Homeschool, Homeschool high school, Homeschool HIGH SCHOOL Made Easy
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Math | Homeschool High School Made Easy 12

Welcome to the month-long series “Homeschool HIGH SCHOOL Made Easy,” a follow-up to the popular “Homeschool Made Easy” series (now published on kindle). I’m sharing tips from my experience as a homeschool graduate and homeschool mother, showing YOU how easy and enjoyable these high school years can be for you and your teen. Be sure to sign up for the entire series so you don’t miss a thing!

While we look at individual subjects our homeschool high school students face, I keep reminding you of two things:

  1. Your why will make each course, every decision, every class easier. Keep your priorities in focus so you’ll maintain clarity.
  2. Your student learns best his way, using his own learning style and his own pace.

What Your Homeschool High School Student Needs to Study in Math

There is no subject this is more apparent than mathematics. Your student will complete three or four years of math in high school (depending on your state’s requirements). But what exactly those are will depend on where he starts, which depends on two things:

  • where he left off in middle school, and
  • how quickly his brain matures to handle algebra.

I want to talk about that last point a bit because this is something I really wish someone had explained to me clearly when my first student was in middle school. This is the one fact that would have saved me and my teen over a year of frustration, agony, disagreement, and despair. It would have saved us both from hours of raised voices and crumpled papers, blaming and scribbling. Because once we both realized this, our math lives were never the same. So I’m giving you the secret, and you’re going to write it down and memorize it and apply it and watch the clouds part over your math lessons, too. Ready? Here goes:

Until the student achieves the mental maturity for abstract thinking, algebra is a big waste of time at best and roadblock to academic pursuit at worst.

It doesn’t matter how fast your child learns math facts. It doesn’t matter how quickly he races through math workbooks in elementary. It doesn’t matter how much he loves using math in middle school. It doesn’t matter how bright he is, how articulate he is, how quick he is with his figures. He will not do algebra until his brain grows into it.

You can’t rush mental maturity. You can’t force it, you can’t push it along, you can’t lesson plan it. Like physical growth and puberty, each student will reach mental milestones at his own pace, according to a God-ordained timetable that we can’t see. We can expect it in a general time frame, we can guess based on external physical clues, but we just don’t know when that mental growth spurt is going to occur.

So here’s my math education theory: Until the student achieves the mental maturity for abstract thinking, algebra is a big waste of time at best and roadblock to academic pursuit at worst.

Homeschool Made Easy

Sometime between ages 14 and 16 (and sometimes younger for girls), students experience this mental growth. Up until this point, their learning is very literal. They learn words for what they experience with their own senses. They apply rules for what happens into their own lives. They learn from their five senses, using skills of visual, auditory, and kinesthetic learning. And this is how they learn math — manipulating objects, describing the patterns they experience in nature and time, memorizing math facts that they know by experience hold true in their real world.

Algebra changes all that. Suddenly, students are demanded to imagine a world in which nothing is literal, letters are abstract concepts, and patterns occur on imaginary horizontal and vertical planes. None of this makes sense in their universe. They try with varying success to apply this to the literal world they live in, but soon the lessons and concepts become so abstract and complicated that application to money or counting objects or cups of water becomes impossible. Math has become, at this point, entirely abstract.

There are two possible choices for a student at this point. In my case, as a thirteen-year-old homeschool student, I chose the faith route. I decided math was an abstract game that meant absolutely nothing to my real-world existence, so I would just play the game to win. I copied down the rules my textbook told me to follow. I memorized formulas that meant absolutely nothing to me. And I taught myself that when the question uses these words, use this formula; if it says those words, use the other formula. I played this game successfully for four years, completing two years of algebra, trigonometry, calculus, physics, and college statistics successfully by blindly following these rules.

When my oldest son turned the corner from pre-algebra to algebra around the same age, he refused to take abstract math on faith. He insisted on choosing the fight to understand. So when he missed a problem, I would point to the formula with vigor. Do it this way! That wasn’t good enough for him. WHY? Why does it work? Why is that the rule? What does the answer mean? How does this apply to the real world?

I don’t care! Do it this way to get an A! That answer infuriated him. Voices were raised. Pencils flew. He had to see the answer, and he wanted it to be as clear as understanding why six groups of seven is forty-two and why two halves is three-sixths. He had to know it, to see it clearly in his mind, even while I insisted it didn’t matter, that he just had to have faith and get it right. I insisted on the faith route, but he was fighting for real understanding.

His progress in Algebra 1 faltered. He poured over his textbook, he muttered under his breath, he ignored my pleas to just memorize the formula. And then suddenly, one day, he got it. I see it! It all makes sense! And every day of high school math after that, he didn’t work a minute. He knew the answer without trying. And he tried in vain to explain it to me (something about undulating waves that look different from different angles . . . I don’t know).

I have asked him so many times what made the difference. He insists that he just woke up and understood. That suddenly, everything his book said made sense, that he could see the figures and lines and shapes moving in his mind, and he knew what the formulas and problems and abstract equations all meant. And he loved it (probably why he’s now a math major in college).

Don’t tell him, but when he describes a sin wave or why a formula works or how shapes change in space, he giggles. He giggles like his sister does when she finds a new flavor of lip gloss. It’s so funny, but obviously math has become, for him, a source of joy.

Now, there’s a purpose in this story . . .

Each student will reach mental milestones at his own pace, according to a God-ordained timetable that we can’t see.

