“The laws of nature are but the mathematical thoughts of God.” ~Euclid
If you are just now checking in or would like quick links to previous posts in my curricula series, this is what we have so far:
- The Great Conversation (the driving themes behind my curricula choices)
- The Simplicity Version (my top picks for a basic core elementary curriculum)
- History (The Tie That Binds)
- Geography (the “where”)
- Literature: Part 1 (our history-related literature studies)
- Literature: Part 2 (the remaining literature studies)
(The following quotes are taken from The Story of Science: Aristotle Leads the Way by Joy Hakim.)
“[The universe] cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language.”
~ Galileo Galilei, 17th century professor of mathematics
21 centuries earlier, Greek philosopher Plato said:
“The world is God’s epistle written to mankind…It was written in mathematical letters.”
In 1955 Albert Einstein was asked to summarize his philosophy of physics at a lecture at Moscow University. In block letters he wrote on the blackboard:
“Physical laws should have mathematical beauty.”
And a quote from Beauty for Truth's Sake: On the Re-enchantment of Education by Stratford Caldecott, a deeply inspirational book that takes a look at the quadrivium (‘arithmetic being pure number, geometry number in space, music number in time, and astronomy number in both space and time’) and how God reveals Himself through these disciplines:
“Kepler’s breakthrough came because he introduced a “why?” question where the astronomers of his day didn’t see the need for one. He sought physical causes for heavenly motions. And that was not because he believed less in God as the cause of everything, but because he had more respect for the physical world as God’s creation and as the image of God’s mind. It was the first step toward Newton’s cosmos, in which the same universal laws (such as gravity) governed both the earth and the heavens.”
How did I miss those big ideas when I was in school? Oh, I think my schools subscribed to the philosophy that math = worksheets.
The problem, in our homeschool, though, is how to translate these big ideas into the systematic teaching of math skills—especially for a parent-teacher who understands (basic) math intuitively, but who finds teaching math (to a son for whom math does not come intuitively) tedious (and the cause of many emotional breakdowns, for both mother and son).
:: For the sake of sanity and an intact parent-child relationship, we have employed Teaching Textbooks. This program is a God-send. The voice of an infinitely patient math tutor talks the student through each lesson with interactive problems on the computer. The lectures can be watched multiple times, or reviewed at any time.
The student then proceeds through a few practice problems and a series of graded problems for each lesson. Little “buddies” encourage the student as they progress through the lesson. Hints are often available, but the student can choose whether to listen to them (“Remember, if you are finding the difference, you will need to subtract.”). The student can choose to watch the problem being solved after he has entered an answer so that he can see where he went wrong (or right). The student gets immediate feedback. The student can often try a second time to solve the problem if he gets it wrong.
The student can view his grade book at any time to see what lessons or quizzes he has completed as well as his scores. The parent can view (or print) the student’s grade book at any time with a password-protected account. There a parent can also see exactly which problems were missed, how many tries a student took, and whether solutions were viewed. The parent can change the score for individual problems (for instance, if they go over the problem orally with the student) or delete scores so that a student can re-do problems or lessons.
TT is a spiral program—the skills are constantly reviewed. The first few levels have timed math fact drills in the form of a game show quiz. We purchase the workbook/textbook to go with the computer program so that we have a backup in case we need to work on math away from home, if a child would rather do the work on paper and then enter the problems, or if we have a computer malfunction.
TT ensures, for us, that systematic math instruction happens daily. We don’t have a specific schedule. Each of the boys works at his appropriate level and speed regardless of listed grade level. That means that one of my boys works on grade level, the other two boys work 1-3 levels ahead. I have had the boys complete just the quizzes until their grade drops below 90%, and then I have them do the lessons as well. If they score less than 90% on a lesson, I delete the scores for all of the missed problems and have them redo the problems. A parent could also sit with a student and teach the lesson from the workbook/textbook or monitor work as the student progresses through each lesson.
We also continue with TT during the summer to retain math skills. It might not happen quite as often, and we may take week-long breaks here and there. Continuing with math over the summer means that we either complete more than one level each year and/or supplement with other math programs for review and various styles of instruction and approach.
