When do people use (or need) mathematical thinking?

(A rapid Project-Based Learning activity)

Goals:
1. Get us going on the goal of CE1, namely, "to 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."
2. Begin the touchstone exercise, which involves updating a wordpress post each week by using the ideas and tools of the week's activity to think about how to analyze and depict inequalities—of how different components of any aggregate (e.g., society, population, the economy) fare differently.

Preamble: The course does not impose a definition of "mathematical thinking," so we fill in a definition(s) through our activities and CEs. That said, the touchstone exercise and many of the activities correspond to an overall notion of critical thinking about mathematical thinking in the course, namely, the traditionally emphasized tools and skills of mathematics (ranging from addition to calculus and beyond) need to be considered in tension with an alternative. The alternative: People learn mathematics, and people develop and apply views about themselves and others as mathematical thinkers, as part of developing ways to address systematically the real-world complexities of the social context in which mathematics is applied.

Activity:
1. As a warm up to this activity, do the preparation listed for before the first session if you haven't had an opportunity beforehand: Peruse http://www.gapminder.org, which helps us visualize inequalities within and between societies. Make your touchstone post on the wordpress site and in it make notes about ways that advances in technology have made visualizing these inequalities possible. (10 minutes)

2. In the main part of this activity, use the internet to search for two kinds of presentations, relating to
a) claims that what students and/or workers need to know about mathematics is different from what it was a generation (or two) ago (depending on what kind of student and/or worker one is thinking of); and
b) claims that students and/or workers have been diverted from getting to know what they learned a generation (or two) ago (e.g., children no longer know their 10x10 times table).

Feel free to focus on whatever strikes you as fitting the label mathematics, whether it is doing mental arithmetic when seeing if you have enough money in your checking account to cover a check you want to write to visualizing how no light can escape from a black hole.

Submit these using this form. (No limit to the number of entries you submit.) (30-40 minutes)

3. Look for patterns—either commonalities or key contrasts—across the entries concerning the claims that everyone has assembled. Post these to the wordpress site. (15 minutes)

4.Go around on what struck you about the claims, commonalities, or contrasts. (15 minutes)

5. Plus-delta feedback on activity (5 minutes)