Sue Jones, trying to make math cognitively accessible
… I’m looking to collaborate and cooperate and make sums that are bigger than the wholes of their parts
@sujones i have lots of thoughts on this. you posted this 3 months ago, but if you are still looking to collaborate then id like to at least talk with you.
qualifications: i am terrible at math and unusually good at making math-related processes easier to understand. big points for using a turn of phrase that is mathematically impossible.
caveat: i have now read more in other posts and i am confident in saying that theres not a great deal i can do in the deadline of a few weeks from today. let me know if you are looking for new ideas in the future as well.
THe deadline is just for that step in the process (and to keep me making time for it). I am definitely interested in talking to you and your perspective. Right now I’m using positive and negative integers for my “first sample lesson” – what are your thoughts on that?
integers are clean and accessible, and if you dont grok them fully, theres little hope for decimals or fractions. it is probably as good a foundation as any.
i am no mathematician. i took algebra in year 8, struggled, and finally got it later on. i managed through geometry. with trig and calc, ask most people on the street to explain it, and some will manage.
i can (and frequently do) use trig to plot the points in both circles and spheres, which is a lot of fun if you dont have to look up or calculate the values by hand. you can iterate from -pi to pi, at (2pi / the number of points you want) resolution, and the cosine of that value times the desired radius will give you the x points, and the sine of that value times the desired radius will give you the y points.
the formula is very basic, but one i spent most of my years in primary school trying to get my hands on. and this is what you can do with it: https://zippy.gfycat.com/BigBabyishGrebe.webm i really wish one of my math teachers had known the formula for a circle, because i was told that exponents produced curves (they do) and i spent years trying to guess how to produce one lousy circle with exponents or even the sine function. obviously, that isnt how you do it.
if you iterate backwards through y, and slowly increase or decrease the radius, you can draw a cone. if you stop changing the radius, you get a cylinder. a lot of this is more tedious on paper, and the tedious parts distract from learning the concept (anecdotal evidence, but its a starting point to explore.)
however, i say all of this to make the general point that sums up my ideas about teaching math in the 21st century. ultimately, people are going to need the basic concepts (number lines were useful when i was learning, i never struggled with those. two number lines for graphics are wonderful too.)
but if we managed to make coding as universally important as math, coding is a gateway to math (as much as the other way around) that allows you to abstract math lessons in a way that is more interactive, less boring, and potentially more accessible.
potentially because mandatory math lessons have rarely failed the population, and coding has gotten more complicated over the years, more quickly than math has (at primary school level.)
you can be certain i am not suggesting we replace math with coding, nothing like that. i am saying that if coding can be made accessible enough (a separate topic, but one im very keen on) then it can illustrate, demonstrate, and support math teaching like no other tool really can.
regarding your approach right now, i certainly applaud it. though i prefer coding graphics now whenever possible, i have to tell you how i got into computers-- it was (originally) using a raster paint program, not entirely unlike the one youre using, with a mouse (in the mid 80s at that, and not on an apple) that led me to love coding and text so much. and also to hate math less.
my own programming language includes a few trig functions (including arctangent) but i only use them for making pretty designs.
one of the things regarding education that i believe very strongly in, is that we need to connect more educators with developers (hackerspaces, such as the one @offray.luna is involved with http://hackbo.co/ could prove very useful with this) to create small programming languages that are well suited to education.
as a fan of olpc and sugar, im hardly saying that full languages like python are not useful to education. but the ideal ages for learning python (for most people) are a bit older than the ideal ages for older programming lessons based on basic and logo.
while i think python is definitely useful in a high school setting (in high school, we learned with qbasic-- python was very, very new and not well known then. .net would not exist for years, and gopher was more popular than the web) i think the time to get the basics in is prior to that.
i reject the idea that schools should focus on industry standard anything. thats very useful for industries, but not always useful for computer literacy and understanding the fundamentals of coding. it really is so much easier to teach the (practical, usable) fundamentals of coding, which gives a better foundation for the various industrial fashion trends that people will be dragged through later.
i mean, you wouldnt start a 1st grade creative writing class out (intially) with how to do apa citation, at least i hope not. the reason is, this would kill the love of writing for years, in so many students. pointlessly.
i believe school (through little fault of the teachers, though there is too much complacence. i do consider teachers to be victims of the school nearly as much as the students, but the job of teacher is the job of fighting for the education of students as much as the job of librarian is that of fighting for the rights of readers) and this is not in just one country-- creates a visceral fear of learning through many of its approaches and conventions.
you can find that fear live on in adults, most of whom approach the concept of learning new things as a visceral threat. i am being extremely broad here, though its something i witness (in countless well-educated adults) every day.
theres a lot to be done. making lessons easier to understand (without gutting any of the true essentials) is certainly a key part of all of that.
at least you have a summary of my ideas now. i could go into more detail on parts of that. i can tell from your question that youre doing a more bottom-up approach. ultimately my approaches are also bottom-up, its my concept of the overall problem to be solved thats top-down.
I like your example of starting first grade creative writing w/ apa citations. It is so easy to see things through a ten-years-later lens!
Yes, you’re right… I’m thinking bottom-up but I value input from your kind of thinking. I tend to be very linear and verbal… “big picture” is a real effort but it’s how lots of people do get the stuff to make sense so that needs to be built in for things to be accessible.
Thanks for giving me ideas to chew on
youre very welcome. i had a very mixed experience with school. no matter where i went, at any level, i found that the worst teachers were dismissive and the best were constantly trying (but not hysterically scrambling) to integrate the best ideas they could find. they constantly learned from their students, and it was a trade, rather than an imposition. just imagine, if all school experiences were like that.
of course, most of my life ive been reinventing constructionist learning, simply for the fact that i loved it whenever i unwittingly encountered it-- even if i wasnt really familiar with the concept directly. im certain its not all there is-- its just so much, and continues to show rich potential as technology moves forward. it has to be said that no matter how many new examples we create, the philosophy behind them has existed for more than half a century.
as teachers in general struggle (over and over) to implement lessons with technology, constructionist learning shows the same basic concepts (which havent aged poorly) on how to make things easier (and richer) for students and teachers at the same time. the reason it works so well, is it begins with steady exploration, rather than putting the cart before the horse and beginning with mastery. the demands on the instructor and the learner are lighter, and it becomes a learning experience for both.
constructionist learning does not even have to be adopted to help-- its concepts can be used individually, like dishes from a menu or clothes from a rack. to use eastern philosophies as metaphors for educational approaches-- the constructionist approach moves away from the awful confucianist structures and is a little more like the tao te ching.
of course this is a metaphor, but confucianist education is the predominant model throughout the world, and it is relatively oppressive and unhappy-- without the need to be. you dont have to live on a mountain for years to learn this, just look around you and watch how students suffer.
i like to bring up olpc because it is pure constructionism-- it seems very hippie-like but m.i.t. loves it. m.i.t. carries on constructionist learning with the media lab. they keep logo alive and relevant. but i stress that with oer, we can use these ideas without having to adopt the same implementations. we can treat all this as a store, and shop as we need fresh ideas, because this is a global, ad hoc collaboration.
remix is so core to contructionism that its at the core, implicitly. its so fundamental, it doesnt generally even need to be said. outside of that context, its worth pointing out now and then. industry is always trying to chisel things (including students) into products. we can actually leave things in a slightly more uncarved state, and let people learn by transforming them into new things. most industrial products arent made with that built into the design, but art supplies and home improvement materials are.