Do we need to reimagine how we teach math?
If AI will be as ubiquitous as we believe it to be, will its inevitability require a pronounced emphasis in math throughout our education system? While it doesn’t require every individual to become a mathematical expert, there should be a new scrutiny applied to how our systems can better deliver this subject to maximize societal participation and provide greater benefits to future careers.
According to Conrad Wolfram of the famed Wolfram Alpha, mathematics holds a far more significant purpose within education – a transformative role that society urgently requires. He stresses, “Presently, we confine the study of mathematics primarily to the confines of school. However, this perspective and approach inadvertently isolates the subject from its broader applications in the real world.”
Math Performance Continues to Wane across the United States
In 2022, the National Assessment of Educational Progress conducted a nation-wide exam, evaluating a cross section of fourth and eighth grade students. It concluded that following the pandemic, math scores saw declines across nearly all states:
- “A mere 26 percent of eighth graders demonstrated proficiency, exhibiting a decrease from the 34 percent recorded in 2019.
- Fourth-grade students fared slightly better, yet the declines were observed in 41 states. A mere 36 percent of fourth graders displayed proficiency in mathematics, representing a decline from the previous 41 percent.”
The pandemic has exacerbated the educational challenges faced by the most vulnerable students in the country. Their test scores have suffered more significant declines, and the journey toward achieving proficiency has become even more challenging for them.
Dr. Trena Wilkerson, President of the National Council of Teachers of Mathematics (NCTM) wants a different approach to help students connect math to the outside world to “sustain their interest”:
“The industry (researchers, teachers, innovators) needs to think in terms of broadening the purpose of learning mathematics inside of school and throughout a young person’s life, outside of the classroom. With that approach, we [the industry] reveal a path forward for a student to build upon, to be able to critique the world around them. Further, this mindset allows for the inclusion of statistical reasoning, data literacy and data science – the necessary building blocks for the careers of the present and future.”
Society’s Reticence Towards Mathematics
Math has been largely perceived as difficult, abstract and challenging to understand. Grasping mathematical concepts has been one of the struggles that eventually leads to frustration and lack of confidence. Moreover, the lack of real-world context has been the biggest gap that has rendered the subject irrelevant. Traditional math has often focused on rote memorization of formulas and procedures without adequate demonstration of how it’s relevant to real world situations. The binary nature of mathematics, demonstrated by either right or wrong answers has contributed to this anxiety and fear of failure.
This has to change if society is to flourish within a world where algorithms will influence many aspects of our lives.
The ubiquity of artificial intelligence means algorithms will be sewn into the fabric of our daily lives, how we interact, communicate with each other and our work environment. Emerging careers will stem from this and will require individuals to have at least a basic form of data literacy to enable individuals to interpret data, recognize patterns and make informed decisions. Increased collaboration with AI-driven applications will improve the efficacy of these solutions as professionals in healthcare, finance, marketing and other domains integrate them into systems. Moreover, as AI’s advancement also surfaces ethical considerations, math will play a significant role in how our systems become more transparent, fair and more accountable.
Susan Silver, Deconstructing Math Anxiety
Susan Silver is a colleague and friend, a writer, who thinks of the world in patterns and numbers. They enjoy it but this wasn’t always the case. Susan is no stranger to math anxiety.
“I flunked fourth grade mathematics because I could not do multiplication, nor being able to understand greater than(>) or less than (<). I would stay in at recess with my teacher counting cubes but could not understand grouping. At home, my family was little help. They were resigned to the fact I just wouldn’t be good at math… and that was okay.”
Unable to accept this, they decided to play to their strengths with language. Silver thought that numbers could be letters and proceeded to write out a simple substitution code, “I then rewrote my multiplication problems with letters replacing numbers. This gave me insight into how to read equations as grammatical sentences. I didn’t have problems when working with the letters and was finally able to catch up in fifth grade. I then started making up math games that I could play in my room by myself. I was already prepared for algebra when that came along.”
They recently discovered the baggage they had been carrying from childhood –the realization they never thought themself capable of studying math as a career. They had internalized the negative experiences.
“Although my mathematics improved, after algebra I slowed down again. I had real difficulties with geometry and trigonometry, which are still my weaknesses in math. I never thought of myself capable of studying mathematics as a career. I realize now that I had internalized things my teachers had said about my abilities, people who told me not to pursue mathematics. No one expected me to pass AP calculus.”
