Thanks for your gracious comment.

One other suggestion, since the swirly is supposed to indicate zero, it should not disappear when touched. You want to illustrate the addition property of zero. Hence, it should disappear only when one brings it over to another card, or when you bring another card to it.

]]>Kfir, the app store version allows 4 profiles maximum. Can you tell us why you would need more ? We are working on a school offer that will allow online profiles e.g. to switch users.

Finally, Henry, thanks for your meaningful feedback. As always, it is taken with great consideration in order to improve our products. We wish you the best with your app! Finding ways to improve the way people learn and perceive Maths is our shared goal!

]]>You used the expression “subtract from both sides.” Can you provide one example where the child uses this principle to solve a Dragonbox problem? Is the child able to swipe a card off either side of the display? He can certainly drag a card to each side, but can he do the reverse?

You mention that the app recognizes that (-5)/(-5) is 1. I stand corrected, as I notice that in 4/20 it recognizes (-b)/(-b) as 1. However, in that same problem, the app will not recognize (-b)/b to be -1. Likewise, it will not recognize (-e)/(-f) to be e/f (see 2/20).

Not only is multiplication by 1 not commutative, neither is addition of zero.The app does not recognize that a + 0 = a. If you try to drag the “a” unto the zero, it will be pushed off. (See 2/11). The app is also faulty in not allowing the user to drag the zero (swirl) unto a card before it makes the swirl disappear.

You mention that in later lessons, the child learns that x + x = 2x. Would you please provide the lesson and example number where you observed this? In going through the full app I did not see this once nor do I see how this is possible using the moves presented by the app.

If your 6-year old can make sense of the statement, “A number when multiplied by 5 equals 7” than he certainly is not a typical child!

You may try giving your child this example: 4x+3=3x+9. Can he solve it? If not, my free app The Fun Way to Learn Algebra: Hands-On Equations 1 Lite will enable him to do so in three short lessons.

]]>Have one or more much-older siblings (9+ years older) who are learning algebra and have a lot of patience for their younger sibling. Add a curious six-year-old (or 5-year-old, or whatever) who is happy to bother said older sibling with questions about what s/he is doing. Mix well.

That said, Dragon Box sounds like great fun. 🙂

]]>kfir you mean more than 4 users? i didnt see any way.

]]>Kfir

]]>In response to your specific points.

1. They pretty quickly learn to multiply all terms and add to both sides as a matter of habit. I don’t see this as a particular weakness of an app. A teacher would also remind the student. What is true is that when a child graduates to paper and pencil they are cut loose from this safety belt and they have a new way to make a mistake. But they learn not to forget.

2. This is where a parent voice over helps a lot. “Oh look its 5 plus y.”

3. You can cancel -5/-5 and you get 1. But you are right that multiplication by identity is implemented only by dragging g the one onto the other card.

4. Not true. In later stages you can add x to x and the app processes it and yields 2x.

To summarize, after a few hours of fun you can say “let’s play Dragon Box with pencil and paper” and the child can replicate all of the operations by rewriting equations line by line and a parent can explain to the child what he’s doing. I said things like “This equation says that x is a number which when multiplied by 5 equals 7. We are going to use the Dragon Box tricks to figure out what that number is. By the way we call those tricks algebra.”

]]>A first point: you say that “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.” This statement may not exactly convey the meaning that once the child has placed a card from below the deck unto one of the two sides, the app freezes until the child places the same card in the required locations as determined by the app. An indentation appears to inform the child where else the card must be placed. Hence, the child can simply follow the app prompts without distinguishing when a card needs to be placed once on the other side vs. when it needs to be placed next to or under each term on both sides.

A second point: even when the pictures change to letters toward the end of the app, the card outlines are still visible. Hence, the child can solve these puzzles just as he did previously without being cognizant of the operations that are displayed. He still may not realize that it is only under the operation of addition (and not that of multiplication or division) that you place the card only once on the other side (even if there are several terms on that side).

A third point: In a number of respects the hidden algebra behind the puzzles is a deficient algebra. For example whereas a day card “divided” by day card will give you the one-cube, the app does not enable you to simplify a night card “divided” by a night-card to also give you a 1-cube. In other words, the app will enable a/a to simplified to 1, but not (-a)/(-a) to be simplified to 1. Likewise, although you can “multiply” a card by 1, nothing happens when you attempt to do the reverse. In other words, it recognizes 1(a) =a but is not “aware” that (a) (1) is also a.

A fourth point: As you point out, the app does not require or use arithmetic. You present the advantages of this feature. On the other hand, this feature prohibits the presentation of simple linear equations which require combining like terms. Hence examples such as 3x + x = 2x + 6, or even 3x + x = 8 are not presented and cannot be solved on this app.

This is not to discourage anyone from purchasing the app. The app is a fun app and its developers showed creativity in its development. However, it is very questionable to suggest that a child is actually learning algebra in using the app, especially since the child does not once solve an equation on his own, without the prompting provided by the app…

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