How can educators prevent the development of Mathematics Anxiety?
Arpit Goel
Building AI, Tech, Climate, HigherEd Communities I Founder, AI Capitol I Voiz Academy India WhatsApp Community I Member: HBSO, Wharton Online, WEF Digital I COP28 Ambassador I Learning German, AI and Tech Investor
What use are imaginary numbers in the real world? Do they have purpose or is it just mathematicians having some fun ?
In high school, I used to think this. I had no answer. I visualised to learn new concepts. I couldn’t see the current flow or molecules vibrate. All I saw were equations such as V=IR and (J?K?1).
Dr. Meena Mehta Kotecha's research on mathematics anxiety (MA) highlights the harmful effects of this phenomenon, especially where students perceive themselves as "bad" at math. This leads to restricted cognitive abilities and negative emotions towards math, impacting both academic and non-academic interactions.
During my high school years, I too experienced a fear of mathematics. I agree with Dr. Kotecha's assertion that poor quality of teaching in high schools is responsible for the low participation of young students in STEM subjects.?
But, during my time at Azim Premji University as a public policy student, I took a statistics course taught by a postdoctoral econometrics professor from Carnegie Mellon University. The class had a diverse mix of students, including those with backgrounds in marketing, history, pol-sci, engineering, sociology, and economics not excluding qualified lawyers. The professor shared a personal story to encourage the class struggling with quantitative analysis.?
She found herself completely engrossed in solving a few, difficult problems during a University test, leaving the other problems unfinished. When she received her grade, it was not surprising that she had scored low. However, her professor took note of her dedication and ability to tackle such a challenging problem. Instead of reprimanding her for her low grade, he encouraged her to pursue a career in mastering these difficult techniques. When she arrived at Azim Premji University, the professor dedicated significant effort to effectively teach economics to the students in every lecture.?
Dr. Kotecha suggests that "breaking the cycle of mathematics anxiety requires abandoning old beliefs, questioning assumptions, and acknowledging new positive experiences..." facilitated by the educators. This approach was exemplified by my economics professor.
What Indian high school educators can learn from this experience? Is it possible to bring out the best version of students struggling with math anxiety?
The theory of symbolic interaction (SI) is a sociological perspective that emphasizes the importance of symbols and meanings in human interaction. It suggests that individuals create and interpret meanings through social interaction, and that these meanings shape their behavior and attitudes.
When it comes to teaching math, the theory of symbolic interaction suggests that it is not enough to simply teach students the technical skills and procedures involved in solving mathematical problems. Instead, it is important to create a classroom environment where students are actively engaged in the process of learning and are encouraged to create their own meanings and interpretations of mathematical concepts.
Negative or positive interactions with teachers and peers can significantly influence a student's perception of their learning experiences in mathematics. Unfavorable interactions, whether real or perceived, can trigger negative emotions towards math, leading to the development of negative attitudes and eventually mathematics anxiety (MA).
In practice, this means that math teachers need to adopt teaching strategies that go beyond rote memorization and repetitive drills. They should encourage students to explore mathematical concepts through real-world problems and activities that are meaningful to them. They should also provide opportunities for students to collaborate with their peers, share their ideas, and receive feedback.
AI has the potential to enhance learning by leveraging the theory of symbolic interaction to create more personalized, engaging, and meaningful learning experiences for students. By integrating AI into math education, we can help students develop a deeper understanding and appreciation of math and equip them with the skills they need to succeed in the real world.
When preparing for the GRE, I had the opportunity to use the interactive services of Manhattan Prep. On their website, they offer a wide range of services, including interactive videos that are self-paced and provide immediate feedback when I make mistakes. These videos are designed to help me learn new concepts and approaches in a structured manner, which is essential for mastering a standardized test like the GRE.
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For high school students, Khan Academy have developed unique and effective approaches to learning that have yielded impressive results. Manhattan Prep's interactive learning approach has proven to be successful, with students reporting an average improvement of 7 points on the GRE after using their services. Similarly, Khan Academy's personalized approach to education has enabled students to work at their own pace and receive individualized feedback, resulting in significant improvements in their academic performance.
AI has the potential to revolutionize the way math is taught by leveraging the theory of symbolic interaction. Here are a few ways that AI can add to learning:
We need to teach students to think beyond school teachers and learn the beauty of mathematics on their own. Maybe students do not need tutoring from teachers, but facilitation, mentoring and guidance. Teachers can facilitate how to use imaginary numbers.
They must teach that these numbers have also found their applications in art, music, and cryptography. In music, they are used to represent the frequencies of sound waves, and in art, they have been used to create stunning visualizations of mathematical patterns.?
Here’s what a few educators have to say about imaginary numbers as quoted by The Guardian newspaper:
"They are of enormous use in applied math and physics. Complex numbers (the sum of real and imaginary numbers) occur quite naturally in the study of quantum physics. They're useful for modeling periodic motions (such as water or light waves) as well as alternating currents."
"An example is if you have a pendulum swinging, it starts to slow down and eventually stops. If you want to work out the motion of the pendulum over a certain time (i.e. derive a formula) then the best way to do it is to use complex numbers."
"Imaginary, or complex, numbers aren't much use when adding up your shopping bill or working out your tax, (on second thoughts...) but they have been a vital tool in the development of mathematics. As an example, you probably wouldn't have the weather forecast if it wasn't for imaginary numbers. Although forecast models don't use complex numbers themselves (though you may think they do), the mathematical theories on which the models are based rely on them."
How about a history lesson at the beginning of the class?
That imaginary number as an idea was first introduced in the sixteenth century and was met with much resistance and skepticism. It was not until the eighteenth century that mathematicians fully embraced the idea and began to explore its potential. While they may seem abstract and elusive, they have proven to be essential in describing and solving real-world problems in fields such as engineering, physics, and computer science.
Imaginary numbers not only expand our understanding of the world around us but also challenge us to think beyond the limits of conventional mathematics, leading to new discoveries and innovations that shape our modern world.?
By incorporating the beauty and usefulness of numbers into mathematics education, we can inspire students to pursue STEM fields and unlock their potential for creative problem-solving. It is crucial to move beyond the rigid and limited scope of traditional mathematics education and embrace the diverse and exciting possibilities of the subject.