Author: Dr. Ma
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The balance principle
Balance Principle Suppose you deposit $100 in your bank account and then withdraw $10. At the same time, your account generates $1 in interest. The remaining balance is then $100 – $10 + $1 = $91$. This equation suggests that the balance in your account is equal to the amount you deposit, plus whatever interest…
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Transport fluxes
Engineering Essay In a previous post, I discussed heat transfer and derived Fourier’s law of heat conduction. In one dimension, it is given by: $$ q = -\kappa \frac{dT}{dx} $$ where \( q \) is the heat flux, \( \kappa \) is the thermal conductivity, and \( \frac{dT}{dx} \) is the temperature gradient. It can…
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Fourier’s law of heat conduction
Fourier’s Law of Heat Conduction In science and engineering, we often need to study the transport of some physical quantities. One of the most straightforward examples is the transport of heat, as we all have experience with heat transfer. Imagine conducting an experiment where one end of a metal rod is held while the other…
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What is wrong with our K-12 education?
Best Practices for Showing Work The other day, I was teaching a general physics (algebra-based) lab, and the students needed to measure the length of an object using a meter stick. One group put one end of the object at the 1 cm mark, and the other end was at the 5 cm mark. Then,…
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Calculator: friend or foe?
When I was in middle school, China was still relatively undeveloped with very limited investment in education. Most of us didn’t have access to a calculator, and I never felt the need for one: many calculations were symbolic, and when numerical calculations were involved, they were done by hand. I finally could afford a calculator…
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Reflection: your best friend in learning
Styled Paragraph I once assigned a problem asking students to calculate the speed of an electron. One of the students gave a solution of approximately 1.0 × 1069 m/s. Although I don’t remember the exact numerical value, I vividly recall my shock at seeing such an astronomical order of magnitude. Honestly, I would have preferred…
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Best practices for showing steps in mathematical problem solving
Best Practices for Showing Work In a previous post , I discussed the importance of showing complete steps. If you are convinced, please start to show your work while solving problems. What are the best practices to do so? To answer this question, we must understand that the goal of showing steps is to convince…
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Steps, steps, and steps
Forgive me for using the same word three times in the title. However, I feel it still doesn’t fully emphasize the importance of steps in problem-solving. Over my nearly 20 years of teaching in STEM, I’ve observed a concerning trend: students are increasingly showing less work when solving problems. While I understand that life has…
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Memorizing basic formulas: easy investment with great return
As a college STEM instructor, I often encounter students who question the necessity of memorizing basic math formulas. In an age where technology provides instant access to information, it’s a fair question. However, there are several compelling reasons why committing these formulas to memory remains crucial for students, particularly those in STEM fields. 1. Foundation for…