While they were the slowest in their class, they were able to pass AP calculus. Silver referenced something they wrote previously,
“Unfortunately, some people view our abilities as fixed, instead of helping us grow our potential. For some kids, the time constraints of a semester are not enough time to learn. That doesn’t mean we should give up on them as if they cannot understand…People wanted me to give up on mathematics but I couldn’t give up on myself.”
Silver continued to pursue math communications simply because they were cautioned that discussing it might cause discomfort from other kids. This led to many instances where they faced rejection and isolation because of their love for math, which they had to keep to themselves. Now, as an adult, Silver is committed to never suppressing their conversations on the topic.
In 2018, Silver started blogging about their experiences with math in 2018 in hopes of helping people change their relationship with mathematics. You will find their most recent project at mathcommunications.com. Silver defines Math Anxiety in this way:
“Math anxiety is a sense of fear or panic when presented with mathematics. I write about math anxiety for adults specifically. I believe it is math anxiety that leads to the negative attitudes in society where people believe they are bad at math, are not a math person, and find it acceptable to not be math literate. Most of all, these attitudes impact children and their own phobia of math. It is a cycle of math trauma that I am hoping to stop by educating them. I’m hoping they will reflect on their emotions and realize they can change them.”
Silver acknowledges this relates to AI and why math literacy is imperative. They argue that math anxiety connects with math literacy as it can hamper performance. This avoidance turns into reduced confidence levels and less motivation to succeed. In turn, it impedes memory and the attention required to solve problems.
Silver believes their life would have taken a different path if they had met a mathematician before entering college. These early negative experiences have shaped their attitude for many years, and while they were able to come to terms with how to rectify it, the vast majority of young people with similar experiences have had lasting aversion to the subject.
Gender, Society and its Role in Math Anxiety
Silver alludes to a stat from the Blazer C. Strategies for Reducing Math Anxiety that 93% of people experience some level of math anxiety. This is not reflective of ability, whereas even those who are proficient in math may feel some level of math phobia.
Silver reflects again on their upbringing and how gender impacted their journey:
“I was raised as a girl. Back then, I didn’t have the vocabulary to tell people that I was non-binary. I wouldn’t learn about it until I was studying at Humboldt State around 2005. I was in my twenties then.
The first thing that I noticed was that my whole family was math phobic, including my father who was a partner at one of the top accounting firms. He was very good at math, yet, I could never talk to him without him changing the conversation. When I discovered my love of math, I could not share it with my family.
At school, I was labeled as a “smart” girl. When I spoke up or answered questions in class the other kids were noticeably agitated. I was accused multiple times of being too smart and acting superior. The label of smart was used to dismiss me; to scare me into not raising my voice.”
Today Silver acknowledges that intelligent and outspoken women often face consequences. Being raised as a girl, deprived them of the mentorship their male peers received from teachers, teachers didn’t hesitate to express doubts about Silver’s mathematical abilities.
“I am a slow thinker. I start off behind at the beginning of the school year. I am usually able to catch up by the end of the semester. Yet, I was never praised for getting good grades in math. ”
These environmental factors –teachers’ and parents’ attitudes towards students’ and the children’s ability in math, societal stereotypes on math ability by gender–all shape and deepen the levels of math anxiety. Silver emphasizes that this is more common for girls than for boys, “It is believed to be related to how girls internalize female stereotypes such as men being more gifted in math. It has an impact on self-efficacy, motivation, and even vocational choice.”
This paper provides some context into the problem:
“On an emotional level, individuals suffer from feelings of tension, apprehension, nervousness, and worry. On a cognitive level, math anxiety compromises the functioning of working memory.”
Through a functional magnetic resonance imaging (fMRI) study, math anxiety lights up the part of the brain related to pain and it shows up in the pain and fear networks. Eugenia Cheng wrote an article called “What if nobody is bad at maths”. It asserts that children don’t start off afraid of math, but rather, that develops later in life. She writes,
“…we should teach maths differently, in a way that doesn’t churn out mathophobes. When five-year-olds first encounter the subject, it’s as a creative, open-ended activity, involving play and exploration. They learn about numbers using colourful blocks that join up in different ways. They fit these shapes together and tell different stories with them. Just a year or two later, though, maths becomes a discipline with strict rules and a forbidding regime of right or wrong answers. Instead we should try to maintain that sense of exploration and open-endedness, of trying out different approaches to a problem and seeing what works. What’s important about times tables, for example, is not the answers, but the different possible relationships between numbers. What’s important about equations is not the solution, but the techniques we use to untangle a problem using logic.”
