#### Sacrifices, Decapitation & Imagination at the Temple of the Sun & Moon

December 15th, 2011

Oct 08, 2012 Lainie Liberti World Schooling 23

I’ve been on the receiving end of several judgments and criticisms because I am not insisting my son learns algebra and other forms of higher math. They range from:

“*Ok, so you are going to be a ‘hippy’ about your son’s education that’s fine. But you should at least insist he learns math*.”

to

“*Aren’t you actually hurting your child’s future by not insisting he learns algebra?”
*and

“

**But I ask really, beyond the basics is it important for all kids to learn higher math?**

I agree the concept of basic math skills are important, as they apply to everyday life, and as an unschooled teen, my son is efficient in addition, subtraction, multiplication and fractions. But is really teaching and learning higher math (algebra, calculus , trigonometry and above) **IMPORTANT?** And more to the point, *what is the reason* for learning specifically algebra and other forms of higher mathematics? I could always ask and reach out to algebra teachers, but I decided to tackle this on my own.

There are two main arguments I’ve heard in favor for insisting my son learns algebra:

**1. He will need to know algebra to get into college.**

** 2. Higher math teaches abstract thinking, thus causing the brain to create new connections & function better. (Therefore, algebra builds a better brain.)**

First of all, I’ve asked Miro if he’s interested in studying algebra and he’s said **NO.**

But, the college argument takes care of itself. If my son wishes to go to college at any point in his life, he and he alone is empowered to make that decision, not anyone else. And if he, and he alone, decides college is right thing for him, then he will have to take the steps to play the rules of ‘testing’ in, including becoming fluent in algebra. It’s Miro’s empowered decisions that will determine if he wants to pursue this option.

As for the second argument, “*algebra teaches abstract thinking*”, I have several responses to this.

The greatest love of my life was a neuroscientist. We spent a good part of our years together sitting for hours upon end talking about the complexities of the brain, discussing neural patterns, which neurons fire as a result of different stimulus and how new pathways are created. I have a good understanding of the basic biology of the brain, and equally understand that creating better health to any part of the body is in the best interest of any person. But is higher math the only answer?

I believe a biologically healthy brain can be stimulated through life, abstract thinking can be learned through life situations and being empowered to explore the options and discipline is something unschooled kids regulate over themselves. And logical thinking, which is the basis for most arguments of learning algebra, well life provides challenges that need to be solved (logical thinking), my son engages in many forms of games (strategy, experimentation, problem-solving), and exploration in the ‘real world’.

Algebra and other forms of higher math, in my mind are simply tools which enables a child to get what they want. I would never argue that higher math is senseless, rather it may not be necessary based on the objective of the learner.

The answer provided by any unschooler will be based in their individual interests and passions. And yes, using tools available are one of the keys, however the focus must not be lost within the tool itself. In other words, there’s no reason to vilify the tool, rather focus on the passion itself.

But is learning higher forms of mathematics really important to my unschooled son? Yes, I realize that forms of algebra are used in everyday instances like figuring a budget, or cooking, or even throwing a ball. Algebra has a way of sneaking itself into our lives without a grand proclamation or formal learning. Am I performing some kind of child abuse by not insisting he learns it out of a mathematics workbook designed specifically for his age?

As an unschooling parent, I am concerned with my son’s interests ‘**now**‘. If my son becomes interested in something that requires specific knowledge as a foundation, then I will get him that support to learn what he needs, **NOW**. I can’t worry about what he may or may not be interested in the future, nor frankly is that my responsibility as an unschooling parent. I can only provide for his needs now, based on his interests. This empowers my son and puts the accountability on him, with the responsibility to communicate his needs.

And through natural learning, I whole-heartily believe my son’s brain is making new patterns and connections and finding different unique ways of solving problems. And I am certain he is doing this without the formal instruction of algebra and other forms of higher math. These skills are obtained is solely though a natural learning process acquired through life and applied creativity.

And the natural learning experiences are indeed creating new neural pathways in the brain, without stress and the association of negative emotions. We’ve opted for natural and joyful experiences learning from games, travel, exploration, languages, play and life experiences.

More on math and the unschooler here, by Sandra Dodd.

“We didn’t teach him responsibility or confidence any more than we taught reading or math.

