5 ms·

Watching my kids play DragonBox, methinks a major problem with teaching algebra is the insistence on forcing steps from arithmetic to algebra, bogging down in n

Watching my kids play DragonBox, methinks a major problem with teaching algebra is the insistence on forcing steps from arithmetic to algebra, bogging down in numeric & non-numeric symbols which students have little or no cognitive relationship with at that age. Starting with pure algebraic concepts, devoid of explicit numeric meaning, may be much easier to absorb then transition into meaning-laden symbols.

pbhjpbhj 13y ago
Is that learning mathematics though or is it just learning symbolic manipulations by rote. Yes some rote learning is necessary - and I'd warrant very useful in maths. However, generally in order to build on what you're learning you need to understand why you should perform certain actions. There seems little point in learning to simply mechanically do the actions necessary to solve an equation. It is the meaning that is the reason for doing the learning and I worry that the last transition will be missed and make the entire prologue void of worth.
- ctdonath 13y ago
  generally in order to build on what you're learning you need to understand why you should perform certain actions. Before knowing why you should perform certain actions, it helps to know that you can perform certain actions. Methinks getting these basic concepts ("combine something with its inverse and it disappears", "thing over same thing is 1", "1 'times' something is that something", ...) into a kid's head very early is a good thing - may not yet understand why, but it's a mental tool that can be applied. Don't underestimate the value of having tools even if you don't know why/how they work; give a kid a hammer and he'll figure out it's for pounding nails.
  - pbhjpbhj 13y ago
    >give a kid a hammer and he'll figure out it's for pounding nails. // How old is the kid? I think you'll just end up with everything broken, unless you present it with the nails then the combination of the two is unlikely to happen naturally I feel until the child is quite old (if then).
    - ctdonath 13y ago
      http://steelwhitetable.org/media/images/cavlin-banging-nails-in-table.gif http://steelwhitetable.org/media/images/cavlin-banging-nails... I don't think the basics of algebra will have such results, but both are indeed tools that a kid will figure out a good use for if such tools are on hand and have been played with enough. I could credit a lot of my creative skill to spending inordinate time as a kid just fiddling with a broad range of tools in the basement, regardless of whether I understood them at the time.
sopooneo 13y ago
What you are saying makes a lot of sense. However, I often used that philosophy in my five years of teaching high school math/physics and found that most students had a very hard time transitioning into the symbolic versions of things. Even with exact parallels it was still almost impossible.

pbhjpbhj 13y ago

Is that learning mathematics though or is it just learning symbolic manipulations by rote. Yes some rote learning is necessary - and I'd warrant very useful in maths. However, generally in order to build on what you're learning you need to understand why you should perform certain actions. There seems little point in learning to simply mechanically do the actions necessary to solve an equation. It is the meaning that is the reason for doing the learning and I worry that the last transition will be missed and make the entire prologue void of worth.

ctdonath 13y ago
generally in order to build on what you're learning you need to understand why you should perform certain actions. Before knowing why you should perform certain actions, it helps to know that you can perform certain actions. Methinks getting these basic concepts ("combine something with its inverse and it disappears", "thing over same thing is 1", "1 'times' something is that something", ...) into a kid's head very early is a good thing - may not yet understand why, but it's a mental tool that can be applied. Don't underestimate the value of having tools even if you don't know why/how they work; give a kid a hammer and he'll figure out it's for pounding nails.
- pbhjpbhj 13y ago
  >give a kid a hammer and he'll figure out it's for pounding nails. // How old is the kid? I think you'll just end up with everything broken, unless you present it with the nails then the combination of the two is unlikely to happen naturally I feel until the child is quite old (if then).
  - ctdonath 13y ago
    http://steelwhitetable.org/media/images/cavlin-banging-nails-in-table.gif http://steelwhitetable.org/media/images/cavlin-banging-nails... I don't think the basics of algebra will have such results, but both are indeed tools that a kid will figure out a good use for if such tools are on hand and have been played with enough. I could credit a lot of my creative skill to spending inordinate time as a kid just fiddling with a broad range of tools in the basement, regardless of whether I understood them at the time.

sopooneo 13y ago

What you are saying makes a lot of sense. However, I often used that philosophy in my five years of teaching high school math/physics and found that most students had a very hard time transitioning into the symbolic versions of things. Even with exact parallels it was still almost impossible.