Comments on: [LOA] The Place Where Language And Math Make Friends /2012/loa-the-place-where-language-and-math-make-friends/ less helpful Sat, 18 Aug 2012 04:21:55 +0000 hourly 1 https://wordpress.org/?v=6.8.2 By: Why that blog title you ask? « JUST TELL ME THE ANSWER /2012/loa-the-place-where-language-and-math-make-friends/#comment-492439 Sat, 18 Aug 2012 04:21:55 +0000 /?p=14587#comment-492439 […] was like they were demanding that I not skip any steps on the ladder of abstraction.  Got em right where I want em   Let’s start doin’ some […]

]]> By: Abstraction in Language and in Math « Let's Play Math! /2012/loa-the-place-where-language-and-math-make-friends/#comment-485022 Sat, 04 Aug 2012 15:36:39 +0000 /?p=14587#comment-485022 […] [LOA] The Place Where Language And Math Make Friends […]

]]> By: dy/dan » Blog Archive » [LOA] The Place Where Language And Math Make Friends /2012/loa-the-place-where-language-and-math-make-friends/#comment-484745 Sat, 04 Aug 2012 02:38:26 +0000 /?p=14587#comment-484745 […] Bruce James: When my students complain that I’m smarter than them, I counter that I’m just at a higher level of misunderstanding. […]

]]> By: Aaron C. /2012/loa-the-place-where-language-and-math-make-friends/#comment-478234 Wed, 25 Jul 2012 22:03:01 +0000 /?p=14587#comment-478234 so mathematics is a language and abstraction is a key in any language. In math, quantity -> number -> numeral … in a spoken language like English, object -> sound -> letters/words … same basic process (concrete -> concept used for reference -> symbol ???) right? you move up the ladder of abstraction even further by noticing these human activities seem equivalent …

not that you all aren’t busy or anything, but here are some books that I feel like are related and interesting (edutainment purposes not scholarly journals)

The Math Gene: How Mathematical Thinking Evolved And Why Numbers Are Like Gossip by Keith Devlin {changed the way I thought about math}

Stuff of Thought: Language As A Window Into Human Nature by Steven Pinker {had some applicable bits if I recall correctly}

Where Mathematics Comes From: How The Embodied Mind Brings Mathematics Into Being {currently reading}

It looks like significant previews (if not the entire book) of each of these is on Google Books. I would have loved an undergraduate course where something like this was the reading list; and yes, I like book subtitles. I’d be interested in other people’s thoughts on these works or other suggestions … not that I’m trying to perform a hostile takeover of the comments here or anything.

]]> By: Joe /2012/loa-the-place-where-language-and-math-make-friends/#comment-477487 Tue, 24 Jul 2012 21:58:29 +0000 /?p=14587#comment-477487 I can’t help but be reminded of the “Van Hiele” levels of abstraction which deal specifically with geometry. I was exposed to this interesting research because it is cited as a basis of Michael Serra’s Discovering Geometry curriculum. In that context, he tried to address the assumption made by the standard high school geometry curriculum that all students were ready for the abstraction known as proofs. I’m not aware of a direct analogue to algebra, but I’d be interested to hear about it.

]]> By: dy/dan » Blog Archive » [LOA] Abstracting Abstraction /2012/loa-the-place-where-language-and-math-make-friends/#comment-477478 Tue, 24 Jul 2012 21:29:16 +0000 /?p=14587#comment-477478 […] I mentioned previously, I find the verb "abstract" way more interesting than the adjective "abstract." The adjective is […]

]]> By: blaw0013 /2012/loa-the-place-where-language-and-math-make-friends/#comment-477257 Tue, 24 Jul 2012 15:05:21 +0000 /?p=14587#comment-477257 @Bruce Brilliant!

]]> By: Steve /2012/loa-the-place-where-language-and-math-make-friends/#comment-477022 Tue, 24 Jul 2012 05:55:19 +0000 /?p=14587#comment-477022 Since you mention the abstraction of a chair, you might enjoy the musings of an interesting philosopher named J. Krishnamurti, who used to ask his students to point out a chair in the room, and then having done so, would complain that they didn’t point to a chair they pointed to some strangely constructed wooden object. A chair is an abstraction. Then he would ask again, and they would refrain from pointing, and he would say that any child could see that was a chair over there, and any fool could sit on it.. I think he was trying to get at a similar point that you are — that abstractions sit at different levels in some ladder of consciousness.

You can read some of his conversations here: http://www.jkrishnamurti.org/krishnamurti-teachings/view-text.php?tid=41&chid=1

]]> By: Bruce James /2012/loa-the-place-where-language-and-math-make-friends/#comment-476152 Sun, 22 Jul 2012 20:02:26 +0000 /?p=14587#comment-476152 When my students complain that I’m smarter than them, I counter that I’m just at a higher level of misunderstanding.

]]> By: Iain Mackenzie /2012/loa-the-place-where-language-and-math-make-friends/#comment-475965 Sun, 22 Jul 2012 12:44:43 +0000 /?p=14587#comment-475965 Have a look the work done by David Tall On cognitive development (http://homepages.warwick.ac.uk/staff/David.Tall/themes/cognitive-development.html)
His body of work is vast in trying to understand how we acquire mathematical thinking. I find it speaks a lot to the process of moving up and down the ladder and acquiring the ability to connect abstraction at different levels. His whole work is inspiring and helps me to understand why some students progress and others get stuck on a specific rung.

]]>