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The Paradox of Progress: Technology, Penmanship, and the Authenticity of Writing
The relentless march of technological advancement has undeniably revolutionized education, offering students unprecedented access to information and tools. Yet, this progress has inadvertently created a paradoxical challenge: a decline in penmanship among students, even as the demand for legible handwriting resurfaces in the age of artificial intelligence. From the observation of my own students, ranging from middle school to high school, to the increasing prevalence of typing practice over handwriting in younger children, it is evident that the art of crafting letters by hand is waning. This trend, however, clashes starkly with the evolving landscape of college admissions, where institutions are increasingly emphasizing authentic, on-the-spot writing skills as a countermeasure to AI-generated content.
The digital age has fostered a culture where typing and digital communication reign supreme. Students are adept at navigating keyboards and touchscreens, but the physical act of writing with a pen or pencil seems to be falling by the wayside. This is particularly concerning given the cognitive benefits associated with handwriting, including improved memory, fine motor skills, and creative thinking. Yet, the emphasis on digital literacy in early education, exemplified by my 6th-grade niece’s focus on typing, reflects a broader societal shift towards prioritizing technological proficiency.
Ironically, as AI tools become increasingly sophisticated, institutions of higher learning are recognizing the need to reassert the value of authentic, human-generated work. The surge in AI-assisted writing has prompted many elite colleges and universities to implement new evaluation methods that prioritize spontaneous, handwritten responses. This shift is not a regression, but rather an adaptation to ensure that students possess genuine critical thinking and communication skills, qualities that remain uniquely human.
Institutions like MIT, Georgetown, and the University of California system have begun incorporating timed writing assessments, maker portfolios, and spontaneous response questions into their application processes. These methods are designed to assess a student’s ability to think critically and express themselves clearly under pressure, without the aid of pre-prepared or AI-generated content. For example, Yale University’s use of video response questions and the University of Chicago’s reliance on unexpected creative prompts during interviews push applicants to engage with material in real-time, revealing their genuine intellectual agility.
The implementation of these methods is a testament to the recognition that AI, while a powerful tool, cannot replicate the nuanced expression of human thought and creativity. The ability to articulate ideas coherently and legibly, especially under time constraints, is a crucial skill that transcends technological fluency. The emphasis on legible handwriting, in particular, speaks to a desire for authenticity and a return to the fundamentals of communication. While AI can generate text, it cannot replicate the personal touch and immediate expression conveyed through handwritten words.
This evolution in college admissions is not merely a reactionary measure against AI; it is a proactive step towards ensuring that students develop the essential skills needed to thrive in an increasingly complex world. It is a reminder that while technology can enhance learning, it should not replace the foundational skills that underpin effective communication. The ability to write legibly, think critically, and express oneself authentically are qualities that will remain invaluable, regardless of technological advancements.
As technology continues to reshape education, it is imperative that we strike a balance between digital literacy and the fundamental skills that define human communication. Colleges and universities are leading the charge in this endeavor, adapting their evaluation methods to ensure that students possess the critical thinking and writing abilities needed to succeed. The future of education lies not in choosing between technology and tradition, but in finding a harmonious integration that fosters both innovation and authenticity.
After AP Cal BC – Take Advanced Mathematics in the Age of A.I.
By James H. Choi
http://Column.SabioAcademy.com
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Only a small percentage of American high school students complete AP Calculus BC. As of 2024, about 87,000 students nationwide took this exam, representing just 3% of the approximately 3 million American high school graduates each year.
Mathematics Learning Paths for the AI Era
Students who complete AP Calculus BC before 12th grade now have more diverse options. In today’s AI-dominated era, conceptual understanding and application skills have become more important than calculation abilities, making various learning paths worth considering.
Advanced Data Science and Statistics
If you haven’t taken AP Statistics yet, you should. In the AI era, data interpretation skills are essential, with statistics forming the foundation. Bayesian statistics provides a framework for dealing with uncertainty, while experimental design teaches methodologies for obtaining meaningful results. Data mining techniques help discover patterns in large volumes of data.
It’s important to apply theoretical knowledge through real dataset analysis. Understanding concepts like hypothesis testing, confidence intervals, and regression analysis builds the foundation for data-driven decision making.
Concurrent Learning of Multivariable Calculus and Linear Algebra
Traditionally, students learned Multivariable Calculus before Linear Algebra. However, in the AI era, studying these subjects concurrently is advantageous. Gradient Descent, fundamental to deep learning algorithms, is a core concept in multivariable calculus, while neural network weight updates use matrix operations from linear algebra.
In computer vision, both fields are necessary when representing images as matrices. In natural language processing, techniques like word embeddings utilize vector spaces, requiring understanding of both vector operations and multivariable functions. Understanding optimization problems in machine learning requires comprehensive knowledge of both fields.
Discrete Mathematics and Algorithm Theory
Discrete Mathematics, previously important only to pure mathematics or computer science majors, is now essential for all STEM students. Graph theory forms the basis for applications like social network analysis, recommendation systems, and finding optimal paths. Combinatorics helps understand the decision space of AI systems.
