I struggled with math throughout my childhood, constantly felt inadequate compared to my peers, and cried in the corner of my classroom often. I wholeheartedly relate to learners who reach their threshold of learning frustration, particularly as it pertains to mathematical conceptualization and automaticity. It was not until I found a method of cognition and technique (visualization) that I was truly able to find meaning and, thus, joy, in math. Learners who face similar struggles as I did, often give up, signaling a need for personalized instruction and, quite possibly, a formal diagnosis of Dyscalculia. Here, I will provide insight into the diagnostic definition, overt and covert symptoms, and effective strategies to help learners find their way towards mathematical confidence and, ultimately, feelings of success.
What is Dyscalculia?
Unfortunately, Dyscalculia is misunderstood and unknown to the general public which is one of the reasons that it goes undetected. So what exactly is Dyscalculia? According to understood.org, “Dyscalculia is a condition that makes it hard to do math and tasks that involve math. It’s not as well known or as understood as dyslexia. But some experts believe it’s just as common. That means an estimated 5 to 10 percent of people might have dyscalculia.”
What are the symptoms?
As clearly stated on LDA America, “(Dyscalculia) Affects a person’s ability to understand numbers and learn math facts. Individuals with this type of learning disability demonstrate impaired math calculation skills and difficulty understanding numbers and math facts. Dyscalculia is associated with weaknesses in fundamental number representation and processing, which results in difficulties with quantifying sets without counting, using nonverbal processes to complete simple numerical operations, and estimating relative magnitudes of sets. Because these math skills are necessary for higher-level math problem solving, quantitative reasoning is likely impaired for these individuals.”
Common symptoms of Dyscalculia include difficulties with:
Seeing how numbers fit together
Recalling math facts, like 3 + 2 = 5
Using concepts like “less than”
Using symbols like + and –
Telling left from right
Reading a clock
Working with dollars and coins
Analyzing numerical data, graphs, charts
If you, as a caregiver and/or educator, would like to learn even more about the symptoms of dyscalculia, please visit either dyscalculia.org or childmind.org.
How can you support learners with Dyscalculia?
There are many studies substantiating the efficacy of multisensory, evidence-based practices in strengthening the underlying foundation and application of mathematical skills thereof. Curriculums such as Making Math Real, Touch Math, and Mathematical Mindset Some of these explicit strategies include, but are not limited to:
Manipulatives such as blocks, number lines, and other tools to visualize how to solve math problems
Explicitly develop working memory, concept imagery, growth mindset and self-regulation skills to bolster processing foundation
Advocate for extra time for tests and other tasks that involve math
Allow access to technology like calculators and math apps to help make math easier to navigate
Play card, board and virtual learning games to develop problem-solving skills and a positive association to thinking mathematically
Incorporate mental math organically into daily conversations when you are having dinner, driving in the car, and so forth
Some learners are unresponsive to the above or make slower progress than one would anticipate. This lack of receptivity is the feedback that you need to reach out to your pediatrician and/or psychologist to explore the possibility of a Dyscalculia diagnosis as well as recommendations for placing them on the path towards their potential.
There are many layers of processing, executive functioning, and problem-solving skills that equally contribute to and, thus, are involved in one’s ability to reach a level of mathematical independence. We must establish a strong framework for learners to stand upon before expecting them to lean into discomfort and then rise above adversity. It is imperative to keep in mind that math may never be easy for learners like me, but it certainly can become less daunting and more enjoyable with the right strategies and an open mindset in place.
Mindset matters, as mentioned in our spotlight on Carol Dweck’s phenomenal work with mindset. realizing your potential is half the battle to actually achieving it. If this is true, how do we help learners get to this level of self-awareness as caregivers and educators? Here we explore how grit and perseverance serve as two key factors to successfully rising over a perceived obstacle and coming out stronger on the other side.
