Category: why learn math

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I know that in the last post I mentioned that it is pretty much impossible to explain to immature minds what the benefits of learning math or any other skill is.

But I assume if your a Math Mojo reader, you have a pretty mature mind. (Cool sentence, eh? I get to flatter both you and me at the same time!)

So here are a few examples of concrete benefits I have gained from using “strange powers of the mind.” These are not necessarily the same benefits you will have. Everyone will experience different benefits. (Mileage may vary.)

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That the heck does writing backwards have to do with math?

For me, it’s a sort of warm-up exercise to get me into the creative, non-judgemental flow of opening my mind. This helps let answers come to me that my mind would otherwise have blocked out. It makes thinking less of a chore and more of a “party in my mind.”

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While surfing some of the other math blogs in the blogosphere, I ran across a post in Michael Paul Goldenberg’s Rational Mathematics Education blog. Rational Math Ed is a gem of a blog, and is a must if you are a public school teacher or administrator.

In a recent post of his he mentions an article written by Paul Lockhart entitled, “A Mathematician’s Lament.” It was written in 2002, but has only gotten mass coverage recently, since it was featured on a post at the website of Keith Devlin.

For those of you who don’t know Keith Devlin, you are in for a treat. His writings are among the most lucid you will ever read about math. He makes very complicated things easy to understand. Please do yourself a great favor and visit his website.

You may have heard his lilting voice on NPR as “The Math Guy.” Devlin has also linked to Lockhart’s article, which is available as a free PDF download.

If you have any interest in math at all, even if you are not an educator, you will truly enjoy the enlightening thoughts that Lockhart shares with you. His appreciation, and enthusiasm for math, and teaching it are joy to read.

So take some time and revel in the passion Lockhart will enchant you with. Download the article now from the bottom of the post at Devlin’s site.

Please read both the Goldenberg and the Devlin essays about the article. They say everything I’d want to say, only better.

(Continued from the previous three posts.)

the reader replied to my answer:

thank you professor for answering all of my future qustions, but u never answered my old answer though. What happens if i fail math 9 of coruse ill be end up in emath10 whats emath10 (doesn’t sound good though)Like do i get to go to collage but if u can’t answer that qustion ill ask someone else. Heres a qustion for you though what good paying job are there in this world without math like doesn’t require math because u told me everything involes math. but i am asking you to name some jobs thats don’t require math as a requirement. I am asking you all these qustions because i am scared the world might be a different place when i grow up so i am just prepareing for the future.

Professor Homunculus’s reply:

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(Continued from the previous two posts.)

the reader replied to my answer:

thank you, that really help me but all the jobs your listed are basic math i can do that in my head. But the schools are teaching me alot of bullshit which i don’t know alot about i think there lessons are useless.i guess u need math for everything but can’t we just use techonology like a caluator to help us?

Professor Homunculus’s reply:

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“When I look back on all the crap I learned in high school
It’s a wonder I can think at all.”
- Paul Simon “Kodachrome”

(Continued from previous post.)

the reader replied to my answer:

Dear Professor Homunculus,

remember me my teacher sucks he doesn’t teach.But i am not a lazy sob student i am passing every class i hate math, maht is so gay what name some jobs can i get without math?

-Truman

Professor Homunculus’s reply:

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In 2000 an 2001, I was an “expert” on a website that helped kids with math problems. Most of them concerned problems they were having in school.

I’d like to publish some of the exchanges I had with some of the kids. I must mention some “warnings,” though.

1. These questions were asked by real kids, struggling with real problems. They express themselves like real kids. I appreciated that, sometimes. The grammar and spelling is generally miserable. I am going to try not to edit them. I think it’s important if a kid writes, “I want to mulily by too,” that the form of writing gives you several clues to what’s going on. Sometimes.

 

2. The answers were given by a real person (me.) I do not intend to bowlderize anything. There is quite a bit of swearing in them. Why? Because I tend to do a lot of swearing, especially at hypocrisy. Since the questions had a lot to do with schools, there was a lot of hypocrisy to swear at. I’ll try not to go overboard with it, because on this blog and in Math Mojo in general, I try to keep it to a minimum.
   (When we I publish as Joe Archimedes - Hard-boiled Substitute Teacher, the gloves will be coming off, though).

The real reason I am publishing this stuff, is to “speak truth to power.” If administrators feel offended, well…

I feel that there are a lot of parents, teachers, and especially kids out there who have always suspected the things I’m going to say are true, but haven’t heard it expressed. I think it will help to read it.

So here goes nothing…

I’ll be breaking up this post into parts. Here is the first exchange:

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I read an interesting post by a student writing for his school newspaper, today. It prompted all kinds of thoughts.

The post inspired me to write a long comment to it, which you can also read at the above page (if you’re bored).

