Shifting: Changes in the ways people need to think mathematically
(A CE in which students: identify a range of ways in which changes in work, technology, commerce, and social life have changed our needs and capacities for mathematical thinking; find patterns in them; and consider implications for education, including lifelong learning.)

As work, technology, commerce, and social life change, our needs and capacities for mathematical thinking shift. For example, at primary school before conversion to metric in Australia, I was assigned problems involving weights in units of tonnes, hundredweight, quarters, pounds, and ounces. After weights became measured in grams and kilos and metric tons, addition was so simple teachers found others ways to occupy students' time in class. The arrival of hand calculators helped diminish further the need for arithmetic. That said, my ability to do mental arithmetic applying multiplication tables means that I am quicker at seeing what ball park an answer should be in and thus detecting when someone has made a mistake inputting figures into their calculator. That said, class time for me as a child centered on quiet solitary solving of multiple problems of the same kind so there was little scope for collaboration, peer-to-peer support (except in the form of cheating), or for discussion of alternative approaches.

One side in the "Math Wars" maintains that computational "skills should be memorized and practiced, using time-tested traditional methods until they become automatic" (Wikipedia, n.d. *). We could join or oppose this side, thus taking a position in the polarized arena of the Math Wars (e.g., did the traditional methods actually work back in their time?). However, let us imagine a book that treats the audience as capable of addressing the complexities of change in work, technology, commerce, and social life as it relates to shifts in our needs and capacities for mathematical thinking. Then let us identify patterns in past changes, with a view to helping readers think about the implications for formal education as well as for the ways each of us continues to learn in response to ongoing change over our lifetimes. (*Wikipedia, n.d. "Math wars," https://en.wikipedia.org/wiki/Math_wars (viewed 4 Sep 17))

The end goal for the CE is that the class as a whole produces thought-supporting, constructive 1200 word entries for this hypothetical book. A premise for this book is that it would be unlike other mathematical thinking texts. Indeed, it may be more like a combination of provocations and resources for people—not only teachers—who want to foster ongoing development of people's mathematical thinking. In this spirit, this CE is an experiment—it is not clear in advance what a "pattern" is or what ways you will invent to "help readers think about the implications." (Steps to undertake and when.)

Steps

Between classes 1 and 2.
1. Freewrite for 7-10 minutes, starting from the prompt, "When I think about what has changed during my lifetime that affects our needs and capacities for mathematical thinking, the thoughts and feelings that come to mind include..."
2. Make notes in a workbook or computer file of changes in work, technology, commerce, and social life that have changed our needs and capacities for mathematical thinking, aiming for 10.
3. Use (or adapt) the following template to prepare draft wordpress entries:
4. Make one or more posts every other day on the crcrth650 blog, starting the day after class. Give each post an informative title to help others decide whether to open and read the post, e.g., "How hand calculators improved people's ability to estimate answers," NOT "Peter's 3rd post." Specify the category "Changes" when posting.
Class 2 5-phase Dialogue process (aka Dialogue Hour) to share and clarify what we are thinking regarding the case.
From class 1 through 3.
4a. Continue #4 (see above)
5. Make comments on three (or more) posts of other students, starting any time, but completed no later than middle of week between classes 2 and 3.
6. Prepare a 5-minute work-in-progress presentation for class 3 in which you identify patterns in past changes, with a view to helping readers think about the implications for formal education as well as for the ways each of us continues to learn in response to ongoing change over our lifetimes.
Class 3 Work-in-progress presentations, each followed a few minutes of time to write Plus-Delta feedback using this form, http://bit.ly/PlusDelta, on each presentation.
Between classes 3 and 4.
7. Revise posts in response to feedback. In your notes identify more patterns and compare-contrast your posts with those of others.
8. By class 4, post a draft product for the CE. This product (1200 words plus bibliography of works cited) has the same goal as the W-I-P presentation, but is written so it makes sense to someone who knows nothing about the class but is looking to address the complexities of change in work, technology, commerce, and social life as it relates to our needs and capacities for mathematical thinking.
9. (Optional) Continue making comments on other students' posts (see #5 above) to help them develop the post.
Class 4 Dialogue Hour for Taking stock of this Collaborative Exploration
Between classes 4 and 5.
10. Even as you are starting on CE2, provide comments on one other student's draft product. (Choose a student who isn't being commented on and make a comment that you will be commenting on this draft.)
Between classes 5 and 6.
11. Revise your draft product in response to comments from instructor and fellow student, then post it to the wordpress site (using Category "Report")