Untested draft of method that represents
a) an extension of mathematical thinking (provisionally defined here);
b) follows the premise that no teacher would be prepared to guide every student in developing their mathematical thinking in the diverse ways that interest different people and
c) ditto in developing their life long learning to respond to changes in work, technology, commerce, and social life that continue to change our needs and capacities for mathematical thinking.
Another premise is that there are a lot of lessons and explanations on the internet and, even when the best material is in printed books or journal articles, there are webpages that summarize those printed works.
Preparation: Activity leader creates an educator’s account on diigo, which allows web bookmarking, annotating, and tagging, then creates a diigo group for the activity and invites all participants (e.g., students) to join that group. Participants install diigo toolbar or applet on their browser for easy bookmarking.
1. The activity leader solicits topics that interest participants or proposes some, finds webpages related to the topics (which may be the abstracts for a published paper), then uses diigo to bookmark them. (If there is no suitable webpage for some topic, the activity leader makes a wikipage or blog post that presents the participant’s interest.) This is the start to a thread, Tx, where x is a number that identifies the thread.
2. Bookmarking includes annotating (to highlight key text from the webpage, discuss it, what aspects are relevant to the student’s interest, suggest a revision, etc.) and add tags. The tags should include the person’s initials, the thread identifier Tx, and any other relevant keywords.
(See also 3a.)
3. The original participant or anyone who shares an interest in the topic: i) reads the webpage, ii) adds their own annotations that explains what they do and do not understand and provides their own work on any problems set by the webpage, iii) identifies an issue, organization, person, or concept from the webpage that they want to learn more about, iv) translates that into a google search, and then v) identifies and uses diigo to bookmark a webpage that interests them. Then goes back and repeat #2-3–or even just repeats i-ii; indeed, days may pass with participants working towards the goal of understanding some aspect of mathematical thinking well enough to explain to others.
3a. Except for the very first post by the leader, the annotation should include a line stating the URL of the webpage that was “upstream” of the one they are annotating. Later, they should go back and add any subsequent downstream URL.
3b. At any point, the tag roll for the diigo group provides an overview of the terrain that has been explored. It also allows access to everyone’s posts on any given thread (by a search on the diigo group for the relevant Tx) and any individual participant’s thread (by a search for the relevant Tx and initials tags).
4. Discipline the material. Perhaps with the leader’s assistance a participant initiates a new thread or a streamlined thread (with, say, tag Txa) that begins from a page that highlights the key issues of the original thread for developing mathematical thinking and/or developing life long learning to respond to changes in work, technology, commerce, and social life that continue to change our needs and capacities for mathematical thinking. A subset of the key webpages can be placed in the thread by judicious use of upstream and downstream URLs (see #3a).