Bridging the Gap by Applying What Comes Easy
Silver, in a post entitled, A Writer’s Illicit Love Affair With Mathematics, believes we should connect with things we care about. They illustrate:
“I turned to language and the use of analogy. I remembered my mother’s cryptogram puzzles. Scrambled letters represent everyday sayings using a simple substitution code. The solver must use logic, rules of grammar, and knowledge of common phrases to find the answer. I thought this could also apply to numbers. If a letter could represent another letter then a letter could also represent a number.
I quickly scribbled down this code:
A=1, B=2, C=3, D=4, E=5, F=6, G=7, H=8
Then I transformed my homework problems.
1 x 2 becomes A x B.
And then suddenly — I saw it for the first time.That tiny “x” was staring me in the face.
An equation is like a sentence. A mathematical operator is a form of grammar. You have to understand its symbolic meaning. I hadn’t yet conceptualized what that tiny little “x” was trying to tell me. I was counting cubes because I could only see the numbers.”
Silver believes their affinity for something isn’t only determined by mere skills. Their aptitude in math evolved over the course of three to four years because they found something beyond anxiety and fear in math; they realized that “putting forth more cognitive effort” could actually be an enjoyable exercise. Suddenly, with this newfound interest Silver started creating puzzles and employing code keys to calculate the cumulative values of words, then made comparisons between their values. This process led them to discover the realm of recreational mathematics.
We Can’t Perpetual Societal Disparities
Silver pointed to Robert Moses, a prominent figure in the Civil Rights movement, who engaged with numerous influential individuals during that era. However, his most significant collaboration was with Ella Baker, a strong advocate for community-based empowerment to drive societal change. Together, they founded the Student Nonviolent Coordinating Committee (SNCC), led by students. In partnership with SNCC, Moses ventured into the heart of Mississippi, a deeply segregated region, to register black voters.
Moses later established the Algebra Project, recognizing the potential for organizing people around the issue of math literacy. He observed the disparity at his daughter’s school where the least proficient math students were segregated based on race and socioeconomic status. It was believed these kids were uninterested in math, while Moses understood these kids needed to be challenged and taught in a different way that would bridge math with their daily experiences. More importantly, he asserted that math literacy was a “civil right, both for civic engagement and for socioeconomic engagement” and by attaining it, in the Algebra Project, participants would be empowered to engage in society and be active in the decisions that affect their lives.
Moses writes (from Radical Equations)
“It’s not so cool or hip to be completely illiterate in math. The older generation may be able to get away with it, but the younger generation coming up now can’t —not if they’re going to function in society, have economic viability, be in a position to meaningfully participate, and have some say-so in the decision making that affects their lives. They cannot afford to be completely ignorant of these technological tools and languages.”
Silver points to the prescience of his undertaking and its application to this meteoric rise in AI: “And you know, AI as it is hyped is such a threat of overtaking our decision making in life and our jobs. Publishers still think they can replace their writers with AI (Buzzfeed, Gizmodo, and Hollywood). I am personally so frustrated with the fact that AI is now packaged into everything! You can’t escape it. It has truly taken over all our tech.”
Math Matters in ALL Our Futures
There are two impacts of mathematics that we should consider. One is the labor market for in demand skills.
The US Bureau of Labor Statistics says that they expect a 29% increase in employment in math occupations between 2021 and 2031. Data scientists have a median income of around $100,000 making it a lucrative occupation. Stanford University’s Institute for Human-Centered Artificial Intelligence in a report stated that there were 800,000 job openings in AI related fields in 2022. This shows that fields in computer science are growing faster than most other sectors.
The second impact of mathematics is navigating a world where AI will mediate much of our interactions. Silver emphasizes,
“While the press highlights the AI doomsdayers. It ignores the real harms happening now. We know of one such harm. Content from marginalized communities are under accounted for. Their conversations are filtered out because of the language they use when the content is moderated. Which means what is left often reinforces stereotypes in the data set. AI has bias and it isn’t hard to imagine how that might impact people’s lives. Individuals must understand and sift through the information retrieved from AI. As it is likely to remain unreliable. Critical thinking skills from mathematics are crucial.”
Two Math-Minded Students and Their Journey Back to Math
I recently spoke to two GenZ, currently pursuing Maths in their post-secondary education:
Marissa Gilbride, third year student at McGill University, Montreal and Nathan Jones (and my son), third year student at Wilfrid Laurier University, Waterloo. I asked them about their own journey with the subject of mathematics.
Nathan found math to be somewhat natural from an early age, excelling in basic arithmetic and advancing to complex concepts in high school and university. Despite understanding the majority of concepts, he often made small computational errors due to negligence, affecting his exam performance.
