Applets+&+Manipulatively+Expressive+Software

===2) What are the pros, cons and interesting features of the use of applets (for rehearsal, for specific topics or concepts) and of manipulatively expressive software (dynamic geometry, dynamic function plotting and manipulating, computer algebra systems)? ===

What might be the benefits to a split between, on one hand, centralized processing power and server-infrastructures that might be exploitable by teachers (or other institutionally-vested authorities), and---on the other---thinner clients that support "little applets ... for students to practice and explore with." I've seen a lot of enthusiasm for variations of this idea, especially its "student/applet" alignment, and can't overlook the clear benefits of the applet-model in mathematics education. Certainly the programming paradigm for applets is appealing to many potential "creators"---authors, developers, what have you. Putting together a Java applet is far, far less work than creating and maintaining not only a traditional software system but also a whole distribution channel for its dissemination. Beyond the Java model, tools like Flash and online authoring systems (of which even the blog and the Facebook page are important instances) have created a reality we could only dream of, twenty years ago, in giving technological voice to many interested parties for whom full-scale software development is simply not an available avenue of expression. On the other side of things, web-delivery of program code and the usually-limited user model of an applet's "size" or "scope" have begun to enable teachers around the world to identify and incorporate applet technologies into their practice without having to address frequently-insurmountable problems posed by school acquisition policies, professional development requirements, lab access realities, and so forth --- all the things that arise in practice and prevent teachers from doing with technology that which, in a removed conversational context, they are clearly interested and excited in attempting to do. So, on the creation front: applets broaden the pool of potential contributors and the diversity of potentially-contributed ideas; on the receiving end, they eliminate access barriers and can be shared and used just by e-mailing each other URLs. What's not to like? Well, I think, a couple of things. First, I worry about the atomization and isolation of "content" that is the natural trajectory of ideas broken up into applet-sized chunks. Our de facto curricula in the States famously suffer from an overabundance of obligatory touch-points that become ingredient lists for giant inedible smorgasbords of "content" that lack any global shape or perceivable intellectual coherence. We have spent the past two decades warring to standardize such lists, with the most hopeful promise of that dismal enterprise being the untested idea that at least if we can articulate the "content" we most widely ratify, that we can begin to strip our school trajectories of all the content experiences students don't really need after all---and then focus (in all the time saved!) on some big ideas. In practice, though, these efforts seem to reach a common denominator quickly in which any vision of a student experience of >doing< mathematics, or of thinking mathematically, or of understanding how specific and concrete concepts fit together into larger, more flexible and productive arrangements of ideas, is sacrificed for the clearer delineation of the "content chunk." That makes sense, given the standards-enumerating enterprise, because a big idea, unlike a narrowly defined fact or operation or theorem, is inherently not something we can always identify as the outcome of a single classroom activity or single assessable student assignment; whereas conversely, a "small content check" is precisely the sort of unambiguous, clear, and entirely unobjectionable artifact that can successfully emerge from a committee and be consumed without undue rancor by a broad audience of teachers, administrators, and politicians. Thus, we see the same set of factors that leads to an applet's ease of deployment---narrow scope, minimal context, and limited objectives--in a related guise as the factors that lead to the atomization and deconceptualization of entire curricula. Their ease of digestibility by a wide audience inevitably implies their central blandness; and--to continue the gustatory metaphor---an abundance of convenient snack foods does not equate to a nourishing meal. As usual, my metaphors rapidly turn hyperbolic, and lead me both to risk offending and to risk being misunderstood. I am not arguing that all applets are junk or junk food. There are many great applets and many awful desktop applications! I'm instead arguing that if we settle our ambitions for students' technological involvement with mathematics to platforms as paradigmatically narrow as the "thin client" applet, we exclude from that ambition the possibility of technology providing "maximal" environments and experiences. This is a tremendous loss, because the more we change our emphasis from deep experiences to "thin" content presentations, the more we move from being focused on learning to being producers of textbook illustrations, to mistaking a broadspread ideological investment across education (as across other social institutions) in the hegemonic preservation of the norm, for (instead) a legitimate request from that institution to improve the "accessibility" of ("difficult") innovative ideas. You see this effect in the commercial world, where web-based math-applet-delivery systems thrive provided they offer a facility in which their users--school admistrators---can "dial in" a specific set of curriculum standards that then program the applet instructional delivery sequence to follow the prevailing political program. And at the same time you see "deep" tools---tools with multiple points of access; tools with multiple outcomes and trajectories to them; tools that offer richly cultivated soils for mathematical thinking; rather than narrow monocultures aimed at producing specific "learning outcomes" of predetermined shapes; and ultimately tools that require investment, thought, and effort to use intelligently---now surround themselves with flocks of applet-like spin-off "activities" or "sketches" or "demonstrations" (I'm thinking of things like Mathematica's "Wolfram Demonstration Projects" or my own publisher's "Sketchpad LessonLink") that attempt to narrow down that broad potential to as small a profile as possible. Many of us who work in inservice professional development with technology have found ourselves complicit at some point in a teacher conversation that runs like this: "yes, yes; it's great; I understand it all. But where will I find the TIME? There needs to be some way to make the triangle IN ADVANCE! Ah there is? Good. And you've just done it? Great! Then I can use this one rather than have them build their own. Now: how do we get it so they can't drag any of the points?" These collections of applets seem to me to cater to that dispiriting view of technology's transformative potential. They are no doubt effective sales tools, with their promise of a specific button to produce every desired learning outcome, but do they offer more than that? So, this is the point in this letter where I most tangibly rue not being present with you in your meeting, because I instantly imagine a dozen of your objections to what I've put down. Now that Word is basically cloned as a Google applet, surely he doesn't think an applet has to be "small," does he? (I don't!) He completes misses the point about teacher-tools AND student-tools! (I do! Or rather, I'm side-stepping it to speak only to the tempting voice of the serpent who encourages us to eat from the applet tree....) I would like to clarify, argue, and expand---but that would turn this polemic into a paper, and then you might not read it! If there are any useful provocations here, please take them up yourselves, inspect them, surpass them. And please, honor both the charge and the caution that Anne gave us back in May: "develop an image of a school mathematics curriculum in an ICT 21st century world.... something radical is required!"