Teaching the Scientific Method and the Sciences

Now that officials say it is critical that people “follow the science,” we should reflect a moment on what that might mean. Does it mean to rely on the authority of doctors and scientists to give us the truth, or does it mean to respect the process of the scientific method?

What is the Scientific Method?

This method must include making an observation, making an inquiry, stating an hypothesis, forming a testable prediction, testing the hypothesis, then using the results to verify the hypothesis. Failing verification, a new testable hypothesis must be put forward and each of the steps repeated until adequate verification is achieved. Finally, publishing the results and having the results peer reviewed must follow. The scientific method proved itself more reliable over the centuries in finding the truth than reliance on authority.

The Many Legs On a Fly

Aristotle is sometimes called the Father of the Scientific Method. He was not. Aristotle made many contributions to knowledge, but he did insist that flies have four legs. On that authority natural history texts reported four legs on a fly for a thousand years. Aristotle said it. It was true. Much of the darkness in the Dark Ages came from such  authority determined truth. Aristotle was a central authority for the Church, but a poor father for the scientific method. He might more honestly be called the father of the observational method. Observation is the critical first step in the scientific method.

The intervention of Church authority into natural science locked knowledge in place for a millennium. The mistakes of flies’ legs would have been resolved instantly if any form of scientific investigation was possible. It was not and scientific investigation stopped in the West until the 14th Century. Even then, it was tainted with heresy and accusations of wizardry.

Through the Ptolemaic Dynasty and the Roman Empire, the Islamic scholars continued to expand upon Greek science and mathematics. Abu Ali al-Hasan ibn al-Hasan ibn al-Haytham, known as Alhazan was born in the 10th Century and made the next major contribution to the scientific method. Alhazan developed a robust experimental method for deciding what worked and what did not. He began with the knowledge of the Greeks like Euclid and Archimedes. He enhanced this learning experimentally to develop complex systems and many inventions.  The Mongols eventually stopped the advance of Islamic learning. Most of the ancient knowledge was lost soon enough and the Islamic world became engrossed in mathematical puzzles. Beautiful architecture resulted, but the Islamic experimental techniques and the Greek observational approach only slowly leaked into Europe over the next centuries.

scientific method
L0005471 Medallion portrait of Roger Bacon
Credit: Wellcome Library, London.

 The Franciscan monk, Roger Bacon, benefited in the 13th Century from both the Classical observational methods and experimental techniques developed in Islamic schools. Roger Bacon introduced the next component of scientific method, empiricism. Empiricism is the idea that knowledge comes primarily from the senses. Roger Bacon developed a model of experimental science based on his study of optics. His techniques were used by others to extend experimental science to include new medicines and health care of the body. Most of the steps of the scientific method were in place at this point.

scientific method
“Francis Bacon, Viscount St. Alban,

Missing still was some method to verify a testable hypothesis. Francis Bacon developed and popularized inductive reasoning. This is often known as bottom up reasoning where details are synthesized to form a general conclusion. Induction combined observations with experimental results to come to a conclusion.

scientific method
Descartes: Portrait

Rene Descartes took another path with top down analysis using general facts and deriving specific details from them. Most people are very familiar with the science of deduction from Sherlock Holmes. Crime fiction where detectives use observed facts to solve crimes is very satisfying; however, Sherlock does not purely demonstrate deduction. He used a sophisticated combination of induction and deduction to solve crimes. In this, he is more like Sir Isaac Newton.

scientific method
“Isaac Newton” by paukrus

Isaac Newton practiced this “Holmsian” synthesis of inductive and deductive reasoning. He is the father of the scientific method. He moved systematically from induction to deduction and back in his proofs. He also left clear experimental records that set the standard for documentation of experiments to the present.

scientific method
“Quantum Computer Interior” by IBM Research

Cloud computing and quantum computing mark the next step in scientific proof. These technologies allow many hypotheses to be tested at once, sometimes in parallel. This parallel and iterative investigation allows an accelerated proof of an hypothesis or of many hypotheses. The development of the COVID-19 vaccines in months, rather than years, is a demonstration of these new methods in action. It is probably still the traditional scientific method, but the quantity of data and the complexity of the proofs make it difficult to verify. These advances, particularly in genetics, biochemistry, quantum mechanics, and astrophysics are believed by some to be something new in scientific inquiry and proof. A new method.

