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Yes it is algebra. Take second problem for instance. X + (x + 1) + (x+ 2) = 69. Solve for x.

erroneousfunk 12y ago
I had a little bit of a problem with that question as well. A clever student might just divide 69 by three and take that number, as well as the numbers on either side, as the answer. Is that algebra? Is that not algebra? Is that some sort of more nebulous skill that's also correlated with programming? If they actually wanted to correlate ALGEBRA algebra with programming, I also thought they'd have more straight-forward questions. Using word problems brings all sorts of other issues into the picture.
- relaytheurgency 12y ago
  I would say that it requires algebraic thoughts. You are assigning a placeholder for "x" as "that number that would fit in the middle here". To me, that seems algebraic. Especially at this very, very basic level of algebra we are discussing.
crazypyro 12y ago
Except you are also testing one's ability to set up that problem which is a major key to problem solving ability in the first place? I might agree with you if the problems were already formatted and it was simply plug and chugging algebra and not deciphering word problems.
ludoo 12y ago
Or just recognize that three consecutive numbers mean you divide by three and get the median of the three numbers. So 69/3-1, 69/3, 69/3+1, giving 22, 23, 24. No algebra involved, you just need to interpret the problem and build a tiny model in your head. Exactly like (some kinds of) programming.
- rudolf0 12y ago
  That's exactly how I solved it. I'd consider myself a pretty decent programmer, but I did poorly in algebra and calculus at middle, high school, and university level. Give me "x + (x + 1) + (x + 2) = 69" and I wouldn't know where to start. I could probably turn that word problem into that equation, but I would have no idea how to actually solve the equation algebraically. But given the word problem alone I knew to divide by 3 and add the neighboring numbers. Now, actually dividing by 3 I'd need to use a calculator or spend a lot of time with a pencil and paper, but at least I knew the steps to solve it. I'm awful at rote math and mental math, which is why I'm thankful I can make the computer do it for me.
  - rverghes 12y ago
    Are you saying that if the word problem was "2 consecutive numbers and a third number that was five higher than the second number" you'd be unable to solve it? "Tricks" work for simple cases. Algebra works for all cases.
    - lostcolony 12y ago
      Yeah, I would be unable to solve it, given that I'm pretty sure there is no solution if we assume that "consecutive" implies integers (and I'd be curious what 'consecutive' means if we don't). If instead we made it "2 consecutive numbers and a third number that was five higher than the second number add up to 70" (i.e., 21 + 22 + 27), that's easily solved using 'tricks'. Really, the trick mention (which is what I did in my head, too) is just a rephrasing of the algebra. That is, I would subtract 4 off of the thing that is 5 higher (so that it's now 1 higher; the problem is now the same, get 3 consecutive integers), subtract 4 off of the number I'm trying to get (so 66), so the problem is now 3 consecutive integers that equal 66, and solve the same way (66/3 = 22, so -> 21, 22, 23), and then just add the four back in to the highest (21, 22, 27).
      - rverghes 12y ago
        You're right, my mistake. That "five higher" should have been "four higher". The thing is that your solution is the algebraic solution. You're simplifying an equation by balancing both sides, when you subtract four. Just from our perspective, you simplify to a still difficult state, instead of the easiest possible state. Algebra is just a way of formally stating what you did, and then offering some simplifications that speed up the process. Or offering more powerful methods that making solving more difficult problems easier.
- fragmede 12y ago
  That's still algebra, using the equation (X-1) + (X) + (X+1) = 69 instead.
- analog31 12y ago
  Amusingly, I taught a college math class many years ago. A question on one exam was: x^3 = 27 One student solved it in the following way: 1^3 = 1 2^3 = 8 3^3 = 27 ans = 3 There was a meeting for the teachers to discuss grading standards, and I brought up my student's answer. I got a number of responses: "That's not algebra." "The student obviously doesn't understand the problem." And so forth. Being somewhat of a punk, I asked if any of them had, in their years of teaching, actually taught their students to recognize when an answer is "algebra" or how a right answer of 3 differs from a wrong answer of 3. It wasn't a pleasant discussion. This was a university with a prestigious math department, and I was just some guy off the street. I chatted with my students the next day. None of them had ever been told what it means to "show your work," or any of the other important trappings of school math. They either did it or they didn't. Thinking about it more, I would have sidestepped the issue completely, by changing the problem to: x^3 = 26
- the_af 12y ago
  It seems like you're doing algebra :)
- agumonkey 12y ago
  Found that approach creative and well structured. Point free mathematics :)

