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I'm going to have to go ahead and agree here. As a homeschooler, I can attest that the teachers' guides for teaching math are very, very self-explanatory. If you can read, you can teach elementary math. I find it disconcerting to think that there are people who believe that teaching first through fifth grade math is too hard for the average teacher. Do you really think that the average person, college-educated or not, is so woefully unprepared that they don't understand how multiplication works? This is not rocket science, LOL.
I find it disconcerting that there are so many elementary school teachers who limit their students by not going deeper into the math themselves, and who think it's okay to "teach the book."
Most teachers can "get by" and teach kids to "get by." Is that enough? I have seen that kids are capable of doing much more when they aren't held back by "good enough" teaching.
From your posts, it sounds like you have a find job with the homeschooling (different topic, different thread). My comments come after 22 years of teaching at schools and working with other teachers and hundreds of children, after being asked by administrators to help improve the overall math program, chairing the math committee, and after being frustrated by teachers who think they are doing well enough because they are teaching by the book.
I was also the middle school teacher who got to deal with kids who had been taught by these credentialed teachers (fine teachers, too, for the most part).
So, using an example from my other post, if the book says 6 to the 0 power is 1, and the kid says, "Shouldn't it be zero? Why is it one? And why is 6 to the 0 power the same as 3 to the 0 power?" would you say, "Look, it says it in the book."
The book will give you enough information to do the problems presented. For some kids, that's enough. It must have been for yours. But no elementary text has the answers to all the questions kids have. That is why the teacher needs to have a thorough understanding well beyond what is being taught.
Math makes sense. A good teacher needs to be able to communicate that to the students - both as an attitude and in specific problems.
Again... this is just fearmongering untruths made up. I live with a kindergarten teacher who teaches advanced math to her kids. She never loved math, but she loves teaching.
Besides that, the textbooks are so specific that any college graduate could teach them,
Zarathu
I'm glad for every teacher who teaches beyond the book. It sounds like that's what your wife (?) is doing.
But why do I have to know what 6 to the zero power is? TBH, I didn't know it was 1. Is it really 1, same a 3 to the zero power? I'm a lawyer and quite good at trial work, and have never needed to know this kind of stuff (and if my kid asks why is it important, not sure I'd have a good answer). So help me out here - I'm just trying to wrestle with what difference 3 or six to the zero power makes?
1) In this day and age there are TONS of internet based resources to help teach kids math. The ALEX program I've had both of my kids doing on and off at home. I've also worked some with them 1 on 1 explaining things and they have good teachers. Both of them are 99.8%tile or so at math for thier grade level.
2) Especially in some small towns, the quality of math education...like any topic can be hit or miss.
3) No Child Left Behind, unless your school has accelerated programs your kid managed to get into....means that math is being taught to many kids at a "lowest common denominator level" anymore. Again, with all the web resources I think you have to be taking advantage of them to learn all kinds of things like physics, history, chemistry etc.
But why do I have to know what 6 to the zero power is? TBH, I didn't know it was 1. Is it really 1, same a 3 to the zero power? I'm a lawyer and quite good at trial work, and have never needed to know this kind of stuff (and if my kid asks why is it important, not sure I'd have a good answer). So help me out here - I'm just trying to wrestle with what difference 3 or six to the zero power makes?
I work with math for a living and things like this may never come up.
Let me put it to you another way, you may have taken a law school class or two where you covered stuff that you will never use as a lawyer? However, you might use other things from the course quite often?
In your specific example I believe you are dwelling too much on a specific point of a function.
Graph, y = 3^x and y = 6^x for values of x ranging from -/+100
Distictly different curves as the values grow >1 at at the point where x=0 the lines cross.
I almost never use this kind of stuff but engineers, physicists etc. probably do.
But why do I have to know what 6 to the zero power is? TBH, I didn't know it was 1. Is it really 1, same a 3 to the zero power? I'm a lawyer and quite good at trial work, and have never needed to know this kind of stuff (and if my kid asks why is it important, not sure I'd have a good answer). So help me out here - I'm just trying to wrestle with what difference 3 or six to the zero power makes?
The questions is: Is it useful for a math teacher to know? It has nothing to do with the average layman. The argument is that a teacher in any discipline should know his or her subject in depth (more than what's written in the textbook). A good teacher should be able to explain a concept several different ways using different examples, analogies, etc. depending on the student he or she is teaching.