Like all children, he was born with the intelligence and the drive to grow into an adult and take his place in the world. What would have happened to the human race thousands of years ago if this were not true? It’s a natural process, but parents and teachers thwart human nature by trying to force(or motivate, bribe, trick, persuade, cajole or coerce) children into ways of learning and being that go against their own innate, powerful, brilliant and unique intelligence.”

Trust your children.”

**Here are some thoughts from other unschooling parents surrounding teaching their children math:**

“When it comes to Math we typically take the same approach we do with any other subject. We do not put any specific focus on it, rather we realize that Math skills are improving everyday because it is all around us. We use math in games, on the street, in stores exchanging money, in the kitchen while cooking and so much more. You basically cannot stop learning math even if you tried.”

“I know that they are learning all the time because I invest my time in taking part in what they are doing. If they need to learn a specific type of math, a higher level lets say, then we will figure it out together. Most people though do not have any need for school work type higher level math! When was the last time you used anything that came out of your college calculus course??”

## Mary King, mom to four awesome unschoolers, Victoria, 18; Kalel, 14; Kyle, 9; and Claire, 6. who blogs her experiences at: UnschoolingSuperMom writes:

Math is everywhere. It is something we do everyday in our lives without needing to sit down and learn it from a book. It is in our everyday living experiences of what we do with our lives. It dosen’t need to be forced learning. It is natural to need math to get by and they learn what they need as they need it.

“As an unschooling parent for over ten years I’ve seen how resolutely my kids pursue their interests and goals. Their persistence when they are curious and motivated seems inexhaustible, even through frustration and disappointment. But, as unschooling parents realize, real learning is minimal when a person is disinterested. When they need math is when they learn math. My kids encountered everyday arithmetic living and learning in the world around them: counting toys; playing board games; calculating hit points baking delicious food; making store purchases; measuring distance; balancing their bank account. The reasons for performing these tasks are clear, and the computational skills are picked up unobtrusively along the way—without developing the usual curriculum-induced aversion to math. And many adults living active and joyful lives have no need for more advanced skills.

Yet in the real world mathematics is so much bigger than arithmetic and through years of exploring the world, analyzing situations, and making choices, my kids have developed solid critical thinking, reasoning, and logic skills. It’s that strong foundation of mathematical thinking, along with their everyday computational skills, that I’m comfortable will continue to support them in whatever direction they choose to pursue. If at any point the interest or need to learn more advanced mathematical skills presents itself, that’s when they can be picked up. The time conventional students have spent learning what they know, (say, a high school math curriculum) my kids have spent learning other things that make up their knowledge base. With a lifelong view of learning there is no value in comparing the particular ages at which people learn things. It’s not a competition; there’s no behind or ahead. Time is not lost, just used at their preference.”

**Photo courtesy of Ewan Cross based on a CC license.*

- algebra, brain, calculus, go to college, life learning, logic, mathematics, natural learning, neural pathways, stimulate the brain, trigonometry, unschooling

Lainie and her son Miro are living a location independent lifestyle, slow traveling around the globe and living in the present moment. Lainie writes about staying inspired, participating as a global citizen, volunteering, unschooling & natural learning. Lainie and Miro are both following their interests on the road, as the planet has been transformed into their classroom. Often you will hear Lainie say “we are blessed to be accidental world schoolers” and has become and an advocate for “life learning” at any age. Lainie & Miro have taken this philosophy to heart and are producing a series of family & teen oriented retreats in called Project World School.

**
A single mom & son's travel blog, chronicling their nomadic adventures as they experience global education through world travel; Raising Miro on the Road of Life.**

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For us, higher maths is important and relevant, and my son wants to learn it (despite not being wildly interested in it). That’s because he wants to go to college (he thinks), and study sciences or engineering to build his dream job, so he’ll need the algebra.

I’d also argue that there’s some stuff that is part of the sum of general knowledge that is useful to have. So, pi r squared, Pythagoras, the number of degrees in a triangle, some basic stuff like that. It’s part of the sum of general knowledge in the way that films and literature and pop culture and history is, I think.

One other thing I’d like to suggest here… There’s a general belief, not to say a sacred cow, among unschoolers that a child can learn whatever they need to learn in whatever timeframe they decide on (aged 18, want to be a doctor, oh shit, let’s do seven years of maths in three months…).

And I’m not sure, especially with maths, that that’s the case…

I totally agree with Theodora. Since you don’t know what your kid will want in the future (i.e. college), I suggest you at least immerse him a little bit.