Computing logic is beyond our concern here. Teaching logical analysis and the scientific method to young people is more critical than ever. With these skills, they can rationally examine the world around them.

How to Teach the Scientific Method at Home

The best method for teaching the scientific method in the homeschool, whether or not the family is using a curriculum package, is to create a Perpetual Science Fair. This is a simple. The student keeps accurate records of observations in notes during regular classes. These observations become material for the fun part of science. Experiments. Experimentation is the opportunity to learn the basic reasoning involved in the scientific method. The Perpetual Science Fair should proceed logically.

The student should:

  1. Make observations about something in the current lesson. Use inductive reasoning to come up with a hypothesis that seems to answer the question.
  2. Think about how to test the hypothesis using an “if – then” sentence.
  3. Design the experiment to test the hypothesis by deciding what to measure and how often to take measurements.
  4. Create two groups in the experiment. One group as a control group where conditions will be maintained as close as possible to the original configuration. The second group is the experiment has variables to be modified to examine the accuracy of the hypothesis.
  5. Set up the experiment to control all the variables except the one being tested.
  6. Make the planned measurements and record the qualitative, descriptive data, (color, health, and happiness, usually presented in paragraphs or tables), and quantitative data (numerical data, like height, weight, and number of items that showed a change, analyzed with statistics and presented in graphs in a notebook.) Date all observations.
  7. Analyze the data showing the differences between the control data and experimental data.
  8. Use deductive reasoning to decide whether the results support or reject the original hypothesis. Research whether your findings are supported by others. The Internet is a good source for peer information.
  9. Report the results, explaining the original ideas and how the experiments were conducted, then describe the conclusions.

Unexpected Benefits from this Approach

The process of the Perpetual Science Fair in the homeschool can teach more than simply the scientific method in the hard sciences like biology, chemistry, geology, and physics.

The process can also demonstrate the questionable use of scientific method in the soft sciences. Soft sciences are those disciplines that refer to themselves as science like Sociology, Psychology, and Environmentalism, but lack a strong empirical foundation. Trying to build experiments in these subjects can demonstrate the problems with providing testable hypotheses and replicating experiments. Much of the peer-reviewed proof in these fields comes from statistical analysis and data science, so a growing familiarity with the protean nature of data is a benefit.

Pursuing this approach in other classes can demonstrate that the scientific method has no value in non-scientific inquiry in fields like Politics, Statistics, Communications and Marketing. Political experts often use “science” as a slight-of-hand distraction to hide the flawed results of their findings. They say to trust them because, like Firesign Theatre, they “have a degree in Science.”

Over time, the student can learn to apply the scientific method in scientific subjects, and learn how the method cannot work in non-scientific subjects. “Trust but verify” to  avoid tom-foolery.

scientific method
“You are Here” by tomswift46

 

Math is Hard

Math is hard. This is half lie, half confession, and half true. This is no mathematical statement. Everything new is hard. Math for children, for young students, and for students approaching adulthood should come organically with life. Math for adults should be the necessary skill for the task at hand. Math for the homeschool teacher will be hard too. Parents should not just hand the math off to some online guru. The teacher should grasp anything the homeschooler masters.

math is hard
“Lionel takes interest in Discrete Mathematics”  by  zdw

Math is hard in itself.

Math is a group of languages. Math languages are logical, artificial languages and not natural languages. Artificial and unnatural, math describes only some things in the world. Different cultures needed to describe different things. Romans did not need a zero. Astronomers in Mesopotamia did. “Zero not only represents nothing but it also represents the starting point of anything” said Brahmagupta.

The most confusing part of math is the incoherent relationship among various approaches that describe the same phenomenon, or solve the same problem. Take addition and multiplication. Romans added with cross-hatches. It served the empire well for centuries. Multiplication enhanced addition in Babylon where the merchants had large and complex calculations pre-solved on clay tablets. Just because each method solves the same problem does not require them to remain logically coherent. Common arithmetic is incoherent across the logical boundaries. This is why each type of math starts by learning rules. Addition and multiplication, for example, have logical gaps. After all, is not 3+3+3 the same as 3×3 ?

math is hard
“Algebraic numbers glow dust”  by  Jonathan Lidbeck

Many math jokes come from the illogical boundaries. Most people have heard the old riddle: “Three people check into a hotel. The clerk tells them that the bill for their stay is $30, so each person pays the clerk $10. The clerk puts the money in the cash register.”

