Written by Dr. Steven Reid, Associate Director of Education, York Region DSB; Sessional Lecturer, OISE and Dr. Mary Reid, Assistant Professor, OISE
Talk to the average parent in Ontario about math and you will certainly be presented with a view of its current state in classrooms. You may hear statements such as, ‘math these days,’ ‘I don’t understand this new math,’ or ‘I just don’t know how to help my child be successful in math.’ For parents of children with learning disabilities (LDs), these statements might be elevated. Inevitably, you may also hear anecdotes of personal experiences with math. There seems to be a wide divide between those who see themselves as ‘mathies’ and those who openly state that they are ‘math illiterate.’ This, in and of itself, can present challenges as we consider how to support all students to see themselves as mathematicians, including those with LDs. In fact, we all have a math identity, a way in which we understand our own mathematical capabilities (Reid, 2019). This identity is socially constructed and mediated within the world that individuals engage in each day (Azmitia, Sye, & Radmacher, 2008). Math identities are influenced by an array of variables including math content knowledge, level of confidence, as well as many intersecting identities associated with gender, race, and socioeconomic status (Reid, 2019).
In the early years, children come to school with many math concepts in place, observing math in their daily environments (Clarke, Cheeseman, & Clarke, 2006). However, students can begin to develop math anxiety as early as five years old or even younger. And, by the time students are 10 years old, they can describe their relationship with math, the origin of their math anxiety, and any symptoms they may be experiencing. It is also important to note that math anxiety tends to increase as students get older, which is inconsistent with general anxiety (Carey et al., 2019). Therefore, teachers and parents must understand how to recognize and reduce math anxiety, foster math well-being, and build resilience. These goals should be part of a school team approach with the aim to nurture dynamic communities of math learners among classrooms and beyond.
Recognition of Math Anxiety
There has been significant interest in how math anxiety impacts math experiences, and vice versa. Although more research is required in both areas, substantial evidence suggests that math anxiety affects working memory required to perform successfully in math (Dowker, Sarkar, & Looi, 2016). As some students with LDs can have working memory limitations, these particular students could be prone to experiencing math anxiety and challenges in math. Math anxiety should not be ignored as teachers, students, and parents can experience its symptoms. Like any other type of anxiety, math anxiety can include both physical symptoms (e.g., restlessness, excessive worrying, sweating) and behavioural symptoms (e.g., avoidance, test and performance anxiety, negativity) (Plaisance, 2009). In measuring math anxiety, a continuum exists from low anxiety to high anxiety. Without intervening, math anxiety can increase over time making it difficult for students to view themselves as successful math learners. It is therefore important to be aware of signs of anxiety at school or at home as symptoms can occur when students are asked to engage in math or when students are thinking about future math experiences such as an upcoming test.
- One of the most common symptoms of anxiety in children and youth is restlessness (Ginsburg, Riddle, & Davies, 2006).
- When students are restless during math activities, identify the behaviours. Are they having trouble getting work started? Are they socializing? Are they fidgeting?
- When math is discussed or encountered, a change of expression can be observed in students.
- Persistent worrying about homework can make it difficult for students to concentrate.
- The production of sweat can increase when students feel nervous or anxious. At times, the body engages in a fight or flight state where breathing and heart rate increase, and blood pressure rises, resulting in sweat production.
- When students notice their physical symptom of sweating, it can further increase the production of sweat causing an undesirable cycle.
- Students who hold negative attitudes will likely avoid math activities by finding excuses (e.g., washroom breaks, illness, that they forgot materials in their locker or at home).
- Students’ memories of negative math experiences can lead to resistance to further attempts.
Test and performance anxiety
- Timed tests can present additional stress to students as the focus on the remaining time takes up cognitive load, which reduces working memory load for problem-solving or task completion.
- Fear of performing poorly can negatively affect students’ concentration levels, thereby perpetuating negative perceptions of math abilities.
