found to increase student engagement and this engagement leads to a more positive learning environment (Leighton & Bustos Gómez, 2018). Teachers should focus on three main areas to help their students feel connected: (a) trust, (b) empathy, and (c) support. Trust and empathy are basic attributes for establishing effective relationships and help students feel supported in a positive learning environment (Karreman & Vingerhoets, 2012; Sabol & Pianta, 2012). Table 1 provides several approaches to helping students feel connected. When teachers first begin work with their student, they should take the time to get to know the student. Some students will readily share information about themselves, whereas others will be more reluctant. Student interest inventories can be a great way to learn more about your student, but a teacher should be sure to read the student’s responses and plan ways to incorporate those responses into instruction and conversation. For example, if a student mentions that they play the piano, a lesson on fractions could be related to reading musical notation. Teachers should also discuss with their students what goals they have for themselves and teachers should also share the goals they have for their students. The teacher and student can each list their goals and then place those goals on a Venn diagram. This activity can help the student take more ownership for their learning, and it also demonstrates 166 Intervention in School and Clinic 56(3) Step 1: Connection Positive Feedback from Teacher (example Teacher (T) Student (S) dialogue) T: Let’s check your work together. Can you walk me through the steps you took to solve this problem? S: This one is 142 ÷ 3. I built 142 on my HTO chart. I split the 100 flat into 10 – 10’s and divided those into 3 groups. Then I split the 10 rod into 10 ones and divided those into three groups and then I had 52 in this group. T: You worked really hard to solve that problem. S: Wait – I see what happened now. I should have had two 10’s left but I moved one before I saw that there wouldn’t be a group of 3 and then I didn’t move it back. T: That’s great that you noticed where you made a mistake. Now you can fix it. Can you think of another way to check your work next time? S: I can count each group to make sure they are equal. T: That is a great idea. Nice work! Step 2: Self-Awareness Anxiety Rating Calming Strategies Use anxiety 10-point scale at the start of each session, and as needed before new material or if D has an upcoming test or assignment that is challenging Deep breath, 10 cloud, start with known Step 3: Self-Determination Goal Setting Measures 1. Reduce time to get started 1. Clock – goal is < 30 seconds 2. Complete all assignments on time 2. Check student gradebook – goal is 100% 3. Use long division strategy 3. Record when strategy is used Step 4: Strategic Focus Connections/CRA Long division Unifix cubes/HTO chart Step 5: Resilient If Then If I make a mistake and get upset Then I can take a break and do my 10 cloud Figure 1. Self-regulated learner framework implementation sheet. Note. HTO = Hundreds, Tens, and Ones; CRA = Concrete Representational Abstract. to students that their teacher is invested in their learning outcomes. As intervention begins, teachers should explain how the lessons will be structured and why. If the intervention session is 30 min long, a teacher can post a schedule of the planned activities, and should review these with the student. For example, Today, we will spend about 5 min reviewing how to divide using manipulatives. Then, we will work for 15 to 20 min on dividing multidigit numbers using manipulatives and connecting our models with written numbers. During the last 5 to 10 min you’ll get to practice on your own, check your work, and get feedback from me. This helps students understand what to expect and why they are engaging in the various learning activities. Teachers should ensure that their lesson allows for many opportunities for the student to engage and respond, and should also let students know through their feedback that making errors is part of the learning process. Feedback should be delivered immediately and scaffolded over time to allow the student to move from a teacher-directed correction to a student-directed correction. The sample script in Step 1 of Figure 1 provides an example of how the teacher can implement positive feedback. Finally, the teacher should also periodically ask for student feedback about what is working for them. For example, a teacher might ask, What strategies are most helpful for you to understand this math concept? Do you think we need to slow down so you can have more time to practice? Are the problems we are doing challenging, too easy, or just right? This feedback can strengthen what has been termed the pedagogical alliance (Leighton & Bustos Gómez, 2018), building trust and empathy between teacher and student as the student is supported in the learning process. As the sample dialogue in Figure 1 shows, D’s teacher provided feedback to encourage her to start with what she knew how to do and to use known strategies and tools to solve problems. The goal was to support D’s independent use of strategies over time, to build her confidence, and to Johnson et al. Figure 2. Visual anxiety 10-point scale. give her a consistent starting point for approaching math problem-solving. When providing feedback around errors, D’s teacher emphasized that it was okay not to get the right answer, and that what was more important was the ability to review the work and understand why an approach or calculation was incorrect, then take the steps to fix it. Step 2: Self-Awareness Math-related anxiety and stress have been shown to compromise working memory and attentional resources (Ashcraft & Kirk, 2001), indicating that interventions should include approaches that help students manage their anxiety during the learning process. An important first step toward this end is for students to identify, name, and understand their emotions, as this supports emotion regulation. Emotion awareness and regulation has been demonstrated to positively impact academic achievement (Arguedas et al., 2016). Students who are aware of their emotions can communicate their emotional state to teachers, who in turn can provide more effective feedback and support (Arguedas et al., 2016). One way to support students in developing self-awareness is through the use of a rating scale that gives students a way to identify and name their emotions (Brackett, 