Algorithm analysis provides a framework for evaluating efficiency and complexity, essential for optimizing AI performance. Boolean algebra and logic help understand decision processes and rule-based reasoning. Discrete probability theory forms the basis for AI models dealing with uncertainty, while information theory addresses entropy, a core concept in data compression and machine learning.
Computational Thinking and Programming
Beyond mathematical concepts, developing implementation skills in programming languages is important. Python is suitable for practicing mathematical concepts with its rich libraries for data analysis and machine learning. R is specialized for statistical analysis, while Julia is optimized for numerical computation.
“Computational Thinking” or “Mathematical Computing” courses teach how to decompose mathematical problems algorithmically and implement them in code. Coding matrix operations, numerical solutions of differential equations, and probability simulations helps connect theory and practice.
Practical Approaches
Modern mathematics learning requires balance between theory and practical application:
Project-Based Learning: Solving real problems using AI tools is effective. After learning differential equations, coding physics simulations (like pendulum motion or population growth models) applies theoretical concepts. Applying optimization algorithms to scheduling or resource allocation problems demonstrates practical applications. Analyzing real datasets builds data analysis skills.
Collaboration with AI Tools: Tools like ChatGPT, Wolfram Alpha, and GitHub Copilot should be collaborative partners for concept understanding and problem-solving. Wolfram Alpha helps verify visualizations and step-by-step solutions. ChatGPT provides various explanations to develop understanding. GitHub Copilot teaches different approaches to implementing algorithms. Critically reviewing these tools’ solutions deepens understanding.
Interdisciplinary Applications: Apply mathematics to physics, economics, biology, and social sciences. Physics uses differential equations to model natural phenomena. Economics applies game theory and optimization to decision-making. Biology uses probability theory and differential equations in population genetics and ecosystem modeling. Social sciences employ network theory and statistical methods to understand interactions and behavioral patterns.
Developing Mathematical Intuition: While AI performs calculations instantly, mathematical intuition and creative problem-solving remain uniquely human. Focus on the ‘why’ and ‘how’ to understand fundamental reasons and connections. Try different approaches to problems to develop varied perspectives. Focus on recognizing patterns and generalizing rather than memorizing techniques. Find counterexamples and consider extreme cases to explore theoretical limits. Visual representations strengthen intuitive understanding.
College and Career Preparation
Students who finish AP Calculus BC early can take courses at nearby colleges or through online platforms like edX, Coursera, and Khan Academy. Programs like Stanford’s “Math Camp,” MIT’s “PRIMES,” and Johns Hopkins’ “Center for Talented Youth” offer college-level mathematics experience. “Mathematical Modeling Competitions” and “Algorithm Competitions” develop problem-solving abilities.
Self-directed learning resources include MIT’s OpenCourseWare, Stanford’s online advanced mathematics courses, and Khan Academy. Programs like Coursera’s “Machine Learning” or edX’s “Data Science MicroMasters” apply mathematical knowledge to AI and data science.
For research experience, connect with professors or research institutes for internship opportunities. Many universities offer summer research programs for high school students.
In the AI era, mathematical modeling, algorithmic thinking, and creative application of mathematics are more important than calculation abilities. Designing learning paths to develop these competencies maintains competitiveness as AI technology advances. Mathematical intuition and creative problem-solving are uniquely human strengths that AI cannot easily replace.
Education and Technology
By James H. Choi
http://Column.SabioAcademy.com
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If we look back at history for a moment, the introduction of technology in education began with the invention of Gutenberg’s printing press. Before that publishing revolution, all books were naturally handwritten and passed down, and I read that one copy of a book written that way was worth $30,000 today. The way to mass-produce these expensive books was “reading and dictation.” In other words, one person would read the contents of the book out loud in front of the classroom, and the students sitting together would write it down. This “reading” is “Lectio” in Latin, which became “Lecture” in English, and we translate it as “lecture,” but its original meaning is “reading.” Even now, if you look at the classrooms where we go to hear “lectures,” you can see that they still maintain the medieval “reading and dictation” method.
In other words, the introduction of the first technology related to education only helped to widely distribute books, but did not change the form of knowledge transmission. Of course, it was a big change that books became cheaper, making it possible for individuals to own them and learn on their own using them. However, most students still spend more time sitting in the classroom, taking notes, without asking questions, even when lectures are indistinguishable from reading aloud. The next revolutionary technology was videotape. Since recording allowed lectures to be played back across time and place, it seemed like it would bring about a revolutionary change in education, but this also only had a small impact in a few fields such as cooking and aerobics, and did not bring about any change in education overall. Although videos could convey more information efficiently than books (think of learning how to disassemble/assemble an engine by reading text), both videos and books were one-way transmission media, so they had limitations in changing the education system. The DVDs that came out later were the same, except with higher resolution.