Combined with having watched the great Isaac Asimov’s “I, Robot” on the tube last night, I was prompted, once again, to consider what computers, calculators, the tube, etc. are doing to us, as a global society.

Obviously, considering the medium we are using, I am not a Luddite. Far from it. I like tech. But I like it to further my understanding and appreciation for life, not to nullify it.

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Hey, you droogs,

There was an interesting post on the Whallah! blog about an article in the Associated Press,
http://news.yahoo.com/s/ap/20080626/ap_on_go_ca_st_pe/teaching_math;_ylt=Apnza3sjYQ1Rx08Q5.nf0IOs0NUE
concerning the education of math teachers in public schools.

Apparently the National Council on Teacher Quality has done a comprehensive study to come to the conclusion that everyone who is not an “expert” has known for years: Teachers are not being taught math adequately, and generally fail to teach it well to their students. (Do tell…)

Isn’t it funny that the “establishment” will never admit that? It takes an expensive academic “study” to show what is already known, yet Universities (in general) will not do anything about the way they teach teacher how to teach math. They will try some new, expensive methods that some textbook company has lobbied for, of course. But they won’t try anything that might actually work.

That’s why homeschooling and afterschooling are becoming more and more important. Taking an interest in your own child’s education is more important than ever, as public schools tank in their ability to actually teach, thanks to the natural entropy of society, and the idiotically simple-minded ways some people like to deal with it, as with the subtly(?) sardonically named “No Child Left Behind” act.

According to the AP article:
Author Julie Greenberg said education students should be taking courses that give them a deeper understanding of arithmetic and multiplication. She said the courses should explain how math concepts build upon each other and why certain ideas need to be emphasized in the classroom.
Teacher candidates know their multiplication tables, but “they don’t come to us knowing why multiplication works the way it does,” said Denise Mewborn, who heads the University of Georgia department of math and science education.
This is the key to most of what every student needs to know - how multiplication works. Addition is almost intuitive. It is an extension of counting. Once you extend addition to multiplication, though, you need a good understanding of how the base ten system works, and the commutative, associative, and distributive laws. You don’t need to know the names of those laws, of course, but you need to understand how to use them in order to understand multiplication.

That’s the big issue. Just being able to recite multiplication tables is not actually being able to understand multiplication. And just going through the motions and repeating math steps that a teacher has “taught” you by show-and-tell methods, so you can prove that you can jump through the hoops for the big test at the end of the year usually does more damage to your understanding that anything.

So what is there to do about it? First, as a truly concerned parent or teacher, make sure you, yourself understand some of the nuances of multiplication. Like why when you multiply by a fraction, the product is smaller than the multiplicand. (Did I get you with that one? Leave a comment below requesting the Math Mojo take on that one, and I’ll cover it in a new post).

Second, make sure you have at least two ways of explaining to your students how multiplication works. Not just how to do it, but how it actually works. I’m working on a video series about this now. Send me a nudge (again, in a comment below) to make it a higher priority to get it done and available to you faster.

Third, make sure you have a way to assess if your child or students understand what you taught them. The assessment doesn’t have to be a test. Tests are more about beating kids over the head. Asking questions and asking to demonstrate, in a non-threatening way would be my first strategy. If you must beat someone over the head, start with someone in an administrative position.

Here’s one of the reasons why:
According to the AP article:
Since states oversee the preparation of the nation’s school teachers, the report recommends they set tougher coursework and testing standards.
Why is does the solution always involve browbeating the learners? Why are the words “tough” and “testing” so often involved? How on earth does that teach or inspire? The problem isn’t that, “those who can’t do, teach.” The people who run those studies and teach university level education courses usually can do the math they are supposed to teach quite well.
The problem is that “those that can’t teach, teach.” Then they “train” teachers, instead of teaching them. No wonder those teachers have problems teaching. And no wonder the
As I always say, look up when you look for where the problem lies. You can’t blame a third grader for not learning (unless there is neurological damage, of course). If it’s behavior problems, there might be an issue beyond the teacher’s scope, but most behavior problems are dealt with by good teachers.
But beyond those things, start looking up the chain for someone who needs the butt-kicking. If the teacher can’t teach, were they taught well? (Are they even allowed to teach well in that school?) If the teacher’s teacher can’t teach, were they taught well? Is their administrator constantly putting monkey-wrenches in their teaching techniques? Is something going on at the School Board mucking up the school? Is the State requiring more tests, but providing less resources for teachers and students?
Keep looking up. Here’s a hint: Besides the handicapped, who’s got the parking spot closest to the school entrance? Start with him/her.
Remember, when things are looking bad, begin to look up.
I hope to hear from some of you soon,

Brian (a.k.a. Professor Homunculus)

“Why do I need to know fractions? Square roots? Algebra or geometry? I mean, why do we ever even need them in real life? I am never going to be a mathematician, and I hate math. So why do I have to learn this?”
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