“Later that night, the clerk realizes that she made a mistake and should have only charged the three guests $25. She takes five one dollar bills from the register and tells the assistant to return the money to the guests.”

“On the way to the rooms, the assistant realizes that she cannot split the money evenly among the three people. As the guests don’t know that they were charged the incorrect amounts for their rooms, she decides to simply give them each $1 and pocket the extra $2 as a tip. Each guest gets $1 back, so each paid $9 for their room, ($9 X 3 equals $27). The bellhop kept $2, and $27 + $2 = $29.”

“But the guests originally handed over $30. What happened to the missing dollar?”

The answer is that there is no “missing dollar.” It is an informal fallacy caused by jumping from addition to multiplication at the wrong time and breaking the logical boundary. The different math languages, addition and multiplication,were not developed at the same time by the same people. They have different rules for consistency.

Addition was first used extensively by the Chinese almost 6,000 years ago, so it is safe to say the Chinese invented addition.1 The ancient Babylonians were probably the first culture to create multiplication tables, more than 4,000 years ago.2

Multiplication was a way for merchants to do complex additions quickly by looking at the multiplication calculations on clay tablets, multiplication tables. Today most people get to the same result either by addition or multiplication; however, each method has firm rules. These rules were violated in the joke, so the result seems to reveal a magical dollar. The method of calculating the total is simply flawed. In the end there is still $25 in the register, $3 returned by the desk clerk, and $2 appropriated by the assistant. 25+3+2=30. Right? Addition. Begin there, end there.

Math is not all just fun. Math has natural uses as a tool. Most tasks can use math. This is just common sense. All jobs involve math. Any person that handles money should instantly see through the problem above and solve it by saying in the end that there is still $25 in the register, $3 with the guests, and $2 with the assistant. $30.

The target is math fluency.

How, then, do you teach math in the homeschool. What sequence should math be taught? What if the homeschool teacher is not a math nerd? Schools usually teach math from simple calculation to increasing complexity.  The assumption that the ability to solve more complex problems comes with each math is pretty good, but it need not be the rule at your school. Nothing says that geometry should not come when the student is ready for carpentry, or precision drawing. The homeschool should teach appropriate math when an immediate utility can be seen by the student. Math does not have to be a bleak and dreary time of the day. In the homeschool math can arrive as it becomes organically necessary. Walk, talk, read, write, learn numbers and then counting. Gradually. Then adding things together. Then taking things away. Then dividing things and multiplying them. Eventually, the Mandelbrot sets.

Older students can master household math. Cooking is great to begin the task of learning fractions. At this time various units of measure can also be introduced.

Household accounting with budgets and banking introduces decimals and set theory as soon as the child can learn about money. Mortgages and interest can introduce more complex math through ideas like compound interest.

Geometry is good for crafts and projects, carpentry and landscaping. Any good carpenter must understand angles and lengths. Every math involves memorizing rules. Euclid is difficult for some because all the rules are learned at once and an understanding of each application is not introduced as an example. Memorization is nowhere more important than geometry. Once the rules are mastered, all future woodworking projects are understood, can be planned, designed and completed.

math is hard
“n(n+1)”  by  Jan Tik

Every science class is an opportunity for another set of advanced math tools. Each of the sciences requires understanding specific advanced mathematical languages. Trigonometry is vital in the earth sciences and in video games. Something as simple as planning the drainage in the back yard is a trigonometric opportunity.

Chemistry allows an understanding of all the middle and advanced mathematical languages, and so on.

A good home study course would begin with the foundational math from the basic arithmetic, fractions, percentages to equations, functions and graphs. The full homeschool course would include relative fluency with algebra, geometry, trigonometry, through differentiation, integration and vectors. In the end it should have included complex numbers and matrices. All this can be had from the thousands of sites on the Internet or through any number of very fine homeschool math packages.