- Feelings of anxiousness can lead to students’ negative self-perceptions.
- Negative self-talk, which is associated with low performance, often involves students’ perceived lack of skills and ability to achieve in math. Whereas positive self-talk is linked to improved achievement in math (Thomaes, Tjaarda, Brummelman, & Sedikides, 2019)
Strategies for Fostering Well-Being and Reducing Math Anxiety
With the early identification of math anxiety, strategies can be put in place to support students’ well-being by shifting their mindsets about their relationship with math, as well as what it means to be a mathematician. It is important for teachers to consider their own levels of anxiety, their comfort levels with teaching math, as well as their personal beliefs about learning math. Students should experience the excitement of the challenges that math offers, and embrace complex problems. Together, teachers and students can nurture an environment that is collaborative and supportive of all students who view themselves as math literate. For this to occur, various strategies can be implemented to foster well-being, reduce math anxiety, and develop a genuine interest in math.
Reduction of Working Memory Load
- Students with LDs, specifically those with memory or executive function processing challenges, may experience difficulty with retaining information needed for solving problems. Tip: The resource Understanding Learning Disabilities: How Processing Affects Mathematics Learning helps educators plan learning and assessment opportunities in math.
- Working memory load can be lowered by breaking information and questions into smaller units or steps through visual aids (e.g., graphic organizers, infographics, charts, checklists, calendars).
- Personalized supports should be easily accessed by students during math activities, such as individualized anchor charts, math dictionaries, memory aids, and terminology/procedural/formula lists.
- Assistive technology (AT) can be beneficial for many students with LDs. For those with working memory challenges, AT offers students access to personalized and general supports (e.g., math software, calculators, graphic calculators, speech-to-text, text-to-speech, graphic organizers).
- Research suggests that regular focused breathing techniques are effective in alleviating anxiety among highly math anxious students (Brunyé et al., 2013).
- Engage students to focus on their breathing prior to math activities. Tip: Have students inhale deeply through the nose for a count of four, and feel their stomach expand. They should hold the breath for a few counts (three to five), then exhale slowly. Ensure students keep focused on their breath.
Encourage process instead of speed and correct answers
- Students need to understand the importance of thinking deeply about a question or problem and should be given ample wait time. If teachers offer more time for students to consider the answer to deeper questions, the quality of answers improves as well as the attitude toward learning math (White & Tisher, 1986).
- Students must recognize that mathematicians take their time to consider the problem at hand, determine strategies that can be used, implement the chosen strategies, and reflect back to determine whether the solution is reasonable.
Explore multiple strategies to solve problems
- Students can engage in the creation of their own strategies to solve problems (Mascardini, 2010) as well as explore multiple strategies to solve math problems (Kroesbergen & van Luit, 2002).
- There should be focussed class time for students to reflect on their own strategies, as well as alternative strategies used by others while justifying which approach might be most appropriate or efficient.
Embrace productive struggle
- Students’ learning is enhanced when they are supported by teachers to engage in productive struggle, sticking with a problem even though the solution is not readily apparent.
- Productive struggle is promoted when time is given to students to work through challenging problems in which they are held accountable to explain and justify their thinking (Warshauer, 2015).
Ask open-ended questions
- Open-ended questions allow students to engage with different strategies, as well as begin with their current mathematical understandings.
- As students choose different ways to solve open-ended questions, they can describe the strategies used and learn how others solve problems.
