Questions and Challenges for the Mathematics Community: We welcome your input on any of the topics outlined below - before, during or after the June 20-22 meeting. Comments may be posted here, emailed to [email protected], or tweeted to @tpsemath (meeting hashtag #TPSE2014).

The mathematical education of students in American universities, 4-year colleges, and 2-year colleges increasingly affects their success in our society. We suggest that a transformation of this training can better meet our students’ and nation’s expectations.

As a result of our collective experience and that of many colleagues, we have concluded that the mathematics community today confronts a series of challenges that demand attention:

-- How can we reshape the **undergraduate curriculum** to raise the level of numeracy among citizens and better align current teaching with the expanded role of mathematics?

-- How can we **open pathways **that enable non-majors and developmental students to reach the level of numeracy needed for careers that demand analytical thinking and 21^{st} century quantitative skills?

-- How will **new technologies and teaching** trends affect pedagogy and the economic model of mathematics departments?

-- How can a broader, more relevant undergraduate experience better prepare students for the **workplace of the future**, including interdisciplinary opportunities?

-- How can **graduate students** be equipped to teach more broadly about the uses of mathematics while maintaining depth in their own research?

Following are some of the points that have emerged in earlier discussions of these challenges:

-- Both pure and applied mathematics have evolved rapidly, inviting a **fundamental reshaping of the undergraduate curriculum**.

- While today’s curriculum is sound for some students, how can reformed presentation, emphasis, and choice create productive new paths for others?

- How can the undergrad curriculum be balanced to teach (1) analytical thinking skills and logical reasoning, and (2) how mathematics is used?

- How can we move the curriculum in ways that respond to the current needs?

- Can we (AMS, SIAM, etc.) be helpful to faculty by identifying critical new content that undergrads and beginning grads should know?

- Given the challenge of creating interdisciplinary courses, who will decide which ones should be taught, and who will teach them?

- How can creative partnerships with disciplines whose majors need math be forged, and what shape might they take?

- Do changes in state higher ed funding formulas constrain curriculum reform?

- Should department chairs incentivize innovation for the sake of their students and the health of the discipline?

- Should we re-evaluate the science requirements of the math major?

- How about a return of the math minor – or specialized math certifications for certain skillsets?

- How important are research opportunities at the undergrad level?- How great is the power of the bully pulpit in changing culture?

- Given the expense of curriculum reform, one scenario might be: (1) develop an RFP that would support creation of short courses with challenges based on content; (2) agencies sponsor these courses; (3) students earn “badges” for mastering/ putting them to use in a situation of their choosing?

-- Undergraduate teaching should **open wider pathways** to careers and civic life for non-majors and developmental students.

- How can we address current high failure rates and math avoidance?

- More broadly, how can mathematical sciences departments reshape their curricula to educate a competitive workforce?

- More kinds of careers already need more math: How can we equip students for such careers?

- How can mathematical sciences departments create a variety of pathways into math and the careers it leads to?

-- As new technologies and cost pressures influence faculty and teaching trends, they challenge the **economic models of departments **and institutions.

- How can new technologies and teaching models best serve both educational and institutional needs?

- What combinations of online and other teaching methods, traditional and non-traditional, are best suited to large-enrollment courses?

- What is the potential of new technologies to shape learning?

- How can math departments adapt their business model to the changing environment?

- What would be the outcomes of reduced demand for regular faculty?

- Does undergraduate education suffer when state budget allocations are tied to “performance,” such as number of degrees?

- What lessons have we learned from state-level mathematics task forces?

-- Students may benefit from courses that better prepare them for the **workplace of the future**.

- What kinds of curricula can prepare students for future careers?

- How can mathematics faculty form instructional relationships with other disciplines where math is an essential tool?

- How can mathematicians become more knowledgeable in other disciplines?

- What methods of placement and advising best help students navigate a STEM curriculum?

- From the employer perspective, what do R&D directors want in new hires?

. Is being a “bright young kid” enough?

. Do they need a combination of specific skills and general mindset?

- What responsibility do faculty have in leading educational reform?

- Are incentives required, or are faculty already eager to move if a template is proposed?

- How can we maximize the “value-added” of highly trained faculty?

-- Graduate training must retain its research depth, but **graduate students need new and broader skills **as teachers of undergraduates and as future faculty researchers.

- How can graduate students achieve a depth of understanding beyond what is in the textbooks they will use as teachers?

- How can graduate students learn more about evolving domains (e.g., biology, social sciences) where math has increasingly powerful applications?

- How can they become better teachers without losing their research focus?

We hope that the Austin meeting will provide material for a summary document that frames the issues. We will propose focused follow-up meetings and material that may lead to RFPs from potential funders. More generally, we hope for a “community mobilization” that can drive practical reforms.

We feel that the time is propitious for a nationwide discussion, and for developing a set of appropriate challenges for the mathematics community. The issues above are both familiar and urgent. In many years of work as mathematicians and administrators, we feel that this is the best opportunity we have seen in our lifetimes for transforming post-secondary education.

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