The logical calculus is not taught early enough in the US. Typically, public school requirements for math studies may not even include the courses of study above, but if they do, they usually end with precalculus. Homeschool teachers should set the goal beyond this to be competitive with schools that provide most of the technical staffing in the us. The classes usually labeled AP Calculus.

math is hard
“Calculus”  by  Encel

If you begin to teach math at home, a good target is functional mastery of the fundamentals tested in the college placement exams for better schools. The sequence of learning and the context for teaching do not matter. The checklist of material students need to pass the college placement tests are, according to Derek Owens:3

  • The problems that Calculus solves, introduction to derivatives, finding rates of change from graphs, from equations, and from data, Numerical derivatives, Introduction to Integrals, Approximating integrals from graphs, from equations and from data, the Trapezoid Rule
  • A graphical approach to limits, Describing function behavior with limits, Asymptotes, Rational Functions, Polynomial end behavior, The Limit Theorems, Evaluating limits, Continuity, The Intermediate Value Theorem
  • A graphical look at derivatives, Difference Quotients, the Derived Function, Notation, Numerical calculations of derivatives, Tangents and Linear Approximation, Differentiability and Continuity, the Chain Rule, the Product Rule, the Quotient Rule, Leibniz’ Proofs, Derivatives of Trig Functions, Implicit Differentation, Derivatives of Inverse Functions, Derivatives of Inverse Trig Functions
  • The Extreme Value Theorem, Rolle’s Theorem and the Mean Value Theorem, First and Second Derivatives, Concavity and Inflection Points, Graphs and Curve Sketching, The Calculus of Motion, Max-Min problems, Related Rates, Practice
  • Antiderivatives, Integrals, Infinitesimals, Riemann Sums, Definite Integrals, The Fundamental Theorem of Calculus, Properties of Definite Integrals, Numerical Methods, Integration by Substitution, Average Value
  • Derivatives of exponential functions, Derivatives of logarithmic functions, Derivatives and integrals of base b exponents, Integrals with variable limits, Logarithmic Differentiation, Integrals of trig functions, Intro to Differential Equations, Examples and applications, Slope Fields, Euler’s Identity
  • The area of a plane region, The Calculus of Motion, Real world applications, Integrating to find volumes, Plane Slicing, Solids of Revolution, Cylindrical Shells

    Cover these areas before matriculation and the periodic achievement tests required for your homeschool will not trouble you or your student. Most homeschool parents are not fluent themselves in the components of pre-calculus and calculus. Look for getting help on any bullet in the list that seems a mystery. This is essential for getting the better technical jobs or getting into the better programs at university.

    Fluency in higher mathematics is not critical for learning computer science, but helps.

    math is hard
    “Amazing Grungy Fractal Tree Photoshop Pattern 8”  by  webtreats

    Computer literacy should begin early with some computer language suited for young programmers. For example, Scratch is a free programming language for kids. It was developed by MIT’s Lifelong Kindergarten Lab. Blockly is Googles’ offering. Many languages like these can begin in kindergarten. Once the hook is set, more complex projects can be developed in Python, a free programming language every adult with a computer should and probably does not know. This really opens up the project world of companies like Adafruit. This is the world of Maker science and technology. Projects like this can alleviate the relative tedium of learning abstract math.

    The goal is math facility.

    The little human should be able to use math tools at every juncture of life. Not everyone will find a vocation that uses discrete math or calculus, but it is not a door that the homeschool should shut on young minds. It is easy to teach. Everything can be taught online. Everything can be taught from the myriad Goodwill books on math. Remember, something invented in the 17th Century is just as accurate in an earlier edition of the textbook.

    math is hard
    “physics”  by  Hash Milhan

    Using math should be as natural as reading and writing. One student may never master geometry but discover a passion for statistical analysis and the logical calculus. She may not grow to be a civil engineer, but a computer programmer instead.

    Exposure to and a grasp of the basics in all the fundamental mathematics is critical for success in modern technical society. Math exercises memory, logical application, and problem solving. Sure, math is hard, but every new thing in life is hard. The homeschool teacher must make math as organic to the day as any other lesson. If you have a math wizard, you may find that by the time he or she graduates, you have learned enough discrete math to untangle algorithms yourself.

    1https://www.reference.com/

    2 https://www.theguardian.com/lifeandstyle/2014/may/17/ask-a-grown-up-who-invented-times-tables

    3 This list derives from a course developed by Derek Owens who graduated from Duke University in 1988 with a degree in mechanical engineering and physics. He taught physics, honors physics, AP Physics, and AP computer science at The Westminster Schools in Atlanta, GA from 1988-2000.

