## Friday, Apr 29 -- Holt 173, 4:00pm

### Zack Reed (Embry-Riddle Aeronautical University)

**Title:** Using Calculus I Final Exam Items as a Lens for Instructional Design

**Abstract:** A basic model for teaching characterizes the phenomenon as being composed of an instructor’s *intended*, *enacted*, and *assessed* curriculum. The interdependence of these triad elements allows us to discuss the implications of one element for the entire practice of teaching. I will use results from a study of the *assessed curricula* in Calculus I as a lens through which to discuss and make recommendations for the *intended* and *enacted* Calculus I curricula at U.S. institutions. I will begin by discussing insights gained from an analysis of a large sample of Calculus I final exams from U.S. colleges and universities. This analysis sheds light on the intended calculus curricula of U.S. undergraduate institutions, and allows us to consider the alignment of this intended curricula with recommendations from the mathematics education literature. I will offer recommendations for creating exam items that do require the application of productive mathematical meanings identified in the mathematics education literature, and will conclude with a discussion of some recently designed activities and formative assessments developed to support students’ adoptions of recommended mathematical meanings.

## Friday, Apr 22 -- Holt 175, 4:00pm

### Ian Agol (UC Berkeley)

**Title:** Ribbon Concordance of Knots is a Partial Order

**Abstract:** We will discuss a resolution of a conjecture of Gordon that ribbon concordance of knots is a partial order. The proof makes use of representations of knot groups to SO(N) and the subquotient relation between them induced by ribbon concordance.

## Friday, Apr 8 -- Holt 173, 4:00pm

### Daniel Vallieres (Chico State University)

**Title:** The Number of Spanning Trees in Some Infinite Towers of Graphs

**Abstract:** In this talk, we will try to see if one can predict how the number of spanning trees varies in some infinite towers of graphs. The motivation for studying this problem actually comes from number theory, but studying this question in the context of graph theory is appealing since graphs are easily visualized. This talk will be targeted towards undergraduate students at any level.