The next technology is computer-based education, which is where we are today. Now, it is strange to not have computers in schools, but learning the knowledge/concepts embedded in computers began in the 1980s. The reason why this decades-old educational method has become mainstream these days is because it has become cheaper and easier to distribute, has become smaller and more portable, and the development of the Internet has made group collaboration possible. And because its performance has improved, it has become smarter and has begun to take on some of the role of a teacher. For example, in math, even if the problem is not multiple choice, if the answer is a+b/2, it can be graded as b/2+a or (2a+b)/2. In addition, it has become possible to know when, what, and how students studied, record it, and even report it to teachers/parents, which is the first time in history that the conflicting hopes of “cheaper and more detailed student study” can be met at the same time.
This revolution is finally changing the “reading + dictation” education format with the powerful technology that allows two-way information exchange. On the one hand, online university lectures are appearing, and on the other hand, opposition is rising that can be summarized as “Education is definitely about teachers and students meeting face to face and discussing…” At the same time, the question is being raised, “Is it right for the winner-takes-all system to reach the education sector?” The future is unpredictable, but I think that computers will now take center stage in education and change everything around them. How should our children prepare for this unprecedented world? Ironically, the most important thing is not the ability to use computers well, but motivation. This is because automated education is provided at a low unit price and is almost free, and in such an environment, how much students learn is determined by their will/curiosity/desire. In the past, there were understandable reasons for not receiving education, such as “because their family was poor,” but in the world in which today’s generation is growing up, there will be no other reason than “because they are lazy.” And what is even more important is self-control. Computers that have the ability to teach students in this way can also make students buy products and become addicted to games. In fact, all technologies used in education are technologies developed/distributed for entertainment purposes, so there is no technology that only teaches. Learning with computers always requires the ability to resist such temptations.
Expensive “Free” part 2
By James H. Choi
http://Column.SabioAcademy.com
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In the last article, I discussed how pricing something as free when demand exceeds supply not only benefits unintended beneficiaries but also shifts where the money ultimately goes—and, in the end, the consumer will pay for it somewhere, somehow.
But what about the digital economy, where supply is infinite? In that case, prices truly are free. Engineering courses at MIT and philosophy courses at Harvard are available for free on edX, and you can read encyclopedias at no cost on Wikipedia. Beyond that, there are free products of all kinds, from the most basic operating system, Linux, to word processors and spreadsheets. Today, you can accomplish almost anything using free software.
You might be wondering, “Why pay for something when you can get it for free?” But all free things come with distortions. For example, if you donate large quantities of wheat, bicycles, or shoes to a poor neighborhood, the local wheat seller, bike shop, or shoe store will go bankrupt and may struggle to restart their business. Likewise, when an expert donates their talent for free, others with similar skills—or those aspiring to enter the field—are affected. This effect is especially pronounced in the digital economy, where products are infinitely replicable. Unlike wheat, bicycles, or shoes, a single digital contribution can be used and reused globally, amplifying its impact.
Consider word processors as an example. Currently, Microsoft Word is the only widely recognized paid word processor. Beyond that, many excellent word processors are available for free. While this benefits consumers, it also raises questions about the future. If our children, who will one day need to work and contribute to the economy, aspire to make money from word processing software, that path is already closed. If they insist on staying in that field, their only option is to join volunteer teams contributing to the improvement of free alternatives. Of course, the software world is vast, but nearly every type of software now has a free counterpart. Just think about how many paid apps you have on your smartphone—if you’re like me, you likely use free versions. In today’s world, the only way to succeed is to create a paid product that surpasses its free competitors.
Of course, one can contribute to humanity without prioritizing financial gain, offering their work for free. But to do that, one must first secure an income. Take Wikipedia, for example. We admire the contributors who write and share knowledge, but behind the scenes, financial support is always present—whether through direct sponsorships or through employers who pay these contributors enough in their regular jobs to afford working on Wikipedia without financial strain.
If a company were to offer its products for free, as Wikipedia or edX do, competitors worldwide would protest, and courts would likely rule it as dumping. Yet, when knowledge and talent are “dumped” in this way, they are praised rather than condemned. Regardless of whether it is praised or criticized, the economic effect remains the same. For instance, a professor at a second-tier university might find themselves at odds with administrators who would rather stream recorded lectures from Harvard professors than pay for local instruction. The current generation may fight to hold onto their positions until retirement, but for the next generation, opportunities are shrinking, and barriers to entry are already high. Of course, one can also take advantage of this landscape. In fact, success depends on doing so. Nearly all the necessary server software, databases, and programming languages are now free, meaning what once required a $100,000 investment in the early 2000s can now be accessed for just $50 a month. While the barriers to entry have risen for the average student, for those who understand this new infrastructure, know how to utilize it, and have innovative ideas, the world has opened up to unprecedented opportunities. Barriers and opportunities create polarization, and I hope, dear reader, that you will prepare yourself for this new economic era—so that you can position yourself on the favorable side
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