2019). D used a 10-point anxiety scale, similar to the 10-point pain scale used in the medical field (Hjermstad et al., 2011). The anxiety scale we used for D is included in Figure 2. To introduce the scale, the teacher explained: It is very common to feel stress or anxiety about math, but did you know that when we feel anxious about math, it can make it harder for us to do? We are going to work on some ways to ease anxiety, but to do that, we have to think about how we feel. This is called a visual anxiety scale. On this end (points to 0–1) we feel okay—not anxious. At this point (points to 5) we feel pretty nervous. You might be thinking things like “I can’t do this, I hope math class ends soon. I really don’t want to be here.” And then on this end (points to 10) we are feeling very anxious, so anxious that we can’t really focus on anything else, you might even feel panicky. You might be thinking things like, “I am not doing this. I am not even going to try, I hate this.” It is okay for you to be at any level on this scale, and I want you to be honest about how you are feeling. That will help us figure out what we need to do next. 167 When students are provided with tools and words to label their attitude toward the learning task, they can start to make connections between their frame of mind and the outcomes of their learning (Brackett, 2019). Nonjudgmental and consistent language can help students understand that it is okay to experience emotions, but that if they want to be successful in their learning, they may need to use a strategy to be more effective. For example, if a student is anxious about an upcoming math test, it is important for them to acknowledge their anxiety and those feelings can be validated (e.g., “The pressure of doing well on a test can make you feel anxious, let’s think of some ways that you can feel more prepared.”). In addition, for students who experience significant anxiety, a targeted technique may be needed. Before each session, D would indicate how anxious she was feeling about math, and on days when she indicated higher levels of math anxiety, her teacher started with an opening routine that D could confidently and independently do. D’s intervention began with a “10 cloud” activity, in which she would draw a cloud on a white board, and then write out all of the ways to construct the number 10 (e.g., 3 + 7 = 10; 2 + 8 = 10). This routine was chosen for D because she had a strong knowledge of addends to 10 and she enjoyed the opportunity to write on the board as she typically avoided volunteering to do so in front of her classmates in the general education classroom. The goal of this intervention step was twofold. First, it served as a reminder to D that she has competency in math. Second, it served as a calming routine that helped her get started with the lesson, to orient her mind toward math, and to have an early success in the intervention period. Step 3: Self-Determination Self-determination plays a critical role in supporting students with LD to have authentic and personal agency over their learning and fosters positive academic outcomes. Students with LD often struggle with setting goals, attributing their effort to achieving outcomes, and therefore, may need support with goal setting and progress monitoring (Rogers & Tannock, 2018). Supporting students with LD to develop self-determination may initially require teacherdirected support that is gradually shifted to become student directed. For example, teachers can support students by setting realistic goals and connecting the effective use of strategies with goal attainment (Botsas & Padeliadu, 2003). Goals can be set to focus on a variety of areas, and for students with LD in mathematics, this process should focus on small, attainable goals that will lead to improved learning over time. For example, due to her math anxiety, D initially took a very long time to get started with a math problem. Together with her teacher, D created a graph to set and monitor progress toward a goal of reducing the time 168 it took to get started. This promoted both self-awareness (i.e., helping the student recognize it will be challenging to develop math skills if they do not use intervention time effectively) and self-determination (i.e., setting and monitoring progress toward goals can be a strong motivator for students). After several intervention sessions, D started to meet this goal and she and her teacher created a second goal focused on independent completion of her math homework. Step 4: Strategy The next step focuses on teaching a strategy or strategies to address the particular math domain of focus. The goal is not to teach students an algorithm that they then apply in practice sets, but rather to develop their cognitive and metacognitive processes and strategies to facilitate learning. Cognitive strategy instruction has been highly effective for students with LD in mathematics who typically do not acquire strategies on their own and have difficulty selecting and applying those appropriate to the task (Montague et al., 2011). Cognitive strategy instruction is a general approach to teaching that includes six stages: (a) developing and activating background knowledge, (b) discussing the strategy, (c) modeling the strategy, (d) memorizing the strategy, (e) supporting the strategy, and (f) independent performance (Montague & Dietz, 2009). In this particular case, D was struggling with long division. In her general math class, students were taught to use a partial quotient model, but this student did not feel confident in her ability to use the strategy, and this would trigger a negative cycle of making lots of errors, which further convinced her that she could not complete the task. It is highly likely that her working memory challenges made the use of the partial quotient model quite difficult. Drawing on evidence-based practices for math instruction, D was taught a strategy to use a Hundreds, Tens, and Ones (HTO) chart, and the Concrete Representational Abstract (CRA; Steedly et al., 2008) progression (see Figure 3). The strategy was first taught using base-10 blocks and the HTO chart, which D had used to develop her knowledge of place value and ability to add and subtract with regrouping. Instruction progressed through the representational and then abstract, and D was explicitly shown the connections across the three. This approach supported D’s conceptual understanding and connected that conceptual understanding to the underlying procedures. D was