Last night Connor asked for some help with work he was doing on the mathematical proofs for triangle similarity.

Strangely, I have never, not once, had to use this knowledge myself since forgetting it immediately after the required subject test for it some thirty-odd years ago.

When Connor asked me, I couldn’t think of a single circumstance where I would ever even need to use this knowledge – maybe if I need to know the height of a tree?

Of course I see the value of maths to society. I see the value of it in many professions. I sometimes use moderately-advanced maths myself for various analysis tasks. What I am really struggling with is the value in learning something with a 99% probability of it never being used again (yes, I get the irony of this sentence!) simply to be able to pass a module test and then safely and comfortably forget it until the point in your life that your child asks for help with it before their subject test.

I couldn’t dredge up any memory of these proofs, other than residual feelings of fear and frustration. I knew that I had done them, but remembered nothing of them. But, I was able to do a quick search, watch a video and learn them in less than ten minutes well enough to teach Connor. What disturbed me however about this process is that Connor was not able to do that. He was so frustrated with beating his head against something he sees no point in, to sit a module test simply for the sake of the test, that he simply couldn’t learn it.

The simple answer perhaps would be to drop maths, or reduce it from his curriculum. For better or worse maths is the only subject we have mandated he study. This year he has completed the entire maths curriculum for what would, in school, be two years of national curriculum maths study. He has done that in less than two hours a week of study. We have done this because for some unknown to me reason the school systems seem to place a huge premium on maths ability as an indicator of achievement and we want to leave open the chance for him to easily return to the school system should he ever need or want to.

I see him using the knowledge and skills from his humanities studies every day. I have enjoyed the last ten months of having Connor more and more able to pick up references, make political judgments and connections to history etc. These studies are having an obvious impact on who he is as a person.

Maths, not so much. Unless maybe by way of dealing with boredom and pointlessness.

Every time I need to do some more advanced maths for finance calculations or data analysis etc., it never ceases to amaze me how effortless the learning process is (and for stuff that I do regularly, I retain it), compared to my experience in school. My musings then are not about the value of maths – I think that is obvious, but rather around the way we teach it. We force it, we shove it with no explanation other than “you have to do this” at kids. It has no relevance to them, or most of us.

Surely, natural learning is a better way to teach it? Connor is interested in economics at the moment. That interest will naturally lead him to learning and doing the related maths. If someone is interested in physics, that interest will lead them to learning what they need. Both students will learn different things, but so what?

Ironically, I need to go now and help Connor with some trigonometry. Apparently if he is going to sit for the SATs (unclear given the International Baccalaureate and other possible paths, but we don’t like shutting down future paths), maths as taught is required, so we have no choice but to force it on him the way the curriculum demands. Frustrating to say the least, when it seems clear that a natural need-based approach to it would yield much easier, and more relevant results.

This is something I want to give more thought to.

I’ll be following this thread–it’s a question I ask a lot. How much math will we pursue in our studies? How much math SHOULD we pursue? If they hate it, can we quit once we pass the basic skill level? I’m glad that someone who seems comfortable with higher math is asking it–I worry that my questions about the value of math are related to my personal history of struggle (and defeat). I’m trying to be excited about the opportunity to be engaged by numbers as I teach my children about them:(

LikeLike

Yeah. It is interesting, having just spent an hour explaining quadratic, linear and non-linear equations to Connor I am no closer to an answer.

It was lucky that I use these fairly regularly for my work, but that is just random – most people probably don’t. I really want to do more reading on learning maths and try to figure out a strategy that works better.

I did notice that he enjoyed this more because I like this area of maths and know what it can be used for, so he saw the purpose.

Funny though, my memories of it at school are terrible and it is only as an adult doing my MBA that I got over that trauma and realized that they were fairly easy and very useful. School maths was just awful for me and I dropped it as soon as I could.

LikeLike

I also struggle with these same thoughts. I learned to do math in school, and although it was never my passion I did what I was told, memorized and worked hard and made decent grades. But I lacked any kind of fundamental understanding and had a fair amount of math anxiety. So I think that just because a student makes good grades doesn’t mean that real, meaningful learning has taken place. And I don’t think all the higher math and science classes that I was pushed to take in high school were a good use of my time. In my real life, I’ve never used any of it. It’s not my passion, and I should have been encouraged to spend more time learning about things that I cared about.

I’ve been homeschooling a long time, and I can’t say that I’ve come to any hard and fast conclusions about this topic. My older two were not drawn to math, but we did use various curricula and then they both chose to go to high school, so they ended up following a traditional path ultimately. But neither of them “like” math- they’ve just done enough to get by.

My younger boys seem to think mathematically, and their mental math skills are impressive. I can’t do mental math at all- and to me that says the most about the way school failed me. But they don’t just sit down and do formal math without me asking them to. I guess ultimately I’m not comfortable with a pure unschooling approach (as much as I like it in theory) so I do ask them to do a bit of formal math on a regular basis. My 12 yr old much more than my 9 yr old- but the older one also says he wants to go to high school, so I want him to be roughly where his peers would be.

There is a huge emphasis on science, technology, and mathematics in our society, and I’m not sure that these skills are more valuable than other skills. There are many ways to be an educated, literate person, and I suppose my goals for my kids aren’t necessarily aligned with what most parents are supposed to want for their kids. That being said, my younger boys are very tech-oriented so I don’t worry too much. I see my job as being more about making sure they love literature and nature, things like that.

Great post!

LikeLiked by 1 person

Such a thoughtful post!

Yes, despite what we thought setting out, we are also a bit hesitant with heading to a full unschooled approach – mainly because it seems that it could close off options for going back to school. If he did, we would want him to be able to attend a good school, and that would be hard if he was missing entire subjects.

LikeLike

The lack of relevance in studies is a real killer. I struggle with this even with my six year old. I am constantly trying to give what we are learning a context in his life, and I think it will only become harder as he gets older.

I just found myself reading this article which is loaded with ideas of how to give life to mathematical theories. There might be something here you can use.

http://lauragraceweldon.com/2014/11/26/natural-math-100-activities-resources/

LikeLiked by 1 person

Thanks Dave. I just read it also and am checking out some of the resources.

Unfortunately, and naturally I guess, the ideas for naturally teaching things like trig and quadratic equations etc. are pretty limited. I did see the Cartoon Calculus one which looked interesting – just wish that it was an e-book.

Really interested to hear that you are beginning to find it harder, as I have been incredibly impressed at everything that you have written about in this area.

If it is so hard to find examples in the world we live in and we have to do so in such a contrived fashion, I have to question the value of it.

Not disparaging maths at all, as it is obvious how important it is to society, but I am certainly questioning the need for all kids to cover such a wide base of largely useless material, versus having them focus in areas that impact their interests.

Will watch what you are doing with interest – just wish Connor was younger so that I could model off you!

LikeLiked by 1 person