GRIT: Guts, Resilience, Initiative, Tenacity
What is grit really? We hear the term thrown around all of the time, but do we really know what it is and how it applies to nurturing our learners’ learning habits? I, an educator and mother of four, didn’t even realize the depth of the term myself until I happened upon Angela Duckworth’s 2013 TED talk, “The Power of Passion and Perseverance.” According to her website, Angela Duckworth is the founder and CEO of Character Lab, a nonprofit whose mission is to advance scientific insights that help children thrive. She is also a professor of psychology at the University of Pennsylvania and in 2013 was named a MacArthur Fellow. Prior to her career in research, she was a STEM teacher at public schools across the country. Dr. Duckworth continues, “Grit is living life like it’s a marathon, not a sprint…To be gritty is to invest, day after week after year, in challenging practice. To be gritty is to fall down seven times and rise eight.” According to Duckworth, GRIT stands for Guts, Resilience, Initiative, Tenacity. These are the single most determinable characteristics for success as adults and, thus, should be shaped in learners early on. Talent does not make one gritty. We need to be gritty about helping our children become grittier. The good ol’ role model theory is proven true here time and time again. By allowing children to explore passions, schedule elective/after-school activities and set SMART goals, we are helping shape their lens of what they are capable of achieving. This insight opened my eyes to the value of allowing children to select their own passions and the empowerment that comes once they follow through on the commitment they made. Strength of mind is what allows learners to pursue passions and see themselves through a challenge.
Perseverance is Key
“If you are not struggling, you are not learning..If we believe that we can learn, and that mistakes are valuable, our brains grow to a greater extent when we make a mistake.” Jo Boaler
Dr. Jo Boaler is the Nomellini & Olivier Professor of Education at Stanford University and is another scholar who has, in conjunction with Dr. Carol Dweck, shed light on the profound impact of seeing yourself as capable of achieving your goals through several works, primarily her books Limitless Mind, Mathematical Mindset, and youcubed, a site dedicated to revolutionizing the way we teach and perceive mathematics as a whole. Boaler postulates that depth and accuracy are much more important than speed; she has proven the tell-tale theory of quality over quantity is what makes the difference in how one feels and connects with math. As educators, we must understand learners’ why, allow their voices to be heard and known and help shape failures as an integral part of the learning / growth process as it is a clue to work harder to achieve one’s purpose. By allowing opportunities for learners to try new things, lean into discomfort and walk through fear, they learn to rise to the challenge and realize their potential as a result. Based on her research at Stanford University, Boaler found that students who struggle more and learn slower than the “norm” are showing higher levels of success later on as adults. It is the learned behavior of perseverance that helps push learners through the challenge, then the feelings of success kick in thereafter. Although it can be challenging for the adults involved, helping learners see the value in setting and sticking with personal goals can make a huge difference in how they approach learning in the long run.
The combination of a growth mindset, grit and perseverance is the ideal algorithm for rising above learning (and, let’s be honest, life) obstacles. Nurturing learners through the process can shape their view of their potential for lifelong success in learning and beyond. I have seen great benefit in modeling this theory and you can too, one step at a time!
As schools look to return fully in person next year there will be many uncertainties educators will face. While, there are hundreds of questions going through the minds of teachers, there are even more going through the minds of parents as they have had to navigate the ill prepared education system over the last 14 months. There are numerous resources to measure and prescribe curriculum to meet the academic needs of students as they return to the classroom. However, the social and emotional requirements of students have changed while the resources and training necessary have not caught up to the needs of our families, teachers and students. As parents advocate for their students, it is imperative that they have awareness of the social emotional and Executive Functioning needs of their students. Creating informed relationships and partnerships with the educators, tutors, counselors and any other support your child is fortunate to have in their family will ensure a happy, healthy student with a bright future.
How did you become interested in/passionate about SEL growth?
My favorite Maya Angelou quote has always been: “I’ve learned that people will forget what you said, people will forget what you did, but people will never forget how you made them feel.” Reading this quote as a teacher stopped me in my tracks and made me rethink everything I was doing in my classroom. As an educator in an inner-city school, I felt the pressure to ensure my students were achieving at academic levels of their uptown peers. I didn’t want them to continue in the cycle of poverty they had come from, so I felt a personal responsibility for their future. However, after years of district prescribed, skills-based teaching and testing, I knew there was something missing. No one had ever asked these students what they wanted, what they needed and what they thought. This was my first step into the realization that relationships are as important (if not more) than the lessons in any text book. This was where my passion for social emotional learning (SEL) began.