supported to make connections across math concepts (i.e., in this case how to regroup using the HTO chart, using base-10 blocks to build numbers) using tools and supports that were familiar to her because she used them to learn other math concepts. Throughout the intervention, she was encouraged to explain her reasoning as she worked through the various steps. Intervention in School and Clinic 56(3) Step 5: Resilience The last component of the self-regulated learner framework is designed to help students persevere, think flexibly, and regulate their emotions. High levels of stress associated with the school environment can make school itself a risk factor to a child with LD (Bender et al., 1999). When children with LD and attention deficits are not supported, their accumulated failure to be successful in the classroom can lead to negative affective characteristics (Rogers & Tannock, 2018). In order for children to be emotionally healthy, socially adjusted, and achieve academic success, they must have the ability to manage their emotions (Durlak et al., 2011). A proactive approach to supporting students to become resilient may be the most effective. Creating a positive and safe learning environment, where all students are encouraged to participate, to take risks, and to support each other is an important way to help all students cope with stress. Building a shared vocabulary of words to describe feelings and emotions allows students to communicate their anxiety and also allows others to understand how to support their classmates and peers (Kitzmann, 2012). It is important for teachers to support children’s emotions and talk to them about their feelings in order for them to understand their own reactions to stress (Nolan et al., 2014). Fostering children’s abilities to learn from their mistakes by setting examples, being a positive role model, and the consistent use of the term “give it a try” strongly support children’s resilience within the classroom environment (Nolan et al., 2014). Teachers need to model this behavior for their students as well (Nolan et al., 2014). Modeling appropriate responses to stressful situations, communicating, and encouraging collective problem-solving are all ways that teachers can model behavior that promotes resilience in the classroom. Students with LD may require more intensive approaches to develop resilience. To build resilience and give students a strategy to continue working, an “if-then” approach can be used. “If-then” planning is used extensively in behavioral change to provide a plan for managing obstacles encountered in pursuit of a goal (Baumeister et al., 2007). The plan is developed and rehearsed before challenges are encountered. When intervention first began, D would become very distraught when she made an error, sometimes shutting down for the remaining intervention time. D’s teacher first used an if-then plan connected to D’s calming strategy of the 10-cloud. The if-then plan was, “If I make a mistake, I will take a break and draw my 10-cloud.” This allowed D to step away from the work that was frustrating her, but still stay engaged in a math activity. As D was drawing the 10-cloud, her teacher would comment, “Remember how the 10-cloud was difficult for you at first, but you kept practicing and now you can do it automatically?” This helped D remember that learning new things was a process. Johnson et al. 169 Long Division Problem Solving Template 1. Write the Division Problem: 142÷3 Hundreds Tens Ones 2. Make groups of 3, starting with hundreds (0 groups, break the hundred to 10 tens) 0 groups of 3 4 groups of 3 7 groups of 3, R 1 3. Check my work. Do I have equal groups? 4. Write my answer: 47 R 1 Figure 3. Strategy template using Hundreds, Tens, and Ones and Concrete Representational Abstract for long division. Over time, D’s teacher helped her use a new if-then plan to focus on breaking down the steps to identify where the error occurred, and to be able to take steps to fix it. The if-then plan was, “If I make an error in solving a problem, I will use the break it down strategy to review the steps, and my reasoning.” The break it down strategy is a graphic organizer to lead the student through the process. This strategy consists of six steps: (a) write down the problem, (b) identify what you know, (c) identify what you need to find and what operation(s) you will use to solve, (d) solve the problem, and (e) check your answer. This accomplishes two things. First, creating an if-then plan signals to the student that making errors is an expected part of learning math. Second, the if-then cue card is always placed on the student’s desk as a prompt for what to do next and provides the student to use the tools they have learned to solve problems. This process should be scaffolded by the teacher, with the goal of supporting the student to become independent over time. Conclusion Students with math-related LD are more likely to experience math anxiety than their typically performing peers (Devine et al., 2018). Currently, the interventions used with students with LD in mathematics typically target lower level skills such as fact recall or competency with procedures only (Marita & Hord, 2017), and most do not address self-regulation or math anxiety directly. The approach to intervention as described in this article presents a promising 170 Intervention in School and Clinic 56(3) way to address the comprehensive needs of students with significant LDs, anxiety, and self-regulation deficits. The success of this intervention design will depend on teachers’ understanding of the self-regulation and math intervention frameworks. This comprehensive model addresses the various aspects of anxiety, self-regulation, and math strategy knowledge to help students learn to persist in math and understand that productively struggling in math is a natural part of learning (Hiebert & Grouws, 2007). Acknowledgments The authors acknowledge support from the M.J. Murdock Charitable Trust and the Cambia Foundation. The opinions expressed are solely those of the authors. Declaration of Conflicting Interests The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Funding The authors received no financial support for the research, authorship, and/or publication of this article. Note 1. The vignette reported in this article is based on an authentic situation and only the names have been changed to pseudonyms. References Arguedas, M., Daradoumis, A., & Xhafa, F. (2016). 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