impactology

impactology, 6 days ago

"Traditional curriculum designers butcher mathematics the way colonialists used to divide conquered continents: with crude and clinical cuts that are profoundly insensitive to any and all organic connections between the constituent parts"

"Such an approach makes sense for those who take their own authority for granted. Intellectual Mathematics does not use such totalitarian techniques. Borders are not drawn where they do not belong and organic connections are respected"

In traditional mathematics, when facing a new concept, the goal is to reach the requisite results without making any technical errors. Crossing the t's and dotting the i’s are the alpha and omega of traditional mathematics. Traditional mathematics is anti-human. It fetishises robotic manipulation of symbols and involves no emotions except a crippling fear of genuine and free human thought. In traditional mathematics, the character and bulk of any given proof usually has next to nothing to do with why that particular theorem is true and every- thing to do with incidental technicalities. Students soon get the hint that mathematics is not about actually thinking and trying to figure stuff out; rather it is clearly a formal game completely divorced from common sense. Indeed, formal proofs are sometimes accompanied by an informal heuristic argument, only to be followed immediately by the admonition that “of course this is not a proof!” Much more than giving the student some shred of intu- itive insight, such passages convey more than anything that honest thinking is futile and impermissible in mathematics because a proof only counts if it is packed with technical jargon that has nothing whatsoever to do with the specific matter at hand.

impactology, 6 days ago

"Mathematics is not severed from physics, nor differential equations from calculus, and so on, regardless of the administrative efficiencies of such compartmentalisation"

"You do not read every other line of a Shakespeare play in one class, and then the remaining lines in another class the following year. But in mathematics we routinely do precisely this. Such an approach is incompatible with intellectual respect for the students"

impactology, 6 days ago

"In traditional mathematics, things are taught because they are replicable and testable. The teacher is so dependent on the drillmaster paradigm that only topics that fit it can be taught"

"If a topic doesn’t allow for fifty-eight near-identical drill problems at the end of the section, then that topic is unteachable in traditional mathematics. It will not be taught no matter how important or crucial for understanding the true purpose of the entire subject"

impactology, 6 days ago

"Conversely, topics that do lend themselves to endless drill problems will often be taught for this reason alone, despite being utterly pointless & contrived"

"In Intellectual Mathematics, presenting topics in an inherently interesting and meaningful way is the first and foremost consideration"

"The purpose of the problems at the end of the section is not to force students through a repetitive obstacle course, but to convince the students of the value and importance of what they are studying"

impactology, 6 days ago

"This is the opposite of traditional mathematics teaching, which treats students like circus animals who need to be taught to jump through hoops by means of mindless drill training"

"The traditional approach fosters robotic, unthinking students. It selects for obedience and punishes independent and critical thought. Intellectual Mathematics does the opposite"

"Traditional mathematics is written for robots and nitpickers. It is obsessed with being technically correct at the expense of all else"

impactology, 6 days ago

"Again and again the ugliest proofs and the most contrived order of presentation are favoured in the traditional approach on the sole grounds that they are the easiest to write down in a manner that cannot be faulted with respect to logical correctness"

"In Intellectual Mathematics, when facing a new concept, our primary goal is to understand how and why it works. The standard by which this is judged is our own sense of satisfaction and understanding"

impactology, 6 days ago

"Emotion, passion, and the joy of insight are therefore essential components of Intellectual Mathematics"

"In traditional mathematics, when facing a new concept, the goal is to reach the requisite results without making any technical errors. Crossing the t’s and dotting the i’s are the alpha and omega of traditional mathematics"

"Traditional mathematics is anti-human. It fetishises robotic manipulation of symbols and involves no emotions except a crippling fear of genuine & free human thought"

impactology, 6 days ago

"In traditional mathematics, the character and bulk of any given proof usually has next to nothing to do with why that particular theorem is true and everything to do with incidental technicalities"

"Students soon get the hint that mathematics is not about actually thinking and trying to figure stuff out; rather it is clearly a formal game completely divorced from common sense"

impactology, 6 days ago

"Indeed, formal proofs are sometimes accompanied by an informal heuristic argument, only to be followed immediately by the admonition that “of course this is not a proof!”"

"Much more than giving student some shred of intuitive insight, such passages convey more than anything that honest thinking is futile & impermissible in math because a proof only counts if it is packed with technical jargon that has nothing whatsoever to do with specific matter"

impactology, 6 days ago

@hipsterelectron

impactology, 6 days ago

@GeePawHill Completely agree!

impactology, 6 days ago

@GeePawHill You're a good educator if you can strike that kind of excitement in students

There is one guy that comes to mind who has that infectious joy while teaching to code — Daniel Shiffman from NYU tisch (they basically make art via coding)

https://thecodingtrain.com/
https://natureofcode.com/
https://www.youtube.com/channel/UCvjgXvBlbQiydffZU7m1_aw

impactology, 6 days ago

"If a single number is able to convey the general idea of quantity, and the matrix conveys an even more complex and general idea of quantity, then it becomes more obvious as to why matrices are so useful in describing the universe"

impactology, 6 days ago

@stephenpa wow!

impactology, 6 days ago

@stephenpa haha wow so interesting to have an audio narration over a flowchart

impactology, 6 days ago

@stephenpa Ooh its by the potsdam folks, they have one of the best information design department https://uclab.fh-potsdam.de/

impactology, 6 days ago (edited 2 days ago)

@smallcircles @stephenpa @uclab_potsdam

I absolutely love their work, along with giorgia lupi, stefanie posavec, https://pudding.cool/ I think of them as example of exemplary infodesign work.

Wish they really consider making an online course for people across the world

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

Oooh I love this idea, it would be very useful for giving policy presentations for example. Like to convey anything that has multiple factors and consequences as a narrative

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

Actually recently I had this idea for democratising legal knowledge, specifically knowledge of a constitution

What if a country's constitution was contextualized according to everyday life events and scenarios of people

https://mastodon.social/@impactology/112564714040324982

https://mastodon.social/@impactology/112564768958757130

Science communication equivalent for Law — "Lawcom" Using visualizations to democratize law to aid in understanding legal processes and the impact of policies on constitutional autonomy guarantees Does this exist?

impactology, 6 days ago (edited 2 days ago)

@smallcircles @stephenpa @uclab_potsdam @bret

Oh I didn't know Bret was on fedi, I'm such a huge fan of that guy man. My design philosophy, pedagogical tenets & principles and a vision for online learning and education is inspired by his interface design work.

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

Argument maps is a great idea to incorporate yes!

And maybe perhaps using a conversational turn by turn voice interface for search?

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

True, also for the problem of panning across an infinite canvas...I think there could be solution by looking at this example of a tool for curriculum construction

Basically they created a graph of concepts, what's the interesting thing here is that when you click on the nodes it "desaturates" all the concepts that are unrelated thus reducing curricula load

https://mastodon.social/@impactology/112564050549320833

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

Its interesting because most of the times default design choice of node-graph interface people is to highlight interconnections, these guys did the opposite — Hide the ones that aren't heavily interconnected :D which I feel is a creative design choice

https://mastodon.social/@impactology/112564120489957266

In the hands of a creative UI designer that could lead to making a powerful tool for curating a really context-specific interdisciplinary curriculum

impactology, 6 days ago

@smallcircles @stephenpa @uclab_potsdam

And this same design principle of hiding the irrelevant via selection of some components on can be used for so many infoviz