1. Bible
There is only one thing needful in a child's education: the Lord Jesus Christ. Reading, writing, and arithmetic are all very important, but of what eternal purpose do they serve if our child's soul is lost? Don't get me wrong; we can't save our children. Their salvation rests solely upon the grace of God. But instructing our children in the paths of righteousness is a parental commanded uttered from the mouth of God that we must obey - for our sake, and more importantly, so that our children would be given every opportunity to enter into a saving relationship with their Creator. (Ephesians 2:8; Proverbs 22:6; Deuteronomy 6:6-7) How To Produce Godly Children is one of the best articles I've ever read on the subject.
Not to mention, that Scripture is given by inspiration of God, and is profitable for doctrine, for reproof, for correction, for instruction in righteousness, that the man of God may be perfect, thoroughly furnished unto all good works (2 Timothy 3:16). It is here where our children will learn God's pattern for society, how we are to live and work, and all that makes for a peaceful and joy-filled life.
2. Reading and Writing
God has chosen to reveal Himself in His written Word which we are commanded to read. From the plumber who writes out a bill, to the pastor in the pulpit, to the mother who reads bedtime stories to her children, reading and writing are life skills used every day by people everywhere. These are the greatest gifts you can give your children. With them, they will be able to discover the Word of God for themselves, engage in every other secondary subject (science, history, foreign languages, etc.), and accomplish necessities like writing out checks, following a recipe, and filling out health card forms, etc.
3. Mathematics
Though perhaps not consciously, people use math skills everyday in construction, cooking, banking, and grocery shopping. Basics like adding, subtraction, multiplication, and division allow the homemaker to be a prudent spender (and saver), and enable most men to land a job and excel in the workplace.
4. Their individual, God-given gift
If your daughter is naturally fascinated with horses, run with it! Delving into something she loves can be the most effective means of teaching her about everything else she thinks she's not interested in. You can't learn a lot about one subject without learning something about the others.
What about all the other subjects and how do you teach them so that it sticks?
As much as I hated it, I aced biology in school merely so my grades would stay high. Ask me to name the parts of a dissected frog now I'll give you a blank stare. I had no purpose for it. I knew how to memorize something just long enough to pass a test.
Show me an ultra-sound, on the other hand, and I could probably tell you the gestational age of the baby. I know what the purpose of a placenta is and what it looks like, why I need a rhogam injection each time I get pregnant, what a molar pregnancy is, and what happens when the body miscarries a child. I know these things because I love babies. I've experienced the miracle of childbirth and have grieved at the loss of life inside my womb.
History, Science, Handwriting, grammar, music, art - I would love it if each one of my children excelled in these subjects, but I know they'll survive if they never manage to sing on key, speak French fluently, or understand the recessive genes in fruit flies. These facts are merely useless trivia that will be forgotten soon after the assignment has been handed in unless they know why or how it relates to real life. Focus on their God-given strengths and they'll learn something of all these things in the process.
- Can she develop her math skills by calculating how many square feet a pasture for five thoroughbreds needs to be? At $X per eight feet of fencing, what would the total cost be? Could she describe the thrill of winning her first race for a creative writing practice? What new words from the thesaurus could she learn how to spell to replace the ones in her story to make it even more exciting? Does she know how often the horse is mentioned in the Bible or what it is compared to? How has man's use of the horse shifted over the years? Could she make a historical timeline that documents the major changes? Is it possible to watch a foal being born at a nearby barn? Have her look at various horse paintings by different artists. What style does she gravitate to? What influenced the artist's rendering? Could she go riding for a few hours every week or help muck stalls for exercise?
Now you've got a child who's thrilled about learning because it involves something in His Creation that God has given her a passion about. Horses maybe just a quarter inch in the string of things there are to lean about, but her knowledge is a mile deep and in the process, she has learned valuable Math, English, Bible, Science, PE, History, and Art skills that she will never forget. Find out what your child is interested in and facilitate experiences in that area.