Have you seen Dragon Box?  Once you do, you will be a believer in the power of technology for learning.  I wasn’t before, I am now. My son is 6 and after about 4 hours of fun he can solve simple one-variable equations.  Here’s how it works.

In the first level of Dragon Box you see a screen with two halves, “This side” and “That side.” There is a box on one side and some cards with random pictures on them.  Your job is to isolate the box on one side, i.e. remove all the cards from the same side of the box.

This is very simple at the beginning because the only cards on that side are these funky vortex cards and all you have to do is touch them and they disappear. Vortex cards represent zero, but only you know that.

Later, other cards start appearing on the box’s side but then you learn something new:  every card has a “night card” which graphically is represented by a card with the same picture but in negative exposure.  Negative.  If you slide a card onto its night card (or vice versa) the card turns into a vortex which you then dispatch with a subsequent tap.

Later again it happens that cards appear on the same side of the box but with no night card.  But then you learn something new. You have cards in your deck and you can drag them onto either side of the screen.  A card in your deck can be turned into its “night” version by tapping.  Thus, you can eliminate a card on the box’s side by taking the same card from the deck, “nighting” it and then using it to vortex the offending card.

But any card you drag from the deck to one side of the screen you must drag to the other side also.  This represents adding or subtracting a constant from both sides of an equation.  After you have isolated the box on one side you have shown that the box equals the sum of all the cards remaining on the other side.  But only you know these things.

Later still, cards appear with “partners,” i.e. another card right up next to it with an inexplicable dot connecting them.  If the box has a partner you can eliminate the partner by dragging the corresponding card from your deck below a line which magically appears below the partners as you drag.

Dragon Box requires that whenever you drag a card from the deck below the line of any card, you must drag the same card below the lines of all card-groups on both sides of the screen. Once you have done that you can drag the card that is below the line onto its duplicate above the line and they together turn into a card with looks like a die with one pip showing.  Such a card can then be dragged onto the box leaving only the box.

Here’s a demonstration (by me of an early level.)

The partners represent multiplication, the line represents division, the die with one pip represents the number 1 (i.e. the identity) and 1 times the box is just the box. After you have isolated the box you have shown that the box equals the sum and/or products of cards that appear on the other side.  But only you know this.

Finally, the box mysteriously becomes the letter x.  The cards lose their pretty pictures and become numbers and other constants.  Night cards are now negative numbers. The vortex becomes zero and the die becomes the number 1.  In the dividing zone between the two sides of the screen eventually appears an equals sign, and all the operations the child has learned now take their more familiar form and by pure sleight of hand he has been tricked into porting the very very simple logic of combining symbolic operations into the otherwise tedious world of “solve for x.”

I personally am astounded.

A few final thoughts.

1. The reason a six-year-old can learn algebra with Dragon Box but could not before is that Dragon Box unbundles algebra from arithmetic.  You don’t have to know what crazy-frog times lizard-fish equals to know that Box = CF times LF.  Simplifying the right-hand-side is beside the point.  Conventionally algebra comes after arithmetic because you need arithmetic to simplify the right-hand side.
2. Actually what you learn from this is that algebra is far more elementary than arithmetic.  My son can add numbers (up to one digit plus two digit) but just barely grasps the concept of multiplication.  He has no idea what division is.
3. Someone who already knows arithmetic can still learn algebra faster (and have more fun in the process) because Dragon Box shows how all the arithmetic can essentially be saved for the very end, modularizing the learning.
4. Dragon box also rewards you if you solve the equation with the precise number of operations recommended.  (This is usually the minimum number but not always.)  This is a clever addition to the game because all of my kids refused out of pure pride to move on until they had solved each one in the right number of moves.  Imagine asking a kid learning algebra to do that.