You don’t have to teach him an hour of algebra every day. You could talk about it a few days a month, you know? Basic knowledge is key, in case he does decide he wants to be an engineer or Dr. in the future.

At first, I thought I would hate math. Once I learned a bit about it in grade school, I actually fell in love with algebra. So you never know

– Maria Alexandra

Maria, I think to Rob’s point, we are actually getting forms of higher math as life lessons in our lives without having the need to study it formally. The key to natural learning and interest led learning is not to force my intentions on my son, rather let him lead through his interests. Once learning higher math becomes important, he’ll want to study it, make it part of his love. Until then, I really don’t see the reason to focus on something he doesn’t want to focus on now.

I agree with you on a lot of the points, Theodora. But as you’ve said, you son has an interest which includes college as part of his plan. I know your son is 11 and he’s done a great job at expressing his desires with you about his future now, therefore there will be no need for scrambling, doing 7 years of math in 3 months. It’s great you are both on the same page about that. And for you, as you stated, it’s relevant.

And for us, until it becomes relevant, it’s not going to be a part of our lives. And through general knowledge, pop culture and personal interests, my son is exposed to pi squared, Pythagoras from a historical perspective (as he’s the father of numerology too) and even sacred geometry (flower of life, etc.).

I know math is is hot topic for many, but I feel we have and are making the right choice for us; living without formal instruction of it.

Hi Lainie, of course it is yours and Miro’s choice to learn algebra.

and there are many ways to learn skills such as problem solving, decision making, reasoning, and creative thinking without learning algebra.

I think part of the problem is the label “algebra” for some reason people seem to fear the word.

In your response to Theodora you stated “until it becomes relevant, it’s not going to be a part of our lives.”

I think you probably use algebra every day, for example, you and Miro are travelers, every time you calculated time and distance, you used algebra.

When you need to problem solve a situation that involves money, time, distance, volume of something, comparing prices when you shop, rent something – cost versus time you have used algebra.

Have you used a budget? If you have to budget your money to make sure that you have enough for the whole day or month. Mental algebra is used to determine costs of things, options for purchasing basic needs, paying rent and of course having money to eat.

When you play sports you have to mentally determine the angle you throw the ball to make an accurate throw or if you are trying to win a prize at a carnival game. You approximate distance, but you have to determine how much force to apply to your throw. It also applies to soccer (or really any sport that involves kicking, throwing, passing) when you are kicking the ball to another player or into the goal.

Want to build something? A bike ramp or a skateboard half-pipe, you will use algebra whether you know it or not.

Science, engineering, any business that you run, accounting, architect, financial math, art, sound systems, restaurant management, cooking, design, urban planning, banking, computer programing, game design, computer coding, all involve algebra in one way or another.

Plumbers, electricians, doctors, nurses, computer programmers, auto repair shops, home builder, insurance investigators, investor, banks, landscapers, animators, special effect directors, computer scientists, forensics specialists all use algebra.

Miro is interested in cryptozoology, to be a crypto-zoologist you need to have a firm grasp of algebra.

As for other “higher” forms of math I agree one most likely not relevant to most peoples lives.

excellent point, Rob =)

I think those are great points, Rob! I agree, algebra is a part of our every day lives, therefore the actual need to study it becomes moot. I think though, we’ve been figuring out how to implement the attributes of higher math into our lives through life lessons and not really needing to study it as a formal discipline.

The role of an unschooling parent is to support and facilitate my child. Once the need for higher math becomes important or relevant in my son’s life, I’ll get him what he needs. I tell you Rob, it’s hard to know what the correct thing is to do in situations like these. I can only trust my instinct as a parent and my son as a human being that he’s letting me know what his needs are.

Fabulous. You have a way of echoing nearly exactly what we also feel:) I agree with Theodora that in general knowledge purposes it is important but I also feel that these things come up and are within my guys general knowledge set even though they do not spend an hour a day in front of a math book:)

They learn it all the time, even algebra, we just don’t call it that! When it becomes relevant then we will address it. For some they know it will be important in what they already love and want out of their lives but even if my boys need to cram to get into college, it isn’t super advanced math that they will need to enter a basic algebra college course! Math isn’t really that hard when the person is ready and willing…much like any area of life!

Thanks Mary for your comment. I’m realizing through everyone’s comments that Miro is indeed learning higher forms of math through every day life situations. I love that. Again, once it becomes important or necessary on other levels, and the desire is there, I will get Miro the support to learn what he is interested in.