As a parent of three sons who struggled with learning disabilities, I knew the emotional hardships learning could take on a student and their family. Schools would focus on their reading and math skills, which often left them feeling disconnected and defeated. I knew that they learned differently and struggled constantly, but my greatest concern was that they were also not learning skills on how to be successful in life. Although the boys were well behaved, teachers were always frustrated and impatient with them because teaching them was so difficult. One by one they lost confidence in themselves and began to show signs of struggle in their social emotional skills and overall mental health.
What is Social-Emotional Learning and why is it important?
The Collaborative for Academic, Social, and Emotional Learning (CASEL) defines social emotional learning (SEL) as, “The process through which all young people and adults acquire and apply the knowledge, skills, and attitudes to develop healthy identities, manage emotions and achieve personal and collective goals, feel and show empathy for others, establish and maintain supportive relationships, and make responsible and caring decisions.” They remind us that SEL is an integral part of education and human development. These systems of emotional intelligence help us navigate our self-awareness, self-management, social awareness, and relationship building skills, which lead us to responsible decision making.
How do learners present when they are facing SEL challenges?
Students who struggle with gaps in their SEL might be: insensitive to other’s feelings, judgmental of others, have a hard time accepting criticism, argumentative, blame others, have emotional outbursts, exhibit bullying behavior, struggle making friends, overreact, have poor coping skills, or feel the need to always be right.
What role does Executive Functioning play in SEL?
Along with their learning difficulties came large gaps in their Executive Functioning (EF) skills. These are areas of learning such as adaptable thinking, planning, self-monitoring, self-control, working memory, time management, and organization, which help us to navigate the world as we focus our attention, remember instructions, multitask, set and achieve goals and control impulses. The EF skills combined with SEL, support student success because when students have self-awareness and self-management skills they have stronger social awareness which leads to successful relationship building.
With a lack of EF skills and/or low social emotional skills there are many issues that could arise, such as socially inappropriate behavior, trouble controlling emotions or impulses, easily distracted or hard time paying attention.
For my own sons they withdrew, struggled with attention, became depressed and one even ended up with school-based anxiety. Although this is a worse case scenario, when the needs of students SEL and EF are not met, this can become the outcome. This is why in my own classroom, with the school I led as a principal and in my own home I have become an advocate for programs that support the whole child.
What programs or curriculum have you utilized to address said struggles?
Many schools, including the ones I have worked in have successfully used curriculum, training and ongoing professional development from Second Step, Soul Shoppe and Positive Behavioral Interventions and Supports (PBIS). I have found these to be powerful tools if they are used and monitored to fidelity. The schools that educate parents, teachers, school staff and students find the most success with these programs. The entire culture of a school can be positively changed with a commitment to social emotional learning as families, teachers and students feel safer and are happier. These types of programs bring awareness to struggling students and provide resources to teachers, families and students, so that stories like my sons’ don’t have to happen to others.
Using what I had learned about SEL and EF I was able to help my boys become successful young men who are passionate in their careers, thrive emotionally, and build healthy relationships. They went from students who lacked confidence and deemed themselves as, “dumb,” to adults who run their own business, manage others and are compassionate beyond their years.
About the Author
Dr. Sheila Murphy is the founder of Alma Bonita Animal Rescue and an educational consultant focused on equity, diversity, social emotional learning and inclusion. Sheila went into education specifically to advocate and address gaps in the system that failed her own three sons. With a Doctorate Degree in Educational Leadership, a Master’s Degree in Education, a Master’s Degree in Supervision and Administration and as a Certified Life Coach, Sheila has focused her life’s work on giving to those who are most vulnerable in this world.
Making math enjoyable is ideal for driving learner engagement. I had a chance to speak with Federico Chialvo, who shares this passion and is on a mission to spark joy in mathematicians of all ages.
Briefly tell us about your career/experience in education.
I knew I wanted to become a teacher by the time I finished high school, because as a Latinx immigrant, “English Language Learner” with ADHD and Dyslexia I had first hand experience about how hard it could be to navigate the school system, and I could point to a handful of teachers that made all the difference in me making it through my K-12 experience. I wanted to dedicate my life to making education work for those who, like me, weren’t being served equitably.
