Children Will Learn Calculus When They Really Need It

“How will they learn the things they need to learn like Calculus?,” was a question posed to me the other day when I was explaining unschooling to a person at a BBQ. It was a good question, because we have a child who at the age of twenty, actually needed a mandatory high school Calculus course to pursue the university STEM program that he was interested in. He was the second child in our family of five that needed the course.

Our child applied for a university program on March 1, and discovered this need in late February when he examined the program entrance requirements. It was a month too late to register for an online course as they all started Feb 1. We looked at our state requirements for the school course and purchased a textbook. Actually, two textbooks. One for our son to self-study and one for a tutor in case we needed it. Then the child went to work and everyday worked through the Calculus course as well as the Grade 12 teacher-taught math 30-1 course he needed to finish. He worked on math for three hours every day. He finished both courses in time for June marks, and wrote the final exams on which he did very well.

In the meantime, his parents were off traveling to other countries. My partner is good at math and offered help whenever he could, but math teaching is so different from the way he learned forty years ago, so he took that second textbook and would study up alongside our child in order to tutor and explain what he knew. Over Zoom and Discord, Father and son would each take the same problem, work on it, and compare answers, over two oceans – the pacific and the Atlantic, while we traveled to five different countries in five months and the child was at home.

Being unschooled his whole life was never a problem. The child was motivated. Taking the course was his idea and he knew he needed it for possible university admission. His first teacher-taught math class was grade 8 and then he took grade 10, 11 and grade 12 math courses, either self-taught, or online or through a teacher-taught classroom because he knew he would apply to university some day and wanted a formal high school math record. Like our other four kids and many unschooled children, he caught up 8 grades of “paper” math in one year because his brain developed his abstract thinking ability and although he was exposed to math concepts in daily life and play, he was ready to apply his experiential learning to paper math. “Caught up” is the wrong phrase. It’s not like he was not learning math through his play from ages 1 to 13. He was learning number theory, but not from a book, or lectures, but from his own observations through play and projects. In one year, he caught up on learning math calculations on paper at age 13, and had been experiencing math since birth. He never had time or a classroom of peers to develop a phobia about math, or think he was bad at it. Years of non-assessment built his confidence. It was fine to make mistakes, because he liked the challenge of working for the correct answer. Math was a challenging puzzle to be unlocked. Learning was doing and he liked math because it has definite correct and incorrect answers and is the same concepts studied worldwide.

I’ll be honest. When he started math in grade 10, his lettering was not the best. He didn’t have years of practice writing numbers in perfect proportion on paper. But again, he didn’t need years of practice to develop a nice neat math worksheet. It took only two months. When the brain is ready, kids can learn very fast. Here is a sample from the first day of school in grade 10 and a sample from 60 days later. There was much improvement.

Math Grade 10 Day 1
Math Grade 10 Day 60
Math Grade 11 Day 200

Not every child who attends school needs to learn Exponential and Logarithmic Functions in order to get a career, start a business or attend post-secondary education. Those that do need to know it, will learn it and be more motivated to excel. Teaching it to every child just produces anxiety and math phobias.

Our years of unschooling in math were very helpful in producing children who loved math for the tools it offered to solve problems. For example, we ordered a half a cheesecake from a bakery, and when we opened up the box, it didn’t appear to be half a cake. This was a great teachable math moment where I introduced the kids to pi. I showed them how to measure circumference and how to use the pi formula to work out how big the radius should be if we really did get half a cake. They saw the power of the proof on paper that we were short-changed.

We used pi to measure the cake!

This combination of experiential math and paper calculation provided our five kids with motivation to continue their math education through high school, grades 10-12 whether it was self-taught from a textbook, teacher-taught in a classroom or self-taught through online classes. Four of my five children went into STEM pathways in engineering, (read the blog post on the unschooled engineer) bio-science, energy science/chemistry, and mathematics. Unschooling math served them well.

I replied to the BBQ guest, “When they need to learn Calculus, they will go at it with gusto!” She smiled with that polite, “I don’t believe you,” look and went to get another burger. We need to trust that children want to learn and there is no stopping them when they are ready to see the value for their future.


Read more about Unschooling to STEM careers in the book, Unschooling To University:


Here are some more blog posts on Unschooling and Math. Many parents are worried about letting go of formal math instruction and leaving children to unschool math. These posts may be helpful to calm worries!

Ways to Learn Math Without A Workbook

Unschooling STEM

STEM Classes for Kids-Do They Help or Hinder Curiosity?

Play Enhances a Love for Science

Unschooling and STEM-How do Children Learn?

Video Games Give Kids a Bigger Academic Edge Than Homework

Create a Learning Environment That Teaches Without Textbooks


Learn add and subtract fractions with a pizza game
Doors made a great angle measurer
Learning about faces, vertices, and edges
Measuring for carpets (area) and baseboards (perimeter) teaches measurement
Play with stamps to learn about place value
Cooking and baking teaches fractions and percentages

Lego teaches variables
Learn skip counting through body movements

Perfect squares teach the Pythag

About Judy Arnall, BA, DTM, CCFE

BA, DTM, CCFE, Certified child development specialist and master of non-punitive parenting and education practices. Keynote speaker and best-selling author of "Discipline Without Distress", "Parenting With Patience", "Attachment Parenting Tips Raising Toddlers to Teens", and "Unschooling To University."
This entry was posted in Elementary-Primary Children Ages 5-12, High School Children Ages 15-18, Homeschooling, How to Unschool, Junior High School Children Ages 12-15, University-College Ages 18-25, What is Unschooling?, Why Unschool? and tagged , , , , , . Bookmark the permalink.

3 Responses to Children Will Learn Calculus When They Really Need It

  1. Swabhava.World says:

    the bottom line is that 99% of the math that public school students learn is a waste of time. i went to college for geology and then got a masters in organizational behavior. yeah i know, completely different subjects. anyway, i am a payroll manager now and all i need to know is how to add, subtract, multiply and divide and most of the time a computer or calculator does that for me and i make enough to support a family of 7. imagine the potential if we stopped having our kids spend 12-16 years studying things they actually never use in the real world?????

    Liked by 1 person

  2. Tupac says:

    Uhh dude. Math is a foundational skill but also a foundational piece of development for higher reasoning and conceptualization. Math needs to be taught much more rigorously. This is evidenced by the fact that early math skills have the highest significance of mid-career success! We need to start teaching algebra when kids are learning arithmetic so it opens up conceptualization of math. Everyone wants to blame the “the applicability” but school is supposed to be more than that. It’s supposed to develop cognitive skills by challenging individuals and introducing them to new concepts they might have an interest in.


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