Schedule: This is an 8-week course that meets three times per week, one hour each session.
Format: Lecture to cover concepts, with as much class interaction and individual practice during class that we can get. No grading; homework is optional but recommended. (We can have some grading upon request.) Text optional.
Cost: $499 per person for a group class of 4 or more students; $1499 for one-on-one tutoring.
Materials: Pencil, paper, and a graphing calculator like a TI-84, TI-89, HP Prime, or Casio is recommended. Text optional.
For more details or to schedule a class, contact Michael by email at michaelgold@goldams.com or by phone at 281-770-2276.
“My daughter truly enjoyed the class and has motivated her further study in science. She also appreciated Mr. Gold’s passion and excitement for science!” –Chigusa, parent, about the Outschool class “Logic Corner: What Is Science?,” 12 Feb 2020
Class Description
In this 8-week course, which will meet three hours per week, we will learn how to prove that all the planets go around the sun in elliptical orbits, by starting with ancient human thought and following science through Newton’s work. We will trace the development of ideas historically, and thus will learn heliocentrism inductively and fully. This is an essential course in learning how to do science and learning what science is.
It is an essential, important course for you to do well in your future career as a scientist or as someone interested in science.
This is a class for everyone — science is all around us! — but especially for those who want to go into science or engineering careers, or study science in school.
We will use a combination of lecture, interactive discussion, Q&A, and in-class work. Be prepared to think, to learn, to take notes, and to have new horizons open up.
Prerequisites: algebra and geometry. Students need some knowledge of geometry: circles, arc measure, parallel lines, transversals, polygons, circumference, arc measure, parallel lines, similar triangles, right triangles, the Pythagorean Theorem, basic trig (sine, cosine, tangent in a triangle), circles, tangents to circles. And some knowledge of algebra: ratio, proportion, squaring, square roots, equations. But we will review these concepts in class. (We will not use calculus or precursors to calculus, though we might introduce the subjects.)
Tentative schedule
Week 1
Day 1: Intro. The scope and aims of the course. Why this course matters. What science is. Some misconceptions about science. Early astronomical knowledge: ancient, Mesopotamia, Egypt, Thales, Anaximenes, Pythagorus, Anaxagoras.
Day 2: Early astronomical knowledge: ancient, Mesopotamia, Egypt, Thales, Anaximenes, Pythagorus, Anaxagoras.
Day 3: Socrates. Plato. Aristotle. The start of science. The importance of philosophy. Errors in the Rogers book, 2.
Week 2
Day 1: How Eratosthenes calculated the size of the earth.
Day 2: How some Greeks (e.g., Aristarchus and Hipparchus) calculated the distance of the moon from the earth.
Day 3: How some Greeks (e.g., Aristarchus and Hipparchus) calculated the distance of the moon from the earth, continued. How Aristarchus calculated the distance of the sun from the earth.
Week 3
Day 1: Astronomical theory based on the circle. Ptolemy and Ptolemaic theory: circles, strengths, flaws, philosophic mistakes.
Day 2: Ptolemaic theory: circles, strengths, flaws, philosophic mistakes, continued.
Day 3: Copernicus and heliocentrism. How Copernicus calculated the distance of the “inner planets” to the sun.
Week 4
Day 1: How Copernicus calculated the distance of the “outer planets” to the sun.
Day 2: The length of a year of the planets. The velocity of the planets. Tycho Brahe. The cross staff.
Day 3: Kepler. Getting the orbit of Earth and Mars. Kepler’s Laws of Planetary Motion. Equal areas law.
Week 5
Day 1: Kepler’s Laws of Planetary Motion, continued. Equal areas law. Elliptical orbits law. Look at data and do some calculations.
Day 2: Kepler’s Laws of Planetary Motion, continued. The R-T law. Look at data and do some calculations.
Day 3: Galileo: the mechanics of motion. Inclined planes and pendulums.
Week 6
Day 1: Galileo: the mechanics of motion. Inclined planes and pendulums.
Day 2: Galileo: the mechanics of motion. Projectile motion.
Day 3: Galileo: the telescope and astronomical observations. The moon, planets, and other moons.
Week 7
Day 1: Newton: force and mass. Newton’s laws.
Day 2: Newton: the mechanics of circular motion.
Day 3: Newton: the apple and the moon.
Week 8
Day 1: Newton: universal gravitation.
Day 2: Newton: tides and more. Cavendish: weighing the earth. The context of Newton’s work.
Day 3: Conclude. The importance of philosophy. The nature of science.
Learning Goals.
To know how to figure out how far the moon and sun are from the earth, and how far the planets are from the sun.
To know how to show that planets’ orbits are elliptical.
To know how to derive Kepler’s Laws from experience.
To understand (not merely to memorize or to believe) that the planets go around the sun in elliptical orbits, with the sun at one focus.
To know the steps necessary for an inductive proof of that proposition.
To know how astronomical science developed through history, and to know the mistakes and successes scientists made.
To know why philosophy is important in science.
To know how induction works.
To know how science works.
An important goal is to avoid suffering this fate:
1. “Science students learned the facts of their specific field without understanding how science should work in order to draw true conclusions.” –David Epstein, Range: How Generalists Triumph in a Specialized World
2. “Part of the problem, [Arturo Casadevall] argued, is that young scientists are rushed to specialize before they learn how to think. They end up unable to produce good work themselves and unequipped to spot bad or fraudulent work by their colleagues.” — Range: How Generalists Triumph in a Specialized World by David Epstein
3. “Few [scientists] are philosophers. Most are intellectual journeyman, exploring locally, hoping for a strike, living for the present.” –E.O. Wilson, Consilience: The Unity of Knowledge
And an important goal is to be like what Barbara Benham describes in “Biomedical science education needs a new philosophy, Johns Hopkins researchers say:”
“For their part, Casadevall and Bosch write that science education reform should result in scientists who are:
-Broadly interested, creative and self-directed, as were some scientists in the era of Louis Pasteur, Marie Curie, Albert Einstein, and Linus Pauling
-Versed in epistemology, sound research conduct and error analysis, according to the “3R” norms of good scientific practice—rigor, responsibility and reproducibility” (See https://hub.jhu.edu/2018/01/03/biomedical-science-education-reform-casadevall-bosch/)
(You can find other info about John Hopkin’s R3 Program (aka R3ISE) on the Internet. And you can listen to my interview with Dr. Gundula Bosch here: https://www.spreaker.com/user/11043023/episode-40-gundula-bosch-phd-johns-hopki)
“We really enjoyed the Ecology class with Michael Gold! He chose a wonderful textbook for my daughter to use: “Minnesota’s Natural Heritage.” He made it interesting, relevant, and understandable. As a homeschool mom, it’s always a challenge to find good teachers that I can rely on to supplement the holistic education I try to give my children. Michael does just that! He’s knowledgeable, thorough, logical, and even brings a sense of humor to the class! I can’t recommend him highly enough for someone who, like me, wants more for their children. Thank you, Outschool, for providing such good teachers at reasonable costs! We’ll be signing up for more classes soon!”
–Melanie K., parent, about the Outschool class “Ecology (Chp 5 by John Tester): The Northern Coniferous Forest,” 4 Feb 2020
“My son (13yo) loved this class, he loved learning math he had not learned before, the instructions were very clear and he enjoyed them a lot. He loved learning the historical context and is already looking for other classes with this teacher. He really enjoyed the class! Thank you!”
–Judith V., parent, about the Outschool place “Inquiring-mind Science: How Far Is the Sun? How Far Are the Planets?,” 1 Apr 2020