Over the past 20 years I have worked as an educator in a wide variety of environments, as a teacher in all grades K-12 and in public, private and international schools. Most recently, I served as the Director of Mathematics at Synapse School, a project-based K-8 independent school that integrates SEL throughout the curriculum, where I had the opportunity to build a math program focused on providing all kids with a rich and joyful experience of mathematics.
I took the 2019-2020 school year off to be a “stay at home dad,” and found Joyful Mathematics in hopes of sharing math games and toys that spark joyful math moments. During that year, I also worked as a curriculum writer for Illustrative Mathematics. When the pandemic hit, I had to extend my time away from the classroom to tend to our children. However, last month I started a new job working as a Curriculum Designer at Dreambox Learning, which is an online platform that seeks to ”change the way the world learns by inspiring all students to think differently about math–and love it.”
How did you decide to dedicate your efforts to math?
It’s hard to pinpoint how I decided to dedicate my efforts to math, because it feels like my whole life pointed to that choice.
I had a tumultuous relationship with mathematics growing up. One minute I thought I was good at math and enjoyed it, and then I’d hit a wall and feel completely lost. My mathematical abilities were probably hidden or misunderstood in part due to being 2 grade levels below in reading and coping with ADHD. One year I’d be in remedial math classes, then in GATE, then back in regular math class, only to be put back into the accelerated track. I failed a semester of math in high school, only to take two courses the following year to make up for it. Meanwhile, my father, the biophysicist, would blow my mind at home or in his lab with conversations about fractals and chaos theory.
Despite all my struggles with math in school, I made it through to college with a hint of the beautiful structure that lay behind the cold and rigid way mathematics was taught.
I was lucky enough to take a few math classes in college that reaffirmed the joy and wonder inherent to mathematics. It was in diving into the deep well of pure mathematics that I discovered the profound beauty, creativity, and wonder mathematics had to offer. I was awarded an NSF undergraduate research grant for my research into a simple proof of the four-color theorem, and for a brief moment, I even considered becoming a research mathematician.
Just as I was entering my senior year, I was offered the opportunity to design and teach a project-based seminar class at City High School. From the moment I saw a student’s mathematical identity flip from negative to positive, I was hooked. I felt like I could make an impact, by helping students foster a positive relationship with math. That’s been my main focus ever since!
Why is it important to learn math throughout education?
On the one hand, mathematics is extremely useful because mathematical thinking helps us communicate, remix, and debate ideas. It also can be helpful in some lines of work or in general life.
Math can enrich conversations about our world, whether you’re exploring science, social justice, or public policy. Also, math plays an important role in being an informed citizen that can think critically about data and information and act accordingly.
My favorite reason, however, is merely because it is one of humanity’s most ancient art forms, and when we learn about the beautiful world of mathematics our lives are enhanced.
What is the most common misconception about math?
There is a common misconception that mathematics is only about numbers, doing quick calculations, and there’s only one way to do it.
On the contrary, mathematics has a beautiful web of ideas that are interrelated, it’s creative, and there are many different ways to do mathematics and shine through mathematics. Some of the most brilliant mathematicians are “slow” thinkers, visual thinkers, and divergent thinkers.
How do teachers create a joyful environment for math?
Open up mathematics! Curate experiences that give students agency, let them tinker, make mistakes, fail and try again.
Find ways to have your students be surprised by mathematics, to notice patterns and wonder how and why things work.
Center student thinking by giving them the time to work through their thoughts, and creating a safe space to share ideas in their raw and sometimes incomplete forms.
Expand the notion of what is considered mathematics. Puzzles and games can be a great way to spark joyful math moments, but so can learning a little bit of graph theory, topology, coding, etc.
What are some tools you use/have developed to engage learners in the math process?
I love to curate a tool rich environment for students, anything that helps students play, tinker or create with mathematics.
Physical manipulatives have the power to disarm even the most math-averse students, and give them time to sit with concepts. For example, classic pattern blocks, which are actually surprisingly versatile, I’ve used them to explore mathematical concepts ranging from preK-12th grade. Omnifix cubes are such a treat, it’s like Minecraft you can hold in your hands. For learning place value, base-10 blocks, as well as alternate base blocks like base-2 and base 5. For those learning algebra, Lab Gear or Algebra Tiles are fantastic.