    Homeschooling Off-the-Grid

    No government wants people living off the grid. No jurisdiction in The United States allows families to live completely off the grid. Doubly so if you have children. The Back to the Earth movement of the 1960s and 1970s caused a legal reaction in most rural jurisdictions. Local governments implemented anti-hippie regulations in zoning, water rights, sewage, electrical connection, and children. State and federal authorities provided enforcement when necessary.

    Off-Grid Homeschooling

    Families who want to live and school off the grid must first reduce the digital fingerprint. Familiarity with local regulations and local precedent is critical information before putting up a dry cabin, installing septic or electric services, and especially before off-grid homeschooling.

    Some families living off-grid continue to send the children to public school just to avoid the inevitable accusations of child endangerment or abuse. This works only poorly. Local education authorities monitor children in public schools to identify off the grid home behaviors. A casual comment like, “We have an outhouse at home,” can trigger a social services investigation or even a sheriff’s visit.

    Sign Out, Shut Down, Unplug 1

    The issue in off-grid homeschooling is not the schooling. Homeschooling requires at least one child and an adult who can read and write in one language. The next step seems difficult because everybody is more or less institutionalized in the United States in 2021. No computer, smart phone, or the Internet is required to homeschool children. Leaving the compulsory education system is an act of nullification over compulsory education and the indoctrination attached to it. Unplugging from the network is the act of a sovereign individual. Government at every level hates this. The zoning inspector or public health administrator is not a harmless bureaucrat. 2020 taught that rights can be taken away by proclamation, even by your local health administrator. Do not allow the local zoning inspector to derail your homeschool.

    The Spartan Path

    Most children schooled at home in the past learned to read and write using books, pencil and paper, with the regular recitation of previous lessons. Parents can begin with just the materials at hand. Teaching children the basics, then leading them into more advanced subjects with those basics is simpler than teaching them to speak or to use the toilet. The simplest approaches to homeschool start with books, pencils, and paper, whether your family lives in a city apartment, in a small town, in a rural district, or in an RV.

    Even those without any resources, the homeless or off-grid rural families can follow George Washington Carver. Born a slave he scrambled from opportunity to opportunity to get an education. Mr. Carver was literally unschooled.

    He understood that basic learning is a survival skill. He learned to read and write with the Bible. This was bravery. Basic literacy was dangerous to the owners during slavery and could get an individual sold or killed. Learning still happened. Quietly. Off-grid homeschool is bravery too. Parents cannot be sold off, but confiscation of land, vehicles, tools, houses to be sold off by investigators is common in most states. Some states regard digging an outhouse as criminal.

    off grid homeschool
    Education is the Key to Unlock the Golden Door of Freedom

    The Blended Model Path

    Not everybody wants to be completely off-grid. Those who are moving some parts of life off-grid, who must work in the system, but want to substitute solar power or composting toilets and want to homeschool still can. The family can augment the public school curriculum with directed tutoring. This approach is common today among Indian technical workers who supplement the children’s public education with something like the education the parents received in India.

    “I have never let my schooling interfere with my education.” -Mark Twain 

    Alternatively, parents can withdraw students at the compulsory minimum age. Work and homeschool can follow. Going to work was common as recently as the 1940s. In the 1950s most craftsmen and artisans still went to work with just the basic education. School can be the first step in a lifelong self-education. The Great Books Program of Mortimer Adler supplemented the learning of millions of blue collar families over the years before homeschooling was available.

    Now that homeschooling is permitted, the homeschool path can start directly with a set of graded readers like McGuffey. A library card to a nearby physical library helps, but remains difficult in 2021 when most public libraries are still closed. Parents should contact the local librarian to see how access to the collection works. Haunting the used book stores and Goodwill stores for additional books on math, science, history, and other interesting topics also works inexpensively. Thousands of Adler’s Great Books live today in used book stores.

    The Tutoring Path

    Children of corporate workers and suburban professionals can be educated at home by the parents. This was once the choice only of the upper middle class. John Stuart Mill studied at his father’s desk as James Mill worked at home. This style homeschooling is more possible than ever with the COVID distance working making one or more parents available to run the homeschool.

