My #math Mastodon peeps. These days school doesn't emphasize teaching logic and proofs, like they did when I took plane geometry which was really about proof and not really about triangles and such.
Does anyone have suggestions for modern resources I could assign my kids to do beginning proofs? One kid is studying calculus in 7th grade the other is in more normal speed, studying basic algebra. I'd just like to give them maybe a problem a week to prove something but in a thoughtful way.
It doesn't have to be plane geometry but if it was that'd be fine too. I'm imagining a workbook with example problems and then do one for yourself... Or some such thing. Obviously you also need some axioms and some basic theorems. That's why geometry is usually used. The axioms and theorems are not too abstract.
@dlakelan
Euclidean Geometry is great to start out with because the theorems and axioms tie in observation with operation from the get-go. The reasoning behind establishing the theorems and axioms is important to grasp even before you attempt all the abstract rules in algebra.
Having a grasp of what constitutes a valid theorem or axiom prepares a student to grasp how to discern from valid equivalents/operations from false equivalencies--which underscores how important proofs are AND checking your work before you hand it it AND understanding why an instructor insists that you "show your work".
@ClaraListensprechen4
I'm with you 💯
What do you like as a resource for teaching it? This is more or less as a "home supplement" to public math education by a dad with a BS in math and a PhD in engineering. Surely there's a good textbook/workbook combo or something? Maybe with a little gamification using geogebra or something?
@dlakelan
I don't have a single resource recommendation, sorry. I wish I could remember the specific text I learned geometry with in high school decades ago--it was quite clear, beginning with definition and properties of a straight line, and progressed from there.
Incorporating algebra alongside Euclidean geometry would be something of a hybrid teaching method; what I had in mind was Euclidean line, then next linear equations because the mental picture would remain fresh.
Euclidean planes, then corresponding algebraic equations incorporating the plotting on a graph. While still in algebra, go to quadratics and explain those with Euclidean solids and conic sections.
I reeeealllly don't think there's a single text that teaches things that way, but I think you get the idea. Staying mentally in touch with the visual representation of the algebraic abstractions goes a long way towards information retention, I think.
