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Biomedical and Electrical Engineer with interests in information theory, evolution, genetics, abstract mathematics, microbiology, big history, IndieWeb, mnemonics, and the entertainment industry including: finance, distribution, representation

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chrisaldrich

chrisaldrich

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Some resources for pedagogy and education https://indieweb.org/Indieweb_for_Education

 
 
 

A lovely little experiment in visual pedagogy in mathematics! We could certainly use more of these types of simple "explorations" particularly for younger math students who may not always be good at visualizing material. These seem reminiscent to me of Wilson Rugh's <a href="http://pages.jh.edu/~signals/">java applets</a> for digital signal processing years ago.

Some of this pedagogy argument about slides likely fits better into the area of the flipped classroom versus non-flipped. Though slides may be great (particularly if students have copies of them beforehand to take notes on as is often done commercially by many biology textbooks which have 2-4 slides down the left side of the page and note space on the right hand side) for mathematics I much prefer having notes in <a href="http://refer.livescribe.com/a/clk/2G3Md">Livescribe</a> .pdf format with embedded audio. This allows a student to not only relisten to the entire lecture, where often a lot of complicated material (especially in higher level abstract courses) is said very quickly and isn't able to be written down even by some of the best transcriptionists with shorthand (and how many students know this anymore?), but they can skip around to parts they need more work on. As an example, download this <a href="https://www.dropbox.com/s/7g4rekbuzzr8nfz/Lie%20Groups-Lecture%203.pdf?dl=0">.pdf file from a Lie Groups lecture</a> and open it up in the most recent version of Adobe Reader to be able to see the visual and audio functionality.

The particular value often comes in seeing problems worked out in full detail with discussion, which some students need much more of than others. One of my favorite lecture experiences almost a decade ago was hearing an audible gasp from the classroom of undergraduates when Sol Golomb (USC) stopped in the middle of a complicated lecture on combinatorics and worked out a 4th grade simple long division problem on the board to get a final solution. Half the class had pulled out a calculator to get the answer and he'd finished before most of them had the first number input. The class learned more in that one minute of example than most did the entire lecture. Most of the best math is done in the "exploration" and practice than in a stripped down lecture as is highlighted in Ben Orlin's recent post: <a href="https://mathwithbaddrawings.com/2016/05/04/the-essence-of-mathematics-in-one-beatles-song/">The Essence of Mathematics</a>. While it's always lovely seeing theoretical mathematics as if it seemingly sprang fully formed from the head of Zeus, many students should see how the proverbial sausage (or laws) are actually made, especially at an earlier age.

 
 

This is a brilliant exercise!

I have to imagine that once the conceptualization of language and some basic grammar existed word generation was a much more common thing than it is now. It's only been since the time of Noah Webster that humans have been actively standardizing things like spelling. If we can use Papua New Guinea as a model of pre-agrarian society and consider that almost 12% of extant languages on the Earth are spoken in an area about the size of Texas (and with about 1/5th the population of Texas too), then modern societies are actually severely limiting language (creation, growth, diversity, creativity, etc.) [cross reference: http://www.scmp.com/infographics/article/1810040/infographic-world-languages]

Consider that the current extinction of languages is about one every 14 weeks, which puts us on a course to loose about half of the 7,100 languages on the planet right now before the end of the century. Collective learning has potentially been growing at the expense of a shrinking body of diverse language.

To help put this exercise into perspective, we can look at the corpus of extant written Latin (a technically dead language): It is a truly impressive fact that, simply by knowing that if one can memorize and master about 250 words in Latin, it will allow them to read and understand 50% of most written Latin. Further, knowledge of 1,500 Latin words will put one at the 80% level of vocabulary mastery for most texts. Mastering even a very small list of vocabulary allows one to read a large variety of texts very comfortably. These numbers become even smaller when considering ancient Greek texts. [cross reference: http://boffosocko.com/2014/07/05/latin-pedagogy-and-the-digital-humanities/ and http://dcc.dickinson.edu/vocab/vocabulary-lists]

Another interesting measurement is the vocabulary of a modern 2 year old who typically has a 50-75 word vocabulary while a 4 year old has 250-500 words, which is about the level of the exercise.

As a contrast, consider the message in this TED Youth Talk from last year by Erin McKean, which students should be able to relate to: https://www.ted.com/talks/erin_mckean_go_ahead_make_up_new_words

 

How to memorize Dowling's Wheel and become fluent in fast http://mt.artofmemory.com/forums/how-to-memorize-dowlings-wheel-latin-declensions-conjugations-6254.html

Another piece that may help to speed things up is memorizing the "right" words in a specific order. Researchers at Dickinson in concert with others have compiled and documented a list of the most common core vocabulary words in Latin (and in Greek) based on their frequency of appearance in extant works. This very specific data becomes a tremendously handy tool when attempting to learn and master a language. It is a truly impressive fact that, simply by knowing that if one can memorize and master the 250 most frequent words in Latin, it will allow them to read and understand 50% of most written Latin. Further, knowledge of 1,500 of the most frequent Latin words will put one at the 80% level of vocabulary mastery for most texts. Mastering even a very small list of vocabulary allows one to read a large variety of texts very comfortably. Continuing on to memorize more and more provides one with even more facility--though with obvious diminishing returns.

I've written a bit more on the topic here: http://boffosocko.com/2014/07/05/latin-pedagogy-and-the-digital-humanities/

Additionally, I've created an Anki deck of flash cards that is downloadable (https://ankiweb.net/shared/info/1342288910) with the ability to modify the root database, so that one can cross-link it with one's own mnemonic system/images/other to speed up the creation of image relations and memorization/drilling.