My favorite digital tools are ones that increase student’s access to mathematical wonders. Some of my favorites include Desmos, Geogebra, Mathigon’s Polypad, Scratch, and of course Dreambox.
I’m also a big fan of the 3-Act Math lesson structure, and building in math talk routines into a daily practice, because they center students’ voices and thinking.
Finally, I believe game-based learning can play a big role in our learning experiences. I’ve used games like Catan and Set in my math classroom, and have even created dozens of games over the years to teach a variety of concepts. Recently I published a board game called MULTI, which helps students learn their multiplication facts as well as the structure of multiples and factors. MULTI was the culmination of a decade of playtesting with kids.
Is there anything else that you would like our audience to know about math (perspective, tips, tools, etc.)?
I’m on a mission to rebrand mathematics, in hopes of sparking joyful math moments and expanding the notion of who and what is mathematical. I believe mathematics has something for everyone to enjoy, and mathematics can gain something from everyone who engages with its beauty!
Federico Chialvo is a curriculum designer for Dreambox Learning and the founder of Joyful Mathematics. He holds a BS in Mathematics and a Masters in Education from the University of Arizona and has been an educator for 20 years as a teacher, administrator, coach, and curriculum designer. Federico specializes in designing authentic experiences of mathematics through project-based and problem-based curriculum and has a passion for developing games and toys that spark joyful math moments.
Think back (way back for some of us) when you, yourself, were a learner sitting in front of a blank paper in class because your mind went blank. Most of us can relate to the feeling of high level of frustration that writer’s block presents. Well, some learners face that in the classroom environment on a daily basis. Writing is one of the most challenging aspects of learning today. To relieve the pressure, we will explore the elements of prewriting and all that it has to offer.
Brainstorming is the informal method at which a learner can write any and all ideas they have in the mind on the page. Creating lists or stop & jots can serve as a structured method by which learners can capture their ideas without the pressure of writing down their thoughts in an organized manner. Delineating lists in and of themselves is a great practice to start young as the practice strengthens one’s Executive Functioning skills and releases a bit of tension all at once! Additionally, some educators and parents find success with having a verbal discussion with their learners as a precursor to writing as it allows them to filter their thought process before feeling the finality of putting pencil (or keyboard!) to paper. The learner or the educator can take notes throughout the discussion as a brainstorm too. Lastly, as most would agree, Stop & Jots are a brilliant way for learners to write down a quick thought, connection, question, or otherwise on a post-it that can evolve and move based on where it is most useful. Many teachers find immense value in the use of stop & jots when working on literature study as well as when brainstorming, so give it a try!
Another method to reduce unnecessary stress in the beginning stages of writing is to provide learners with sentence starters or prompts to get their creative juices flowing. Sentence starters are transitional phrases (“In this article,…”) or segments of sentences (“then, in turn,…”) that serve as a springboard for learners to dive into initiating their thoughts in written form by providing a frame of reference for them to stand upon. Prompts can be rather engaging, especially when you incorporate exciting ideas for learners to ponder such as their ideal vacation spot, favorite pastime or perfect birthday treat. As an educator myself, I absolutely love to ask my learners (and children) Would you Rather questions at the dinner table because not only do they provide options for the learners to choose from, but they also improve critical thinking skills and allow them to utilize their imagination to respond. Check out conversationstarters.com’s list for ideas, your learners will not be disappointed!
This is probably the most frequently used tool during the prewriting stage of written expression. There are so many outlines to choose from that it is a wonder as to why some learners avoid them at all costs! Even well into adulthood, writers continue to resource graphic organizers as a method to organize their thinking is a low-pressure way. Common outline strategies include concept maps, Venn diagrams, bubble/spider webs, timemap diagrams, hamburger charts…the list seems nearly endless. Acknowledging that various outlines can be used for differing purposes and, therefore, finding what works best for you is key. That way, learners can feel ownership of their prewriting process and lean on what they find effective based on their personal learning style.
In sum, jumping directly into writing a paragraph or an essay can certainly feel daunting for most people. We completely understand the value prewriting can bring to a learner’s final written product and support the use of these tools (and more!) not simply because they organize our thoughts, but mainly because they can drastically reduce unnecessary anxiety and relieve the stress fog that can block beautiful ideas from being expressed in the first place. Brainspill away, learners!