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OK, and I can see where I would have run into problems.
The first:
That would not occur to me naturally. I would not think "I have to get rid of the 4" on my own as a first step. This is an example of the mechanics, if you will, that would have to be specifically taught to someone like me to whom this not come naturally, yet I don't recall anyone ever teaching anything that specific about algebra. It is likely assumed by math teachers that it is obvious, but it is not obvious to me.
I don't think you are alone there. I have a set of balance buckets that I use for tutoring and will put a weight and 4 pennies on one side and then 4 pennies plus however many more pennies I need to balance the thing out on the other side. Then explain that we want to know how many pennies that weight is equal to and that seems to make the idea of "get rid of the 4" more intuitive since it is very concrete, visual and hands on. I've found that helps a lot with kids that are struggling and for my kid that is quit gifted, threatening to pull them out helps his concentration and writing down steps.
Thank you. Can we explore this a bit? I do think that's where math starts to break down for a lot of people. If you prefer not, that's fine.
Oh no, I don't mind at all. I look rather fetching in a dunce cap. Seriously, it has bugged me on and off all my life that the ability to grasp this was something I felt was missing from my brain.
Quote:
Originally Posted by tnff
That's a great way to explain it. Most everyone automatically knows how a teeter totter works and what happens if the kid on one side gets off before the other.
Except that with algebra, there's a kid on one side and a kid and some other identified object on the other side and you are tasked with trying to guess what that might be.
Quote:
Originally Posted by turf3
Well, it's not intuitively obvious that the next step would be to subtract 4 from both sides. That's why it took 50,000 years after humans first learned how to count and add and subtract, for the Arabs to invent algebra in about 1000 AD.
What it is, is a technique or tool, to solve for an unknown. There are a whole set of these techniques or tools, which you are taught in algebra class. You can multiply both sides of an equation by the same thing, you can add or subtract the same thing from both sides, you can raise both sides to a power. The quadratic equation allows you to solve for X when presented in the form ax^2 + bx + c = 0. And so on, and so on.
The purpose of algebra class is to teach you a) how to set up a mathematical problem in a format that can be solved by certain tools; and b) how to use that set of tools to solve the problem.
Unfortunately this underlying concept is not often communicated, and teachers launch into instruction on the use of the tools without explaining what they are or why you're going to use them. Honestly, in my experience, math teachers especially in grade school were amongst the least effective teachers at explaining WHAT we are doing and WHY we are doing it, at least in a way that I could grasp. The first sentence above is why the "discovery method" of teaching math doesn't work for most people. Do they really expect that an 8th grader, who's not overly interested in the subject in the first place, will discover in his Thursday night homework session, what it took generations of Arab mathematicians to figure out? Just teach us the damn tools.
Well, where were you in 1972 when I was sitting in math class feeling completely lost from Day One? It might have helped if someone had explained that you were following a set of rules that you had to learn that were NOT intuitive, rather than me thinking that this there was some sort of logic that other people somehow seemed to instinctively understand while I did not. You seem to be saying that this is something that must be LEARNED by being specifically taught rather than figured out by looking at it, correct? Unless you are John Nash or somebody. At least I always wear my seat belt.
I'm having flashbacks of reading a story of a woman who was illiterate well into adulthood. She had learned ways to get around it, such as telling a friend she was nervous about driving when she had to go somewhere new and couldn't read directions, so she would do a dry run in advance and have the friend read the directions and then memorize every turn and landmark along the way so she could find it herself next time.
That's how I passed HS algebra. My friend would rattle through these steps and show me on paper, and I would take a picture of the paper in my mind and then copy down what she had written onto my own paper. Barely passed, but I passed.
When the illiterate woman finally admitted her lack of ability to read and enrolled in a literacy class at the age of 40, she was shocked to find out that letters represent sounds. She always thought you had to memorize all the words, as if they were pictures. Because of a divorce, she had moved multiple times in first and second grade and never learned the basics of the alphabet. I feel like she did.
THIS IS WHAT I MEAN!!!! How is that the next step? How is it logical to decide that this is what you do? It's not one bit logical to me. It would never in a million years occur to me to write what you wrote on the second line.
Ok, think of a scale.
if you have 4+x on one side of the scale and 5 on the other, how do you get the x on one side of the scale and what would have to balance it.
You need to move the 4 by subtracting 4 from each side to keep the equation in balance.
Oh no, I don't mind at all. I look rather fetching in a dunce cap. Seriously, it has bugged me on and off all my life that the ability to grasp this was something I felt was missing from my brain.
....
I'm sorry, I was not at all trying to imply that. Rather I was hoping to explore what makes that initial step into algebra a roadblock.
Quote:
Originally Posted by Mightyqueen801
...
Well, where were you in 1972 when I was sitting in math class feeling completely lost from Day One? It might have helped if someone had explained that you were following a set of rules that you had to learn that were NOT intuitive, rather than me thinking that this there was some sort of logic that other people somehow seemed to instinctively understand while I did not. You seem to be saying that this is something that must be LEARNED by being specifically taught rather than figured out by looking at it, correct? Unless you are John Nash or somebody. At least I always wear my seat belt.
....
I believe this is where much of the early problem happens. If you aren't taught/don't get those basic rules up front on day one, then things fall apart quickly because everything that happens afterward builds on more complex combinations of those basic rules. That's why memorizing doesn't work; there are simply too many possible combinations of how numbers can be put together to memorize all of them, especially considering you can't memorize what you haven't seen before. Kind of like solving a puzzle. At first it's just a box of pieces but as you work with them you see there are patterns -- this one is green with blue and some yellow and it has a tab. So I need to find a piece with some green and blue and a bit of yellow and a slot for the tab to fit in. Oh, it's going to be a sunflower field.
So funny. I had never seen that before I used the teeter totter in my post!
We used that to teach equations to prek, K and elementary school. It was concrete and they could actually take blocks off one side of the scale or balance board and see if it would still balance.
We used that to teach equations to prek, K and elementary school. It was concrete and they could actually take blocks off one side of the scale or balance board and see if it would still balance.
Yep. I taught equations to second graders using a balance scale.
Things like 4x+26 = 8x + 18
Kids are amazing.
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Seriously, it has bugged me on and off all my life that the ability to grasp this was something I felt was missing from my brain. 