    Dog and Cat Off-Grid
    Dog and Cat Off-Grid

    Homeschooling offline seems radical in the digital culture, but people attempted it recently. The “Turn On, Tune In, Drop Out” movement of the 1960s and 1970s put it’s heart in the right place, as much as mass movements have hearts. Drugs and deep media immersion derailed the the dropping out. Not much off-grid happened.

    The government actively stamped out as many of the freak hippies as it could. Now it focuses on preventing them. Parents who want to walk on this path in 2021 must understand the triggers for the state. The joke in the 1990s was that the Internet was a trap for perverts and criminals to identify them to the police. It is now a trap for the nonconforming. To be avoided off-grid are social programs, especially financial, and medical programs that give the experts an excuse to classify parents as anti-social or even dangerous.

    Homeschools must avoid being demonized, criminalized, and attacked by a bureaucracy that does not want any homeschooling, a state that will not tolerate off-grid activities, and bureaucrats that can use the homeschool as an excuse to confiscate property. Getting off the Internet is the first step off-grid. The autonomous individual should raise autonomous, thinking, reasoning children, and look out for both the bureaucrats who want to end it and the police who will profit from confiscation. Parents should not let a zoning inspector, a child protective worker, or a truant officer end the off-grid dream or disrupt your homeschool.

    Children today can be literate. Even slaves learned to read.

    But Quietly.

    1Margaret Beetem 2021.

    FREE Homeschooling on the Internet

    Homeschooling on the Internet requires no more infrastructure and expense than the cost of a smart phone or tablet, a computer, and a USP connection. Two critical components for parents wanting to minimize state control over the home school are VPN on your Internet connection to keep nosy people out of your family business, and the TOR browser for access to “pirate” websites like Z-Library and Sci-Hub.

    The VPN augments your broadband connection. If VPN is still a mystery, here is a recent article on both free and paid VPN. Brassword Publishing uses Nord VPN because “free” usually comes with a price in reduced privacy.  Hackers hack, so parents should do the research. https://www.techradar.com/vpn/best-free-vpn

     Nobody-is-Watching

    Nobody is Watching

    TOR claims you can “Browse Privately. Explore Freely,” and mostly that is true. https://www.torproject.org/ TOR Browser will not prevent all intrusion, but it makes detection of your traffic harder for state or other malicious hackers.

    Digital Homeschool

    Homeschool parents teach basics after walking, talking, potty-training, and family morality. Common sense says to teach reading by reading, writing by writing, and mathematics by doing math. The Internet provides millions of teaching resources for FREE.

    Digital Homeschool
    “The Replacement for Saturday Morning Cartoons” by Wesley Fryer

    Parents can even teach advanced subjects after the basics. Mastery comes from doing things, building knowledge, gaining experience, and mastering reasoning skills. Science uses reading, writing, and math in combination to master logic, reasoning, and the finer points of the scientific method. History uses reading and media to explore the past. What is the motivation for teaching basic skills? No real learning is possible without the basics.

    Basic Skills

    Christians after the Reformation stressed reading as the gate into the Bible. For hundreds of years families used that book alone to teach reading. Consequently, at the time of the American Revolution, the colonies were among the most literate population on Earth. This continued to be the American tradition. Abraham Lincoln’s mother taught him this way and for this reason. His interests broadened as he grew older, but his fundamental literacy was unquestioned.

    Writing can be mastered with a reflective journal and copy books to show that the material read was comprehended. The digital homeschool can use an e-book toolkit like Calibre to make digital journals and notebooks.

    Young children can learn math as part of household economics. Middle class people after the Reformation taught math to the family as part of the mercantile culture. Learning to make, to buy and to sell, is still a great way for children to master math in the home school. Because the Internet is born in math, limitless tools for mastering every form of math are available online.

    digital homeschool
    “Studying” by Kelly Hogaboom

    Deeper knowledge comes organically to a child from basic skills, depending on aptitude and interest. The dungeon of curriculum should not stop the young organic farmer from mastering the science and math of earth science and horticulture. Neither should it block the young historian from reading and reasoning through the mysteries of the past. Some children may move from crawling to walking to dancing and this should be okay. Maybe Tik-Tok is the right classroom for the young dancer.

    unschooling morning digital homeschool
    “An Unschooling Morning” by Kelly Hogaboom

    Young humans must be free to pursue interests to become expert. Advanced subjects, beyond the comfort zone of the parent, live on sites like MIT Open Courseware https://ocw.mit.edu/index.htm where all MIT courses are offered for FREE, but without certification. If the student can do differential calculus, no certification is needed. The  path for the child aimed at engineering can start with homeschooling on the Internet.

