**The Problem**

Despite homeschool studies’ *ahem* diverse sampling methods and questionable validity, one trend has nonetheless emerged: compared to their regularly-schooled peers, homeschool students are weaker in math. The Coalition for Responsible Home Education has a brilliant article on this, complete with citations and graphs (check it out!).

Why is this the case?

**Potential Variables**

In short: more research is needed.

Studies’ sampling methods, ease of humanities vs. STEM education, cultural focus on humanities over STEM, resource access, resource use, and more initial homeschooler interest in humanities vs. mathematics all potentially contribute to homeschoolers’ limited math skills.

It is also notoriously difficult to learn and teach. These limitations, echoed in America’s 38th place in mathematics, expand when math-adverse parents are tasked with teaching their student concepts they themselves don’t understand.

And, unlike their regularly-schooled peers, homeschoolers have the unique opportunity to avoid mathematics in favor of other subjects.

This likely influences the disparity; the most math-adverse public school student would be exposed to mathematical concepts 5 days a week for nearly a decade, the most math-adverse homeschooler may even avoid the most basic addition.

So we have two problems: choice of math curriculum, and fostering math practice.

How do you help your student excel, or simply become competent in math?

**The Obvious Solution**

Khan Academy. Takes you from grade school through multiple levels of calculus. Anything beyond this, you’ll be in college and going for an advanced degree. It’s comprehensive, free, self-directed, mastery-oriented, and encourages practice and engagement through a points-based reward system. Go check it out. This has been my main math-learning source.

Article done; go start learning.

…wait…you’re still here? Khan Academy wasn’t enough? Or it didn’t work for you? Your student still isn’t doing math? You want something more? That’s alright. You’re not alone. And my contract says I have another 623 words.

**Other Curriculums**

Here are a couple guides for picking mathematics curriculums with suggestions. The first is more general, while the second focuses on elementary. And here are a series of reviews for more curricula. Not every curriculum will work well for every student, and to help it work, see “Operant Calculations” below.

Are you more comfortable with textbooks? Reddit has multiple threads of recommendations. Just make sure to pick up the *Teacher’s Edition* (or you’ll have to do the problems along with your student!).

**When Access Isn’t Enough**

You’re on Khan Academy, you have the textbooks—but your student still isn’t motivated towards math. What now?

Make it matter.

*Everyday Problems*

How well can your student budget? Which is cheaper per ounce, 160 oz. of generic flour at $2.84, or 5 lb. of Pillsbury’s at $2.48? If your student gets a $5.00 allowance, how long until they can purchase an 11.5 in. television? What if they invest in their sister’s lemonade stand that’s made $335.00 last week, and has made $285.00 this week as of Thursday? (Is your sister’s lemonade a growth industry?)

How much wood would they need to build a shelf for their new screen in their room’s wonky 84⁰ corner?

Math was created to help us solve problems.

Ask yourself: what problems can math solve in your and your student’s lives?

After all, why else learn math in the first place (aside from truth, beauty, and the fostering of critical thought)?

This works for tests too. Is your student aiming for college? The SAT and ACT can become the curriculum. Try practice problems; learn anything you don’t know.

*Interdisciplinary Integrals*

Newton invented a new branch of math to explain acceleration.

Whether its fractions for stoichiometry or calculus for physics, your other school subjects will likely include math (that’s why it’s taught!).

What is your student interested in? Chances are you can somehow integrate math.

Find and replace. Student interested in trains? That scalene triangle of 110, 350, and 245 in. has just become Cities A, B, & C (you can name them Metropolis, Gotham, and Star City if you want), 110, 350, and 245 mi. away from each other, respectively! And instead of looking for a perimeter, your student is now looking at how many miles is a round trip. Get creative! Even if it is only tangential or arbitrary, humans respond better to things they like. Start encouraging your student to do it too! Ask them: “what is an example of this?” (Lots of math people say this is the way they solve problems.)

But it doesn’t always have to be that arbitrary. Math is more integrated in subjects than one might think. My interest in Psychology has led me to learn statistics. Art and music have some beautiful mathematical representations.

*Operant Calculations*

But what about encouraging daily practice (or something more frequent than trips to the store)?

Mohamad Jebara, founder of Mathspace, refunds users their membership fee—paying its students—with certain amounts of math practice (Here’s his TED talk about it). Through this program, they saw a significantly higher user engagement.

Just as you tied math to tasks and subjects that mattered above, tie math practice more arbitrarily to privileges or other concrete rewards. It doesn’t have to be cash—though it helps! (**IT DOES NOT**. Keep cash as a final option.) Just make the reward anything your student values enough to work for. Yes, it’s bribery, but don’t you get rewarded for your job?

What standards you set depend upon the subject and your student. A variable-ratio schedule statistically creates most intense and consistent performance. If you’re into precision, this article explains how to create variable-ratio, variable-interval, variable-time, random-ratio, random-interval, and random-time reinforcement schedules in Excel (skip to Methods section).

Too complicated? For a variable-ratio schedule, let your student role a d20 (or d4 or d6…).

**When you dream of derivatives (and it’s not a nightmare)**

Miracle of miracles, your student loves math. What now?

Ask your student what they’d like to do. For higher-grade math textbooks, a college library is definitely recommended.

Then try a math competition! Good for socialization and stretching your skills! The Russian School of Mathematics has this guide to math competitions, and here’s Wikipedia list for math competitions around the world.