Building a Community of Math Learners
“Research has shown definitively the importance of a growth mindset—the belief that intelligence grows and that the more you learn, the more mathematical pathways you develop. But to erase math failure, we need students to have growth beliefs about themselves and accompany them with growth beliefs about the nature of mathematics and their role in relation to it. Children need to see math as a conceptual, growth subject that they should think about and make sense of.” (Boaler, 2019, p. 29)
Teachers are instrumental in all aspects of student learning. It could be argued that the teachers’ role is heightened in the math classroom, as their own values and beliefs can nurture positive attitudes toward math (Wilkins & Ma, 2003) or transfer feelings of math anxiety (Beilock et al., 2010). As students with LDs may experience heightened anxiety (Al-Yagon & Mikulincer, 2004; Wilson, Armstrong, Furrie, & Walcot, 2009), it is important for teachers to pay close attention and look for signs of math and general anxiety in the classroom. As teachers continually build their own capacities in math instruction, a collaborative approach to learning is encouraged. Particular rules of engagement should be promoted in every classroom to ultimately build a community of math learners:
Growth Mindsets - Promoting a safe place to learn together
- Students should regularly be reminded that everyone can be a mathematician with dedicated effort and support.
- Positive attitudes about math are associated with higher levels of achievement.
- It is critical for students to observe mistakes made in math as an opportunity to learn as an individual and together as a group.
- Mistakes are not viewed as a sign of being weak at math, instead, the response to mistakes can lead to deeper learning of math concepts.
- Tip: A teacher’s growth mindset is essential in the math classroom. For students with LDs, those who might not see themselves as mathematicians yet, a teacher’s positive support of a learning stance can make the difference between engagement and withdrawal. Continued professional learning and connections with other teachers can support a positive approach to learning math as a student and teacher.
Respect the learning approaches and starting places of others
- At no time should there be showboating based on the completion of work, e.g., ‘Wow that was so easy!’ These actions can immediately deflate others in the class, making them feel they can’t do math and are too slow. Students must understand that speed does not equate to being strong at math.
- A common belief of students is that mathematicians solve problems quickly. However, solving interesting and complex problems takes a significant amount of time. The provision of additional time is often an accommodation for students with LDs. Students should not feel the pressure of time constraints during math activities. Tip: When complex and time-consuming questions are presented to students, let them know that this will take effort and that grappling with the problem is part of the learning. By doing so, it can reduce anxiety for students who require more time to solve the problem at hand.
Presume positive intent
- Students should presume the positive intent of others while engaging in mathematical debate. With practice, exchanging ideas becomes a process of supporting every student to collectively create knowledge, instead of one student being right while others are wrong. Engaging orally in mathematical processes (e.g., communicating, reflecting, reasoning and proving) can be a strength for some students with LDs. Others may also benefit from exchanging ideas through various adaptive technologies.
- Math classrooms should enable students to exchange ideas about concepts and approaches to solving problems. Students must understand that having different ideas and challenging others are important aspects of deepening math knowledge.
Make math practice active
- Developing automaticity with facts requires authentic practice where students are actively making meaning with numbers.
- Worksheets are not the only means to develop procedural fluency. Tip: Avoid timed worksheets as this could promote math anxiety (Boaler, 2014).
- Fun math games with an element of choice enable students to practice math skills in an active way. The provision of choice can especially be beneficial for students with LDs as multiple entry points to engagement and solutions are offered. Tip: Many examples of engaging tasks and games can be found at www.youcubed.org, an online math resource from Stanford University’s Graduate School.
Active listening without judgement
- As part of active listening, students are reminded to reflect on the responses of others without judgement. Together as a group, ideas are shared to develop a common understanding that is celebrated. Teachers can identify specific accommodations that may be necessary for students with LDs to communicate their thinking. Different mediums may be helpful in expressing the deeper understandings that students possess, thereby encouraging future sharing.
- Students should be encouraged to listen to others so they can ask questions about certain details, summarize what they hear, ask clarifying questions, or provide positive feedback. Tip: Prompts can be provided to students using cue cards that promote active listening, e.g., Why did you choose that strategy to solve the problem? What part of the problem did you find most difficult?