:: To complement our basic math program, the boys memorize basic math facts through Classical Conversations. The skip counting songs (1-15, squares, and cubes) were revolutionary for my son who does not easily memorize basic math facts. All three of my boys find multiplication a breeze. They also memorize basic conversions and measurements (teaspoons to tablespoons, liquid equivalents, linear equivalents), geometry formulas (area of rectangles, squares, triangles, and circles and circumference of a circle), and four basic mathematical laws (associative, commutative, distributive, and identity).
Levi also plays math games with his CC Essentials class each Monday.
:: To add in more challenging conceptual math instruction, Beast Academy has been a good choice. Unfortunately, only level 3 is available at the moment, but all of the boys have enjoyed reading through the full color comic-style teaching guide. They will be adding level 4 soon, so we’ll move onto that as soon as it is available. (Beast Academy is published by the makers of Art of Problem Solving, a conceptually challenging math program for older students. I may consider AoPS for Luke or Leif when they hit advanced math.) We use BA informally (surprise!). Luke uses the workbook when he needs a break from TT. All three boys read and re-read the guide for fun.
:: When we need a quick challenge, Balance Math (and other math/logic workbooks from The Critical Thinking Co.) makes kids think in creative ways to solve puzzles. These workbooks are perfect for a Friday or for taking along in the car.
:: I cannot fail to mention Life of Fred. Life of Fred is tops on my list for “spaghetti education” from a master who is passionate and imaginative in his approach to the subject. Stanley F. Schmidt, Ph.D. dedicates his books “Ad Majorem Dei Gloriam” (to the greater glory of God) in the tradition of J.S. Bach, and his books are like symphonies, albeit much more amusing. The Life of Fred books may not appeal to straight-forward, sequential, give-me-the-facts-and-let-me-do-it, worksheet-loving, no-nonsense kids (or parents). But for kids who love stories, ideas, and silliness, these are another God-send.
The author weaves mathematical ideas and problems into “real” life events, introduces students to very big concepts in a light-hearted you-will-love-this-when-you-get-to-calculus sort-of way, and has no qualms about discussing anything under the sun such as butterflies, Kansas, Christina Rossetti, fine art, healthy eating habits, the inventor of the first paper straw, constellations and the star Betelgeuse, English grammar (including the proper use of lay and lie), book signings, the German word for toenail, the definition of syncope (fainting), a campus newspaper, when to use single and double quotation marks, the definition of naissance and how it relates to Renaissance, the first letter of the Hebrew alphabet, classic literature (Moby Dick, Don Quixote), the history of pizza, Virgil’s Aeneid, and how to set the table—all in the second book in the Elementary series. Seriously.
We have all ten of the elementary books as well as Decimals & Percents and Fractions (the intermediate books are on my purchase list for this next year), and I can tell you they are among the most oft-read books at our house. They stand up to a great deal of wear and tear. Leif rarely goes a day without pouring over one or two or three. They delight and entertain. They show students that math is a joy.
:: The ipad has become a great learning tool at our house. We have a few favorite math apps. Sushi Monster Math is great for addition and multiplication facts. Chicken Coop Fractions is another good one. Dragon Box is a fantastic intuitive game that teaches algebraic concepts in a creative and non-math sort of way.
:: Levi and Luke like to do IXL Math on the computer. Kahn Academy is a phenomenal free online resource for all subjects, but the math instruction videos are particularly excellent. I’m certain we will be using them even more as the boys progress to more advanced concepts and skills.
:: The boys have watched the MathTacular videos over and over again. They are a little bit cheesy, but the boys love Justin. Throughout the series, he introduces all basic math concepts and skills from Kindergarten up through 9th grade.
:: And then we have books and more books. Many are history-related. Just spreading the feast, people.Exploring the World of Mathematics by John Hudson Tiner (one in a series of science-related books by a Christian author)
Why Pi? How Math Applies To Everyday Life (lots of great historical information in this one)
Basher Science: Algebra and Geometry (my boys love all of the Basher books)
Sir Cumference and the Dragon of Pi (A Math Adventure) (and all the books in the Sir Cumference series—great fun!)Math-terpieces: The Art of Problem-Solving (Math and art history? Yes, please!!) and other books by Greg Tang
Many of our science and math books overlap (such as The Story of Science series, which is excellent at communicating the joy and wonder of math, science, and history), so I’ll have more to share when I get to science…