    Your First Trick

    First things first. Homeschooling on the Internet begins with digital copies of books. Put the title of any desired book into your search engine with “PDF” after the title. Not every book is available, but some university students never purchased textbooks in four years.

    Beyond the free search, those parents who want to teach the basics using the free Internet can start with Gutenberg, LibriVox, The Internet Archive, and Calibre.

    Digital Homeschool Public Domain
    SAIL INTO THE PUBLIC DOMAIN by Laure L. Russwurm

    Gutenberg

    Project Gutenberg is an online library of free eBooks.”

    https://www.gutenberg.org/

    The dream of Diderot and Voltaire was FREE information for the people. Project Gutenberg goes far toward fulfilling that dream.

    LibriVox

    https://librivox.org/

    “To make all books in the public domain available, narrated by real people and distributed for free, in audio format on the internet.”

    This is a free version of Audible. The readers are volunteers, so the quality is sometimes uneven, but the price is right. Much of the material is aimed directly at the homeschool. Look at the lists that homeschool parents made just for you. Consider reading your own favorite book into the collection.

    • “Librivox is a non-commercial, non-profit and ad-free project
    • Librivox donates its recordings to the public domain
    • Librivox is powered by volunteers
    • Librivox maintains a loose and open structure
    • Librivox welcomes all volunteers from across the globe, in all languages”
    Digital Homeschool Internet Archive
    Internet-Archive-Servers” by jblyberg

    Internet Archive

    The Internet Archive supplies millions of files for homeschooling on the Internet. Every conceivable form of digital product is freely available. Whereas, Gutenberg has books and Librivox has audio books, the Internet Archive also has movies, television programs, pictures, and software programs. In their words:

    “The Internet Archive began in 1996 by archiving the Internet itself, a medium that was just beginning to grow in use. Like newspapers, the content published on the web was ephemeral – but unlike newspapers, no one was saving it. Today we have 25+ years of web history accessible through the Wayback Machine  and we work with 750+ library and other partners through our Archive-It program to identify important web pages.”

    “As our web archive grew, so did our commitment to providing digital versions of other published works. Today our archive contains:

    “Anyone with a free account can upload media to the Internet Archive. We work with thousands of partners globally to save copies of their work into special collections.”

    Calibre

    https://calibre-ebook.com/

    Calibre is an e-book manager, a program that runs on your computer and allows better viewing of your digital material. Calibre also downloads current newspapers and magazines. An interesting feature is the ability to create and edit your e-books, so it can serve as an interesting digital writing tool for the homeschool.

    “Calibre is also completely free and open source and great for both casual users and computer experts”

    • “Save time on managing your e-book collection
    • Use it everywhere and with anything
    • Comprehensive e-book viewer
    • Download news/magazines from the web
    • Share and backup your library easily
    • Edit the books in your collection
    • Satisfy every e-book need and get support”

    Advanced homeschooling on the Internet can use more advanced scientific and scholarly materials from Z-Library and Sci-Hub. One person’s import-export is another person’s smuggling, so we recommend you follow the wisdom of Chinese students exploring Democracy articles on the Internet to use VPN and TOR for these links.

    Digital information is leaky and researchers from across the globe have been using Sci-Hub to get access to current information in their field without paying the exorbitant fees charged by academic publishers. A single paper on robotics or biology can cost hundreds of dollars, making it impossible for students and researchers in the third world to afford the information they need. The need found a solution.

    Z-Library

    https://z-lib.org/

    Z-Library file-sharing project for scholarly journal articles, academic and general-interest books. Z-Library says the project provides access to more than 6,754,720 books and 80,759,561 articles as of April 1, 2021”

    Sci – Hub

    https://sci-hub.st/

    Sci-Hub the first pirate website in the world to provide mass and public access to tens of millions of research papers”

    “A research paper is a special publication written by scientists to be read by other researchers. Papers are primary sources necessary for research – for example, they contain detailed description of new results and experiments.”

      Papers in Sci-Hub library:
    more than 85,483,811”

    Homeschooling on the Internet really means Homeschooling on the Internet.