I had a little bit of a problem with that question as well. A clever student might just divide 69 by three and take that number, as well as the numbers on either side, as the answer. Is that algebra? Is that not algebra? Is that some sort of more nebulous skill that's also correlated with programming? If they actually wanted to correlate ALGEBRA algebra with programming, I also thought they'd have more straight-forward questions. Using word problems brings all sorts of other issues into the picture.

relaytheurgency 12y ago
I would say that it requires algebraic thoughts. You are assigning a placeholder for "x" as "that number that would fit in the middle here". To me, that seems algebraic. Especially at this very, very basic level of algebra we are discussing.

crazypyro 12y ago

Except you are also testing one's ability to set up that problem which is a major key to problem solving ability in the first place? I might agree with you if the problems were already formatted and it was simply plug and chugging algebra and not deciphering word problems.

ludoo 12y ago

Or just recognize that three consecutive numbers mean you divide by three and get the median of the three numbers. So 69/3-1, 69/3, 69/3+1, giving 22, 23, 24. No algebra involved, you just need to interpret the problem and build a tiny model in your head. Exactly like (some kinds of) programming.

rudolf0 12y ago
That's exactly how I solved it. I'd consider myself a pretty decent programmer, but I did poorly in algebra and calculus at middle, high school, and university level. Give me "x + (x + 1) + (x + 2) = 69" and I wouldn't know where to start. I could probably turn that word problem into that equation, but I would have no idea how to actually solve the equation algebraically. But given the word problem alone I knew to divide by 3 and add the neighboring numbers. Now, actually dividing by 3 I'd need to use a calculator or spend a lot of time with a pencil and paper, but at least I knew the steps to solve it. I'm awful at rote math and mental math, which is why I'm thankful I can make the computer do it for me.
- rverghes 12y ago
  Are you saying that if the word problem was "2 consecutive numbers and a third number that was five higher than the second number" you'd be unable to solve it? "Tricks" work for simple cases. Algebra works for all cases.
  - lostcolony 12y ago
    Yeah, I would be unable to solve it, given that I'm pretty sure there is no solution if we assume that "consecutive" implies integers (and I'd be curious what 'consecutive' means if we don't). If instead we made it "2 consecutive numbers and a third number that was five higher than the second number add up to 70" (i.e., 21 + 22 + 27), that's easily solved using 'tricks'. Really, the trick mention (which is what I did in my head, too) is just a rephrasing of the algebra. That is, I would subtract 4 off of the thing that is 5 higher (so that it's now 1 higher; the problem is now the same, get 3 consecutive integers), subtract 4 off of the number I'm trying to get (so 66), so the problem is now 3 consecutive integers that equal 66, and solve the same way (66/3 = 22, so -> 21, 22, 23), and then just add the four back in to the highest (21, 22, 27).
    - rverghes 12y ago
      You're right, my mistake. That "five higher" should have been "four higher". The thing is that your solution is the algebraic solution. You're simplifying an equation by balancing both sides, when you subtract four. Just from our perspective, you simplify to a still difficult state, instead of the easiest possible state. Algebra is just a way of formally stating what you did, and then offering some simplifications that speed up the process. Or offering more powerful methods that making solving more difficult problems easier.
fragmede 12y ago
That's still algebra, using the equation (X-1) + (X) + (X+1) = 69 instead.
analog31 12y ago
Amusingly, I taught a college math class many years ago. A question on one exam was: x^3 = 27 One student solved it in the following way: 1^3 = 1 2^3 = 8 3^3 = 27 ans = 3 There was a meeting for the teachers to discuss grading standards, and I brought up my student's answer. I got a number of responses: "That's not algebra." "The student obviously doesn't understand the problem." And so forth. Being somewhat of a punk, I asked if any of them had, in their years of teaching, actually taught their students to recognize when an answer is "algebra" or how a right answer of 3 differs from a wrong answer of 3. It wasn't a pleasant discussion. This was a university with a prestigious math department, and I was just some guy off the street. I chatted with my students the next day. None of them had ever been told what it means to "show your work," or any of the other important trappings of school math. They either did it or they didn't. Thinking about it more, I would have sidestepped the issue completely, by changing the problem to: x^3 = 26
the_af 12y ago
It seems like you're doing algebra :)
agumonkey 12y ago
Found that approach creative and well structured. Point free mathematics :)