Marissa found math easy as a child because it seemed logical, involving activities like counting blocks and using money. However, in high school, the rapid introduction of math concepts posed a challenge. Her struggle was not in computation but in grasping the underlying theories and understanding the ‘why’ behind concepts. This gap caused her to fall behind despite being capable in computations.
Both had early experiences which caused them to question their math abilities. In tenth-grade, Nathan struggled academically, because he missed classes and the lacked the commitment and effort necessary. This resulted in failing grades on tests and assignments that “dug him into a deeper hole”. While he knew he needed a better work ethic, how he was labelled by peers and one teacher led him to internalize this belief: “I was told by my peers and teacher that I was ‘stupid’ and that math was one of my weaker points. I started to believe in what I was told about my abilities, completely disregarding what I think and know,” he reflects.
Marissa’s university transition brought unexpected challenges during her second year. The shift from computational math in high school to theory-heavy abstract courses caught her off guard. Daily class attendance, note-taking, and dedicated study sessions still left her feeling bewildered by the complexity of the subject. She contemplated a shift to a Bachelor of Arts, realizing the path she had chosen was daunting. She explains, “I planned on switching to a Bachelor of Arts in my third year because I was so convinced that if I continued on my previously set path I would never reach the end.”
Both eventually found their way back to mathematics. As he matured through high school, Nathan recognized that by taking school more seriously, consistently attending classes and actively engaging with the material, math began to align with his natural aptitude. He realized that his fondness for the subject grew as he progressed through more math courses, “Math has been and is still my favorite subject in school because of the infinite possibilities numbers can provide,” he expressed.
Marissa’s journey back to mathematics was influenced by her perseverance and change in mindset. Despite the challenges of her initial semester, she persisted, convinced that the next term could not be as hard. Her tenacity proved correct, and as classes started, the once-daunting material became more accessible and easier: “My struggles and perseverance had taught me more than I originally thought… I started to love attending class (even the 8:30 ones) and I couldn’t get enough of this crazy subject.”
Both Nathan and Marissa have experienced a revamped self-confidence as they’ve navigated their academic and personal journeys. For Nathan, the process of learning has directly contributed to his growing self-reliance and ease with his abilities. He emphasized the importance of believing in yourself and putting in dedicated effort to succeed.
Marissa, on the other hand, has found that her triumph over mathematical challenges has had a transformative impact on her overall confidence. She believes that her math background has equipped her with a valuable skill set that extends beyond just numbers. Having conquered her initial struggles, Marissa now feels well-prepared to not only tackle various subjects but also excel in a wide range of learning and job opportunities.
Embracing Fear, Discovering Strength and Identity
For Silver, the culmination of their journey has led them to embrace the very thing they feared, “We have to face the things which make us feel the most uncomfortable. They also have the potential to bring us our greatest loves.”
There are those that will continue to evade the very triggers of events they’d rather forget, and that stifles future pathways or missed opportunities. For Silver, they embraced their fear and was able to ultimately enjoy the journey into problem solving by turning to the things that provided the most meaning for them–their penchant for language:
“I leaned increasingly more on my math skills over the years. It was like repairing an atrophied muscle. I exercised my number sense through entertaining activities.
Inside of me, there is a writer with a mathematical muse. The source of my inspiration is the depth of my feelings formed as a child learning to become math literate. These emotions have taught me an important lesson. I have deep emotional attachments to historical mathematicians, numbers, functions, and certain theorems.
Just as you may have attachments to novels or films, these feelings make up my fundamental sense of self. While others perceive my writing skills they may not know much of my inner world of mathematics. Yet both are important to understanding who I am as a person.”
For Nathan and Marissa, this is the advice they offer for those who are anxious about math:
Nathan: “Whether you have a natural understanding in math or not, it is a subject that can be conquered. Math can be a scary subject to some, but taking the leap of faith and putting trust in yourself will always produce the best possible outcome.
What makes a great student and employee is hard work, and math is a subject that requires it. If you remain persistent in your efforts throughout your math courses or any others for that matter, the success will come.”
Marissa: “You have nothing to lose–only something to gain from trying math. It’s scary and intimidating but it’s nothing anybody can’t do. All you have to do it try and you’ll be amazed at what you can accomplish.”
Susan Silver is the writer with the mathematical muse. Author at Beauty of Mathematics, they write anecdotes about their love of math and educate the public on math anxiety. Susan started as a freelance writer creating content for the web over a decade ago. As an engagement specialist at The Social Element they worked with clients like Diageo and Keurig Dr Pepper.
Read the full article here