If I had it all to do over again, if I knew then what I know now . . . I wish I had held off Algebra 1 another six months or a year. Those arguments and frustrations and crumpled papers were a complete waste of time. He would have been better served studying another year of prealgebra or consumer math or more arithmetic. Once his brain grew into it, his highs school math was a piece of cake. In fact, in fewer than four years he completed plenty of math:

  • Algebra 1
  • Algebra 2
  • Geometry
  • Trigonometry
  • Pre-Calculus

He tested out of the first year of college calculus without studying specifically for the test. It just made sense.


The key to successful high school math is staying sensitive to your own student’s maturity. My teen daughter was obviously ready for algebra quickly. She went seamlessly from pre-algebra in seventh grade to algebra in eighth grade with no problems at all. Her high school math will look something like this:

  • Geometry
  • Algebra 2
  • Trigonometry
  • Pre-calculus

I don’t anticipate her needing more than that; she isn’t planning to pursue the sciences, so that’s already more than enough math for college acceptance.

My middle school student is not ready for algebra yet, though he also completed prealgebra in seventh grade. I noticed he tripped over the beginning abstract concepts and struggled with some of the geometry. He could do it, but it was mental work, not obvious facts to him. So during eighth grade, he is taking a review of prealgebra and introduction to abstract reasoning.

I have found a great resource to bridge that gap is Principles of Mathematics. This is a two-year prealgebra course, and my eighth grader is completing both of them in one year for review. The author carefully explains the reasoning behind formulas and algebraic actions and applies them to real-life scenarios. The equations and lessons build in complexity while remaining practical, so students get that mental workout necessary for algebra later. It’s an excellent bridge between practical and abstract mathematics for young teens.

I’m seeing mental changes already in my eighth grader, so I’m sure by his freshman year he will be ready to tackle algebra. His high school math will likely look like this:

  • Algebra 1
  • Geometry
  • Algebra 2
  • Trigonometry

If he were to pursue the sciences or even a degree in mathematics, that is enough high school math. I learned from the head of mathematics at Liberty University (the largest Christian liberal arts college in the world) that high school calculus is not at all, even for math majors. In fact, most science and engineering students have little or no exposure to calculus before high school graduation. Instead, a working knowledge of geometry and a solid algebra foundation are far more important.

Are we cheating our students if we don’t push for more math? Absolutely not. I’ve actually asked educators this exact question; I specifically asked why Chinese students are doing so much better than American students when we know the mental maturity cannot be externally controlled. Both the Asian educators I asked gave me the same answer. The difference between the high-performing Chinese students and our American low-scoring ones are so much more than how quickly they learn algebra. One big missing ingredient in both is application and comprehension. 

The Chinese push for mastery in math, so students learn rote facts and formulas, much more like my own faith-based approach to higher math. In the end, they score great on tests but struggle to apply their education to real-world problems. They may take calculus in 9th grade but, like me, they will have no idea what they are doing on paper. In contrast, American students from institutional education may be pushed along with a crowd of students ahead of their ability or behind their capability, so each individual student may not achieve the level of learning, understanding, and application they are fully capable of. We don’t want to follow either example.

Homeschool students have a unique advantage in math education. We can wait for our teen to grow into maturity and then allow him to take off at his own pace, achieving mastery at his own personal best. And that, my friend, is when our homeschool why makes the very most of a math education.

Homeschool High School Math Made Easy

Your goal before graduation is to prepare your student to:

  • use math consumer math responsibly in his banking account, purchasing, and employment, and understand how math works in loans, taxes, and economics,
  • successfully complete algebra, geometry, and other advanced math courses at his own pace,
  • apply his math education and reasoning to other subjects, and
  • assist others around him in math understanding and application.

How do I help my student study independently? Your student will be successful at learning math on his own if he’s at his appropriate level and pace. So first of all, make sure he can handle the material, then keep him moving forward as he is able. He may sprint through the “easy parts” then slow down on difficult concepts. As long as he is working and making progress over time, he will do well.

How do I hold the student accountable? This is so easy — grade his tests. Math is right or wrong, and students either show their logic on paper or they don’t. It’s so cut and dry, it isn’t even funny.

  • By Algebra 1, I no longer grade homework. My student can check his own work each day to make sure he is working the problems correctly. And getting instant feedback on whether or not he’s doing it right really helps reinforce learning.
  • I don’t even care if the student does all the homework. Usually, they don’t once they hit their stride in math; they just glance over what the upcoming test is over and practice a few hard problems.
  • The test is closed-book, only a calculator allowed. Students should show their work so I can judge if the correct formula and logic was applied to each problem. The tests make up the entire subject’s grade.

High school math really can be easy if we allow our student to learn at his own pace. It really makes all the difference.

What about you? What is your high school student studying for Math?

This article contains affiliate links to help support this site, but all recommendations are products I actually use and love. I am not a legal expert on graduation requirements in any state; please do your own research and plan accordingly. 

1 Comment

  1. classesbybeth says

    Great post! I have been looking at Principles of Mathematics (I think that’s the one that MasterBooks now sells). I can see my youngest (non-math) child benefiting from it. My oldest was definitely one that wanted to know the “why” and not just “memorize this formula”. Math made sense to me, but like you, I memorized the formulas and didn’t care about “why it worked”. My son (middle child) totally “sees” math differently. Thanks for sharing!


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