It's particularly challenging in elementary schools as primary ed teachers tend to be generalists and may not have a strong background in a particular area.
But why do I have to know what 6 to the zero power is? TBH, I didn't know it was 1. Is it really 1, same a 3 to the zero power? I'm a lawyer and quite good at trial work, and have never needed to know this kind of stuff (and if my kid asks why is it important, not sure I'd have a good answer). So help me out here - I'm just trying to wrestle with what difference 3 or six to the zero power makes?
Yes, it is really one... The thing is that exponents follow patterns just as many other mathematical things do. You may never need to know the answer to some problems, but a math teacher should understand why this works.
Here's the explanation with a single number, but it works for any number and you can do this with n instead of a specific number.
6^2 = 6*6 which you already know
6^3 = 6*6*6 which you already know.
6^4 = 6*6*6*6
You know if you do a division problem like
6^4/6^2 = 6^(4-2) = 6^2 right?
try this.. 6^2 = 6^2 (right?)
divide both sides by 6^2
so 6^2/6^2 = 1 because anything divided by itself is 1
The rule for exponents says then that 6^(2-2) = 1
or 6^0 = 1
Yes, it is really one... The thing is that exponents follow patterns just as many other mathematical things do. You may never need to know the answer to some problems, but a math teacher should understand why this works.
Here's the explanation with a single number, but it works for any number and you can do this with n instead of a specific number.
6^2 = 6*6 which you already know
6^3 = 6*6*6 which you already know.
6^4 = 6*6*6*6
You know if you do a division problem like
6^4/6^2 = 6^(4-2) = 6^2 right?
try this.. 6^2 = 6^2 (right?)
divide both sides by 6^2
so 6^2/6^2 = 1 because anything divided by itself is 1
The rule for exponents says then that 6^(2-2) = 1
or 6^0 = 1
Again, yes, I do. Talk to a few random people. A LOT of college educated people don't understand math. Teaching math is more than "just the facts, ma'm".
I agree; however, frustrating younger children by attempting to give them more than one simple way to do it and not allowing them to master that before they find another (in my experience anyway) can backfire. That's when parents start to hear the dreaded "I hate math! I'm stupid!" etc. etc. I like the part where they are trying to get them to understand vs. memorize, but I have a real problem with the pacing and spiraling aspects of it. Most of the time they don't have time to play the games that are supposed to help them learn their facts, and therefore, they don't.
Also, many of the newer programs hand them manipulatives and say 'figure it out" (more or less) and when a parent tries to help, they are often told by their children that their teachers told them "Don't ask your parents for help because they won't know how to do it."
Schools want parents to be more proactive in their child's education which is a good thing; however, it's nearly impossible for many parents to relearn how to do it when they have a measly so-called "reference book" that doesn't have clear steps how to show them.
I think it's still a crime the way its being taught. The sad fact is, most schools are failing at teaching math. And not just at the op's school, but at lots of schools. This topic comes up enough that it doesn't apply to one school.
-Part of the problem is the way schools box you in, into one very strict, rigid, orthodox way of thinking. "Sink or swim". Why? Why does it have to be sink of swim. "Not having time" shouldn't be an excuse.
Kids are in school for 12 years!! 9 months out of the year. They have plenty of time. Don't penalize kids who want to learn, but don't understand it right away. Why does school go "too fast", if you have so much time available? 5 days a week, plus after school, plus winter or summer break. Is the sink or swim policy aimed at the underachievers of math? Or is it aimed at all kids, to push them to unrealistic goals (like everyone graduating on time, or everyone getting the right test score)?
-I dont think kids even understand the basic outline of "reason why". In advertising and sales, there's this concept called "Reason why". If you give people reasons why you're doing something, its more believable. There have been lots of studies and experiments done.
But that information is sort of cordoned off from math. Math is seen as a memorization reflex. There's no deeper logic taught.
Sort of like being taught to play piano. You can memorize how to play certain keys, like hitting the keys for "mary had a little lamb". But that's different than knowing how to read music.
I did ok in math in highschool, but I think a lot of mental blocks come from being rushed too fast through a subject. Mental blocks in a subject I dont think are natural. I think they come from being repeatedly exposed to something that you don't understand, or you don't fully process. Like seeing a slide show on a wall filled with half an answer. If you see that slide, again, again and again....then that's what will be imprinted in your mind. Half an answer.
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