Great tips for increasing numeracy

Here are some great tips for encouraging numeracy in your children!

https://www.forbes.com/sites/rachelcrowell/2018/08/16/should-we-encourage-kids-to-do-extra-math/

Beyond the Science Box: Why a School That Can't Tell a Clock From a Bomb is a Symptom of Deeper Problems

I'm sure by now you've heard about Ahmed Mohamed, the child who got to spend some time in juvenile detention and was suspended from school for three days because the school principal thought his extracurricular project was a fake bomb. Even though much has been said already about the incident, I think there are a few important points that haven't been addressed yet.

MacArthur High School's Administration Just Failed a Very Basic Electronics Literacy Test

Security expert Bruce Schneier said it best: Child arrested because adults are stupid.

When I first saw the released picture of the clock, I immediately identified on sight all of the components.  (See this article for a labeled diagram if you are curious.)  You don't have to be a government munitions contractor to know that bombs have to have an explosive component.  None of those parts are capable of that.

Saying that Ahmed's clock looks like a bomb is like saying that a metal tube with windows cut out from it looks like a plane -- it's obviously missing an essential piece of the puzzle.

No one doubts that electronics are an extremely important part of the modern economy.  How did we get so far removed from them that seeing a box of very basic and innocuous electronic parts is enough to make school officials freak out and call the cops?  How can a school like that possibly do an adequate job educating its students about how things work?

I'm not saying that I expect every school employee to be an electronics expert.  But I have to think that if the school is doing its job there should be enough exposure to basic electronics just by being there that adults won't mistake them for something more sinister, in the same way that you wouldn't expect an English teacher to panic at a multiplication table or think that it was a computer virus.  Perhaps this year in addition to testing its high school students' aptitude in the economically critical skill of filling in bubbles with a #2 pencil, the State of Texas should have a session where students have to build a three-bit adder out of electromagnetic relays.

Schools Want You To Keep Out-of-School Learning Where It Belongs

Irving Chief of Police Larry Boyd unknowingly said it best:  "We live in an age where you can’t take things like that to school."  I learned very quickly in my educational career that school was incapable of helping me pursue my academic interests.  I can count the number of teachers I had that were even interested in nurturing my extramural learning on one hand, and I had very good teachers overall.  Even those teachers were unequipped to devote more than a few minutes in a school year on such things.

Can you imagine what kind of chaos there would be if every student brought their interests to school and expected teachers to help them learn more about them?  As an adult, I see why when children refer to outside learning they might at best get some small praise: it's much easier for the teacher.

Still, I think that encouraging students to bring their interests to school and teaching them more is worth it.  Can you imagine how wonderful it would be, and how much more motivated students would be to learn?  There would probably be a lot of cross-pollination of interests between students as well.  I can't think of a better way of exposing children to new topics.

If at First You Don't Succeed, Fail, Fail Again!

Perhaps the most serious problem is that the school is unwilling to admit it did anything wrong.  Irving Independent School District's insistence that it stands by the teachers and administrators and that the proper procedures were followed correctly sends a clear message: it's ok to be ignorant, it's ok to not learn from your mistakes, and anyone who has the gall to learn outside its walls should be treated as potentially dangerous.

What a bad example!  Now that they know there are serious flaws with their system, if they choose not to address them, we have to assume that they are satisfied with having those flaws.

I know I would never send my children to a school that is satisfied with having them.

Beyond the Math Box: There Are No Dragons!

My mother was a child psychologist and she always used to say that if a child is old enough to ask a question they are old enough to get a straight answer, and that the answer should go into all the depth that the child is interested in. That approach hasn't always been easy with Adam, but it's paid big dividends.

Beyond the Math Box: How a Dad Guides His Boy Through the Amazing World of Math

In school when they tell you you have to learn your multiplication table and graph a parabola before you can learn to do real mathematics they are lying to you! - Vi Hart, What was up with Pythagoras?

Well, "lying" is a bit harsh. "Misinformed" is a better choice. But first, a little background.

I'd like to explain how it is that I've been able to teach my son Adam some math concepts that generally only math and physics majors in college learn.

I should warn you that one advantage I have with Adam is that he learns so easily and so well that I don't actually have to be a good teacher, so there is a chance this technique won't work for everyone. But I think it's worth trying.

I don't push Adam when I'm teaching him.  I'm more of a guide helping him to explore his world. I help him to discover things faster, and I lead him to things I think he's likely to be interested in. Sometimes what interests him and what doesn't surprises me. I'll give him a couple of tries and if he's not interested move on to something else.

We'll study each topic to the depth he wants and then move on to something else that interests and challenges him. It's a lot of fun to see how excited he gets sometimes when he learns about a new concept and sees how it interrelates with everything he already knows.

Sometimes he gets "stuck" on something. I don't mean that he doesn't understand, I mean that he'll just be so interested in something that he'll get fixated on it and  want to do it over and over. Sometimes I have to work a bit to get him to try something else.

Learning about other subjects can naturally lead into talking about math (and vice versa). We watched a video on a large telescope and how it has computers that adjust the shape of its parabolic mirror in order to focus it. That naturally led to a discussion about how a parabola is a shape and the properties parabolas have that are useful for a telescope, and that actually led into the topic of the other conic sections.

A lot of people believe that math builds upon itself in a linear tower, and that you have to master each topic before you can start to begin study of the topic after it, but this isn't true. There are actually a lot of different things that don't build on each other nearly that strongly. That means that you don't have to worry about teaching things exactly in the traditional order.

You don't always have to master one topic to understand the things that are based on it, either. Most people couldn't tell you anything about the Peano axioms (arithmetic is based on them), but they are still quite capable of adding two numbers together.

Even when some level of understanding of a dependency is required, it's often not at full depth.

If Adam gets interested in something that requires him to strengthen his abilities or understanding in some prerequisite, it gives him the motivation to do so. For example, Numberphile got Adam very interested in the Fibonacci numbers, and his proficiency in adding multidigit numbers soared because he wanted to be able to compute the sequence on his own.

So he may not have long division mastered yet, but that's ok -- he's six, after all, and he can divide well enough to do modulo arithmetic and convert numbers to base 12, so he's satisfied. He hasn't really needed long division for much other than that. I'm not worried -- he'll pick it up when he needs it.

Obviously, this technique can't work as well in a large group, but I think it's a great way to do individual tutoring for students of any ability level, especially those that have some level of interest in math.