BY: YELLOW HEIGHTS
After achieving the American dream, he set out to teach his favorite subject — math. He inspired students to learn, grow, and build confidence in themselves. After two years, he received his only performance review— an ultimatum: change or leave. He shares his story in an upcoming book, part of which is at “Unbalance: An Immigrant Teacher’s Life and Perspective on U.S. Education”: Prologue)
Teach the Skills for Lifelong Learning
Lifelong learning depends on three important learning skills: how to learn new subjects, how to ask good questions, and how to think logically. Education should teach students these important lifelong learning skills.
How to Learn New Subjects
The Internet provides plentiful learning resources for all subjects, and any motivated student can learn on their own. The teacher’s role is partly to motivate students and partly to set the right learning sequences, goals, and environment for them to find their own ways of learning new subjects quickly and deeply, as the future will often require them to do so.
When I started careers in climate research, software engineering, and investment management, my formal training was rather limited. However, my math learning trained me to understand a new area at the most fundamental level. It enabled me to learn deeply and have the confidence to challenge conventional wisdom. During the 2008 financial crisis, I learned new financial instruments quickly and developed bold trading strategies against market consensus.
How to Ask Good Questions
Another essential learning skill is the ability to ask impactful and relevant questions that open new horizons of possibilities. During my career, I have watched some great leaders close at work. Their styles differed dramatically, but one commonality was that they all asked questions that cut to the core through layers of complexity, hyper-focused the team’s attention, and pointed to the path forward. Asking great questions adds tremendous value at all levels.
In my first job as a quality engineer, I asked many questions: How can I use the software in different ways to help solve customer issues? How can I find creative ways to test system limits and vulnerabilities? How can I logically explain the behaviors of complex systems and troubleshoot the problems encountered? I excelled at work because I asked good questions.
How to Think Logically
Logical thinking is a mental habit, and math is the best training course. We should strive for the highest standards in logical reasoning. To paraphrase investor Charlie Munger, “I never allow myself to have an opinion on anything that I don’t know the other side’s argument better than they do.”
The logic of life differs from the logic of math. Thinking about every subject like a mathematician can quickly get one into trouble in life, because the world is not idealized and seldom fits perfectly with mathematical assumptions. There are other ways of logical thinking for life, such as human logic, language logic, and probabilistic logic.
Human behaviors are driven by incentives and swayed by emotions, but they still follow certain logic. It requires a deep understanding and keen observation of human behaviors to figure out the logic that works for individuals or groups of people and apply it in the right context.
Language logic focuses on communicating effectively and convincing people. It is important because language plays such a critical role in society. Modern AI models are based on large language models and can be extremely intelligent yet not totally reliable. Because of the dominance of language logic, they can solve challenging Olympiad math but fail at simple ones.
When AI model GPT-4 was asked to calculate “7 * 4 + 8 * 8,” it quickly gave the incorrect answer of 120. Then, it went through the calculation step by step and arrived at the correct answer of 92. When asked about the earlier answer, it responded, “That was a typo, sorry,” using a tactic to save face that sounded like my teenage son when he tried to cover up a goofy mistake.
Even the most advanced AI can produce incorrect answers, just like humans. What makes it dangerous is that its mistakes are deceptively convincing and extremely difficult to detect, because language models prioritize appearing convincing over being logically correct. Once, I asked AI to prepare a lesson on mathematical applications in finance, which I planned to teach. The response was so impressive that I planned to use it with only minor modifications. Only upon careful review did I discover that the example contained a critical mistake—one that nearly fooled an expert like me. Avoiding such pitfalls while harnessing the power of AI requires sound judgment and strong logical reasoning skills, best developed through training in mathematics.
Probabilistic logic assumes that the world is inherently uncertain and can be extremely useful in real-world scenarios. Compared to math logic that treats every conclusion with 100% certainty, it models outcomes as a probabilistic distribution and optimizes decisions based on the maximization of quantifiable goals.
How to Teach Lifelong Learning Skills
I appreciate the importance of these lifelong learning skills and tried to incorporate them into teaching. My teaching methods reflected this:
First, provide multiple solutions and perspectives to connect new content to existing mental models. The key to learning new subjects is to build new connections to one’s existing framework of knowledge, methods, and learning habits. Multiple ways of learning and problem solving will grow a student’s capacity to learn entirely new subjects on their own later in life.
Second, guide students to ask meaningful questions and freely explore new knowledge. Asking great questions needs practice and support. Teachers should recognize the quality of questions and encourage students to develop this critical skill.
Third, encourage students to develop the habit of thinking logically. Math is less about mastering routines than about logical thinking. Once the logic is mastered, math can be creative and intuitive. It is important for students to understand the reasoning completely to build a solid foundation for logical thinking throughout life.
About the author: Immigrant. Parent. Math volunteer. Climate science researcher. Software engineer and manager at Microsoft. Investment analyst, trader, and risk manager at a hedge fund. Entrepreneur. A forty-five-year-old new teacher.