I LOVE your post. We unschool and my DD has decided she wants to go to college so this summer she asked for a GED book to see where she stands and what she needs to work on.

Is she consistent with studying from the book, no. Does that mean she is giving up her desire to go to college? No.

When gets closer to entering college, several years away, and still wants to go, she will also have the desire to do what it takes to get it done.

I agree with the idea that not everything is necessary to learn. When an unschooler faces a situation that requires a specific knowledge about something, they simply learn about it then! At least that way, their learning is fresh and current…not based on whatever fad was hailed as the latest education breakthrough.

Joyfully,

Jackie, who is semi unschooling her daughter all the way to college.

My Attempt at Blogging

Quaint Scribbles

Thank you for sharing your experiences with DD. As a parent, I can never know what the ‘right’ thing is to do. I can only do what’s best for my child. Good luck and keep us posted!

I think you’re missing an important point. Learning math is not necessarily about learning math. It’s about developing the cognitive ability to deconstruct a problem and apply structured logic to derive a solution. There’s few vehicles as efficient in developing this thought process as math.

John, I think we are saying the same thing, only from different view points. Agreed, math is NOT necessarily about learning math, it’s about developing the cognitive ability to deconstruct a problem and apply structured logic to derive a solution, and we feel that’s the experiences we’re getting through natural learning presented through travel. No need to study math to experience those things. That’s my point.

Wow,

Really interesting post. I remember when I was in school and I asked my maths teacher what the point of doing a particular maths exercise (Yes-it was a bit cheeky) and she told me “well, for most people there is no point.” While I believe that it is very, very important to teach the basic fundamentals of subjects – for example maths and english – much of what we learn in Secondary school is long forgotten the first second after the exam is finished.

When we look back at the history education we can see that the form in which we learn now is actually a relatively new method of learning and I believe that it is not always the best way. Many of our greatest minds and thinkers were educated in a more organic form because they retained the passion for learning and delved deeply into subjects that interest them.

As a teacher I do feel it is beneficial to “formally” teach children things but I do question the value in forcing children to learn a full curriculum 90% of which they will never use. However, I also think it could be interesting to introduce some things that maybe they may find an interest in – you are doing this by introducing new experiences every day. You can see this very clearly through Miro’s posts.

Maybe you will be interested to watch a documentary I saw recently about education. It was made by an argentinian director and It focuses on the failures that exist in the modern classroom and how they effect the desire to learn. Very interesting – if a bit long.

Your blog is wonderful, and thanks for raising the math question.

To me it seems a bit like studying to play an instrument. You put in the effort, because even if you do not turn into a concert musician, you will be able to appreciate their art on a deeper level.

Second point: Math is permanent. The creator of things can not take away math, math just is (admittedly, mathematical truths can be discovered multiple times, as in your trigonometry example above). Plus, his/her universe seems to care about math quite a bit, why else could (most) things be described by mathematical models and why else would our collective brain be (barely) capable of understanding them?

Here is the tricky part: Where does one find an inspiring math teacher?

My two cents worth… I was unschooled and when I became an adult and wanted to go to college it was extremely tough! I had to take an extra 2 years of college just to get the math in. Algebra is very complex if you have zero formal foundation.

I truly wish my parents had thought about my future when I was growing up and taught me at least the foundation of formal Algebra.

Just my two cents worth.

Um, algebra, trig, calculus? These are not “higher” math- they are still the basics!!

If your child decides at some point that they wish to learn about how the universe works – physics, etc – they will be at a loss for quite a long time without a foundation of formal mathematics. In this way, I think that not educating them in this is a way of making a future choice – that they will not learn about physics – for them now. I think this is less about what they should know and more about what doors you wish to leave open.

I was schooled in the traditional way. I have a BA in Psych, an AAS in Graphic Design and several Certificates in Healing Arts.

I stunk at math. Never got past Algebra 2 (received a D-).

When I went to college I took Math 100 and never looked back. Bookkeeping and accounting classes were easy because they had real world applications. Philosophy (logical thinking) was so natural to me that my Prof. asked me to tutor.

So from my perspective, pushing a child to go into Algebra and beyond because they might need it someday is pointless. If it is because they truly do want to be a scientist, engineer etc. then their own natural desire will drive it.

My 2 cents!