Math educator and author Eugenia Cheng discusses the goals of math education, the importance of clear thinking skills, misconceptions about math, understanding math at deeper levels, the benefits of learning math, rethinking math education, exploring different starting points, the influence of probability theory and optimization theory, continuing to learn, and breaking down complex skills.
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Quick takeaways
Math education should focus on teaching students how to think well and use their brains in a clear and logical way rather than forcing them to memorize useless information.
Math education can help develop the skill of evaluating and communicating valuable information in an overwhelming world of data, by teaching logical deduction and understanding different perspectives and arguments.
Mathematics enhances critical thinking, problem-solving abilities, and communication skills by teaching individuals to be more precise with definitions, consider different perspectives, and understand logical flaws.
Deep dives
Math Education Should Focus on Understanding Rather than Memorization
According to Eugenia Chang, math education should not revolve around forcing children to memorize things they may never use. She believes that the main memory of math education for many people is memorizing information that seems useless. For example, she argues that memorizing times tables is unnecessary because calculators can perform those calculations. Instead, math education should focus on teaching students how to think well and use their brains in a clear and logical way. This helps develop skills that can be applied to any problem, rather than just solving specific math problems.
Math Can Help Us Navigate an Information-Overloaded World
According to Eugenia Chang, math provides a framework for using logic and logical frameworks to determine what information is good and what is bad. In a world where the amount of information is overwhelming, being able to evaluate and communicate what is valuable becomes crucial. Math education can help develop this skill by teaching how to use logic to deduce conclusions from known information, and understand different perspectives and arguments. By developing these skills, individuals can navigate the abundant information available and make more informed decisions.
Mathematics Teaches Critical Thinking and Broadens Perspectives
Mathematics, according to Eugenia Chang, is not just about numbers and equations, but about using our brains to think well and develop logical frameworks to assess information. By understanding math, individuals can improve their critical thinking skills and learn to distinguish between good and bad arguments, especially in a world flooded with information. Math teaches individuals to be more precise with definitions and to consider different perspectives, enhancing communication and problem-solving abilities. The agreeable nature of mathematics, where mathematicians agree when logical flaws are pointed out, can help dispel misconceptions that math is a conspiracy or brainwashing, enabling a more objective understanding of mathematical concepts.
Math Education Should Focus on Exploration and Playfulness
Eugenia Chang advocates for a more playful and exploratory approach to math education. Instead of solely focusing on correct answers and standardized tests, she suggests fostering curiosity and appreciation for math. This can involve encouraging students to play with mathematical concepts, ask questions, and explore different scenarios to deepen their understanding. By shifting the focus from memorization and speed to exploration and play, math education can cultivate a sense of wonder and create a positive learning environment that encourages students to engage with and enjoy mathematics.
The Power of Understanding the Physics of Motion and Math
Understanding the physics of motion and the principles of math can create interest and improve performance in sports. Math has applications in various fields and can help people understand real-life problems. Abstract mathematics fosters empathy by enabling individuals to follow others' logic and understand their starting points. This allows for better comprehension of opposing perspectives and more fruitful conversations even when discussing divisive topics. Math can help develop critical thinking, problem-solving skills, and provide frameworks to better understand complex concepts.
The Influence of Context, Relationships, and Category Theory in Mathematics
Mathematics is not solely about studying individual objects but also understanding their relationships and contexts. Category theory enables mathematicians to identify connections and patterns between different fields of study, leading to breakthroughs and new perspectives. The focus on relationships and bridges between concepts allows for deeper insights and collaborations across disciplines. Contextual understanding, similar to understanding individuals within their life experiences, enhances mathematical comprehension. Additionally, category theory's abstract viewpoint provides fruitful connections and opens up new avenues of research, transforming the foundations of mathematics.
What should the goals of math education be? What does it mean to "think well"? Is math real? Why are feelings of bewilderment or confusion so common in math classes but not as common in other subjects? Schools now generally offer reading and writing instruction separately — even though both are important for language use — because the skill sets they require can differ so widely; so how might math education benefit from drawing a similar distinction? What should math classes impart to students that will enable them to engage as citizens with complex or controversial issues? What does it mean to ask good questions in math? Can math teach empathy? What is category theory? Can most people learn most things if they just have the right teacher and/or educational materials?
Eugenia Cheng is a mathematician, educator, author, public speaker, columnist, concert pianist, composer, and artist. She is Scientist In Residence at the School of the Art Institute of Chicago. She won tenure in Pure Mathematics at the University of Sheffield, UK, and is now Honorary Visiting Fellow at City, University of London. She has previously taught at the Universities of Cambridge, Chicago, and Nice, and holds a PhD in pure mathematics from the University of Cambridge. Alongside her research in Category Theory and undergraduate teaching, her aim is to rid the world of "math phobia". Eugenia was an early pioneer of math on YouTube, and her videos have been viewed around 15 million times to date. She has also written several books, including: How to Bake Pi (2015); Beyond Infinity (2017); The Art of Logic (2018); x + y : A Mathematician's Manifesto for Rethinking Gender (2020); The Joy of Abstraction: A Exploration of Math, Category Theory, and Life (2022); Is Math Real? How Simple Questions Lead Us to Mathematics' Deepest Truths (2023); and two children's books: Molly and the Mathematical Mysteries and Bake Infinite Pie with x + y. She also writes the "Everyday Math" column for the Wall Street Journal and has completed mathematical art commissions for Hotel EMC2, 6018 North, the Lubeznik Center, and the Cultural Center, Chicago. She is the founder of the Liederstube, an intimate oasis for art song based in Chicago. As a composer she has been commissioned by GRAMMY-nominated soprano Laura Strickling and is one of the composers for the LYNX Amplify series, setting work by autistic poets who are primarily non-speaking. Learn more about her at her website, eugeniacheng.com.
