Title
#share-your-work
Kartik Agaram

Kartik Agaram

05/03/2022, 6:04 PM
Shower thought after chatting with @Jack Rusher: we delay teaching kids geometry until we can trust them not to poke someone's eye out with the pointy end of a compass. Here's a little program to do compass-and-straightedge geometrical construction on a computer: https://gist.github.com/akkartik/20a0c7e7589c6179666fc78bc04b28b4 Pictured below: constructing a second line (in black) parallel to a given line (red) passing through a given point.
i

Ivan Reese

05/03/2022, 6:24 PM
Aside:
we delay teaching kids geometry until we can trust them not to poke someone's eye out with the pointy end of a compass
That... can't be true!? That beggars belief! It's a cute story, but there are countless geometric things that kids learn long before they get to play with compasses.
6:25 PM
Also, any way I can see this program in action without installing Love2d? (Edit) Oh wait — we have a sponsor for that.
Kartik Agaram

Kartik Agaram

05/03/2022, 6:27 PM
I can record a little video later today 👍🏼 Whoa, Replit handles Love2d?!
6:29 PM
And yes, it's a shower thought 🙂 I found myself wondering why we delay geometry until or after algebra. It's a great way to sneak math in the back door.
i

Ivan Reese

05/03/2022, 8:26 PM
Yeah, AGG is the GOAT
Mariano Guerra

Mariano Guerra

05/03/2022, 8:36 PM
Kartik Agaram

Kartik Agaram

05/03/2022, 8:46 PM
"You can modify its own source code while using it." 🤯
10:35 PM
@Ivan Reese Did you get it working on replit? I couldn't. No errors on the console or anything. Maybe I need to type something into the right side after I hit the Run button?
w

wtaysom

05/04/2022, 2:00 AM
I like Dragonbox Elements https://dragonbox.com/products/elements. It's not about geometry, not really; but it does two related things: (1) Categorizing objects based on their properties e.g. a quadrilateral is a figure with four strait sides, in a trapezoid one pair of sides is parallel, in a parallelogram both pairs of sides are parallel. (2) Constraint propagation e.g. line a is parallel to line b, line b is parallel to line c, so line a is parallel to line c.
j

Jack Rusher

05/04/2022, 6:40 AM
@Ivan Reese My contention in the conversation @Kartik Agaram mentioned was a bit differently shaped. Basically, I think almost all real mathematical intuition is geometric in character and we do people of all ages a disservice by teaching them notation and algebraic procedures for manipulating symbols without developing their intuition.
Mariano Guerra

Mariano Guerra

05/04/2022, 7:58 AM
"One of the ways Papert used Piaget’s ideas was to realize that young children are not well equiped to do “standard” symbolic mathematics until the age of 11 or 12, but that even very young children can do other kinds of math, even advanced math such as topology and differential geometry, when it is presented in a form that is well matched to their current thinking processes. The LOGO turtle with its local coordinate system became a highly successful “microworld” for exploring ideas in differential geometry."
Kartik Agaram

Kartik Agaram

05/04/2022, 8:11 AM
Oh yes, @Jack Rusher bears no blame for my brain farts in the shower. One epiphany I had after our conversation (again don't blame him, though!) is that text vs visual/graphics is not a very useful framing. What matters is grammar and geometry.