Dynamic Approaches to Teaching Math
A fundamental goal for every math classroom should include the promotion of dynamic teaching and learning environments. As part of this approach, students must be immersed in environments where they learn from one another and develop deep understanding of math concepts through complex and authentic math tasks (Reid, 2019). This should not be misinterpreted as students only discovering math concepts without teacher support. Teachers play a central and essential role in creating different learning tasks, with differentiated levels of support during activities and throughout long-range planning (e.g., weekly plans, unit plans). As part of a dynamic program, teachers design lessons that require inquiry, problem-solving, and conceptual understanding. Over time, students build mathematical resilience while they actively participate in tasks that are engaging and challenging, and collaborate with others to exchange ideas and share potential strategies (Lee & Johnston-Wilder, 2015). Students also develop procedural fluency, which is the ability to use their knowledge of math ideas in new situations (National Council of Teachers of Mathematics, 2014). It is important to note that a dynamic program additionally focuses on the use of procedures and algorithms, that support the automaticity of math facts. Overall, teachers promote the conceptual understanding of each of these foci within the program (Reid, 2019).
Based on the conception of a dynamic approach to teaching and learning math, questions regarding students with LDs can be asked. For example, can students with LDs benefit from this approach if it requires inquiry and deep conceptual understanding? When research is reviewed in the area of math, there is often a discrepancy between instructional approaches promoted for students with or without special education needs, including those with LDs. A myth that surfaces in the research involves the misconception that students with LDs do not benefit from inquiry during math (Lambert, 2018). It is important to note that accommodations should not exclude the student from inquiry-based learning. It is the excitement of authentic inquiry activities that give students with LDs the opportunity to connect math concepts with the real world (Bottge, 2015). Although explicit instruction can be valuable for students with LDs, research has not shown that it is the only way they learn math (Gersten et al., 2009). In fact, students with LDs also benefit from: inquiry opportunities that connect math with the real world (Bottge, 2015), constructing their own strategies during problem-solving (Moscardini, 2010), and practicing efficient strategies when constructed (Kroesbergen & van Luit, 2002). Overall, student-generated strategies engage students to build deep conceptual understandings for sustained math knowledge.
All students can develop their capacities as mathematicians within a supportive community of learners. Students who are immersed in dynamic teaching and learning environments, experience a collaborative exchange of ideas, strategies, reflections, and justifications. Of most importance is for teachers to be on the lookout for any signs of math anxiety. With early identification, supports can be implemented to reduce anxiety and nurture well-being. Classroom environments must be afforded to students, including those with LDs, that celebrate math learning, acknowledge the specific strengths and needs of each learner, and promote the social context of learning math.
About the Authors:
Dr. Steven Reid has been a tireless advocate for students and has served in many educational roles such as a classroom teacher, principal, and supervisory officer. Currently, as an associate director of education, he is focused on raising the achievement and well-being of underserved and underperforming students. Steven began his career as an educational assistant supporting students with special education needs and came full circle, serving as a central superintendent of special education. He has also taken on various roles with the Ministry of Education including senior specialist and director, as well as chief assessment officer, Education Quality Accountability Office (EQAO). Steven is also a sessional lecturer at the Ontario Institute for Studies in Education (OISE) focused on building the confidence of graduate students in math learning and teaching. Steven’s research and publishing interests have been in the area of math content knowledge and math anxiety of teacher candidates, as well as knowledge mobilization in schools and district school boards.
Dr. Mary Reid is an assistant professor of math education in the department of Curriculum, Teaching and Learning at the Ontario Institute for Studies in Education (OISE). Mary has served as a classroom teacher, instructional leader, education officer at the Education Quality Accountability Office (EQAO), vice-principal, and principal. At OISE, Mary teaches a variety of math courses including Curriculum and Teaching in Mathematics and Issues in Numeracy to Master of Teaching candidates in the elementary division. She has published research in the areas of math content knowledge of elementary preservice teachers, math anxiety in the classroom, the gender gap in STEM, and building efficacy for math teaching. Her research attempts to uncover the complex challenges elementary preservice teachers face as they develop their math knowledge for teaching. Mary’s work would be of interest to those seeking to enhance math education through building the capacities of teachers.
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