Indeed...I agree Albert I think working out that sequence, its dependencies, and lesson resources, would be a great goal
The only practical issue with this is it takes so much time ...that I still can't see its that likely here or in any educational system ...the discipline and time (and money) resources to slow down enough to do the architecture (working out the sequence and implementing it) for that sort of approach properly is the issue ...so everything tends to be done in a more fragmented way Its like a reset is needed - take half a dozen maths and IT types and deconstruct maths learning sequences and curriculum resources like this (over say a year) (there are various research based maths continua and sequences that would make this possible) ...then take a few dedicated programmers who could implement all this into a lesson framework that kept track of pathways and progress If it could be done, I think this would be a very useful resource - 80% of the game in my view I also think we need some more open ended tools - etoys, Scratch, Logo, geogebra, like- for exploring and building models ...and maybe illustrating and playing with concepts from the 'makefile sequence' - 20% of the game All this is loosely on the radar in some commercial places, but still perhaps not as deeply reset as is needed, and its not open source I'd also like to see the maths content get more computer inflected - not just use computers to deliver old content, but modify the content - eg different ways to construct, say polygons, or find primes, or whatever the nominal maths is ...the discipline or learning a programming language could run parallel to learning maths...but that also requires a something of a reset in curriculum in how IT and maths relate... which seems even more unlikely, unfortunately ..maybe I'm wrong Papert's complaint about the state of 'school maths' getting ossified in one historical state really would require maths content to change like this ...and the education system hasn't yet signed on to that, as far as I can see ..computing as productive child's play for learning maths (via say Logo - or maybe Mathematica today) isn't really in view anymore.. (this would shift the 80/20 balance - could allow say 50-50) Re the direct instruction vs constructivism/constructionism thing - I think that one can teach 'directly' in a way that still respects that students have to 'construct' their own understanding ... Most 'direct instruction' maths lesson (indeed most maths lessons everywhere - according to various international video studies) have portions of direct instruction, and portions of students attempting to work more or less independently to apply some of that to 'problems' - which is at least some concession to the need to 'make your own connections' even after you've been 'told' (there is an Australian novel 'all the green year' where the main character praises his new teacher - 'she taught simultaneous equations so well I felt I had discovered the art myself' - which reconciles the two approaches ..and seems a feasible comment to me) If maths learning is always limited to that level it no doubt risks getting too closed and mimetic, (eg may create a culture of maths as simply right answers to closed textbook questions) - but there is still a little nod to constructivism in the need to attempt various problems and work out understanding on one's own - while there is still the bigger challenge of feeling maths as more open and productive - maybe representing learning in another form - say writing a program to model or explore it - is a good way to stretch beyond those limits ... its this I remember from my own schooling as one of the few times that all that math learning really felt creative to me - and why I feel we have left something out of the mix in schools today, even though there are countless more computers around ... even the top end of maths learning in school does not push much creative modelling etc in this sense One thing I liked about the 'drawing on the right side of the brain' approach is that it respects the need to load up your mind with conscious material - to wrestle with it and tackle it - and then also to walk away and turn things over ...ie the role of 'the unconscious' in pondering and delivering insights and solving problems - Poincare like - is not well respected in school I think direct instruction needs to keep this in mind - the grappling with difficult things and coming back to it - constructing understanding - is partly how we learn - not just consciously reciting modelled processes more in the learning stew Rob > -----Original Message----- > From: [email protected] [mailto:iaep- > [email protected]] On Behalf Of Albert Cahalan > Sent: Wednesday, 6 May 2009 5:02 AM > To: [email protected]; iaep > Subject: Re: [IAEP] educational brew > > Kathy Pusztavari writes: > > > "You could set up '4th grade math for Massachusetts' as a list of > > things to master. It's quite similar to setting up a Makefile > > with a target that exists purely to have a list of prerequisites." > > > > Albert - that is exactly what I was referring to. A set of curriculum > > to get you started but a good teacher could then go in and adapt the > > files or make file for their standards (or find a local nerd to help). > > I referred to Turtle Typing. Being a linux numbskull, I accidentally > > ran the MAKEFILE and found out that it seeds your lessons. Honestly, > > I had heard of MAKEFILE but I didn't know what it did. > > Sorry about that. The explanation wasn't any good for non-programmers. > I suppose I can try to explain "make". Here you go: > > Suppose you had a file, commonly called "Makefile", containing this: > > ########################### > > 4th-grade-math: 4th-grade-fractions long-division > > long-division: simple-division big-multiplication > teach long-division.lesson > teach long-division-extra-work.lesson > teach long-division-extra-work-2.lesson > > simple-division: simple-multiplication > teach simple-division.lesson > > 4th-grade-fractions: simplify-fractions measure-fractions > > measure-fractions: ruler > teach measure-fractions.lesson > teach measure-fractions-extra-work.lesson > > ruler: > teach ruler.lesson > > simplify-fractions: lcd gcd simple-division what-fraction-is > teach simplify-fractions.lession > > [ ... lots of stuff missing ... ] > > count-to-3: > teach count-to-3.lesson > > ########################### > > Each item on the left, before a colon, is something you could create. > (in this case, you're creating an education) Each item to the right, > after a colon, is a prerequisite for the item to its left. The indented > lines are commands that are needed to create things. > > To learn 4th-grade-math, you don't actually need to create anything. > You just need to satisfy the prerequisites. So if we ask the "make" > program to create 4th-grade-math, it adds 4th-grade-fractions and > long-division to the list of things you want to learn and starts in > on them. Once those prerequisites are done, 4th-grade-math is done. > > The long-division knowledge also has prerequisites, simple-division > and big-multiplication. Prerequisites must be done prior to starting > a lesson, so we add those to the list of things to learn and keep > going. Unlike 4th-grade-math, long-division has lessons to teach. > We have to come back to those after the prerequisites are satisfied. > > 4th-grade-fractions is more like 4th-grade-math. It doesn't have a > lesson by itself; it is just a list of other things to learn. > > Eventually you get to a starting point with no prerequisites. That is > count-to-3 in my example. There may be more than one starting point, > in which case they may be done in any order. Reasonable starting points > always have lessons. Those are taught, completing the starting points. > This satisfies prerequisites for other things, which thus become > available as starting points. Ultimately 4th-grade-math becomes a > starting point, which is trivial because it has no lessons. Since that > was the original request, you're done. > > If we were actually going to run that file using "make", we'd need a > command called "teach". Maybe the "teach" command sends a text message > to a human teacher, or maybe it runs a Sugar activity. The "teach" > command just needs to ensure that the material is taught. > > There are plenty of details that keep this from working exactly as > written. Students may forget things. I used spaces instead of tabs > to indent the lines. I left out a big chunk. I hope this cleared up > what I meant though. > > That "MAKEFILE" you mention might not be a real Makefile. It might > be a script that runs the "make" command with a particular Makefile > specified. > _______________________________________________ > IAEP -- It's An Education Project (not a laptop project!) > [email protected] > http://lists.sugarlabs.org/listinfo/iaep Important - This email and any attachments may be confidential. If received in error, please contact us and delete all copies. Before opening or using attachments check them for viruses and defects. Regardless of any loss, damage or consequence, whether caused by the negligence of the sender or not, resulting directly or indirectly from the use of any attached files our liability is limited to resupplying any affected attachments. Any representations or opinions expressed are those of the individual sender, and not necessarily those of the Department of Education and Early Childhood Development. _______________________________________________ IAEP -- It's An Education Project (not a laptop project!) [email protected] http://lists.sugarlabs.org/listinfo/iaep
