mathematics community influence their engagement and learning? This article presents a case study comparison ( Hancock & Algozzine, 2017 ) of an undergraduate calculus student and a nonmathematics STEM professor reading a calculus textbook excerpt. Both

### Emilie Wiesner, Aaron Weinberg, Ellie Fitts Fulmer and John Barr

### Chris Rasmussen, Naneh Apkarian, Jessica Ellis Hagman, Estrella Johnson, Sean Larsen, David Bressoud and The Progress through Calculus Team

We present findings from a recently completed census survey of all mathematics departments in the United States that offer a graduate degree in mathematics. The census survey is part of a larger project investigating institutional features that influence student success in the introductory mathematics courses that are required of most STEM majors in the United States. We report the viewpoints of departments about characteristics shown to support students' success as well as the extent to which these characteristics are being implemented in programs across the country. We conclude with a discussion of areas where we see the potential for growth and further improvement.

### Bernadette Baker, Laurel Cooley and María Trigueros

In this study, we analyzed students' understanding of a complex calculus graphing problem. Students were asked to sketch the graph of a function, given its analytic properties (1st and 2nd derivatives, limits, and continuity) on specific intervals of the domain. The *triad of schema development* in the context of APOS theory was utilized to study students' responses. Two dimensions of understanding emerged, 1 involving properties and the other involving intervals. A student's coordination of the 2 dimensions is referred to as that student's overall *calculus graphing schema*. Additionally, a number of conceptual problems were consistently demonstrated by students throughout the study, and these difficulties are discussed in some detail.

### Juan Pablo Mejiía-Ramos and Keith Weber

We report on a study in which we observed 73 mathematics majors completing 7 proof construction tasks in calculus. We use these data to explore the frequency and effectiveness with which mathematics majors use diagrams when constructing proofs. The key findings from this study are (a) nearly all participants introduced diagrams on multiple tasks, (b) few participants displayed either a strong propensity or a strong reluctance to use diagrams, and (c) little correlation existed between participants' propensity to use diagrams and their mathematical achievement (either on the proof construction tasks or in their advanced mathematics courses). At the end of the report, we discuss implications for pedagogy and future research.

### Michelle Cirillo

The history and the mathematics used by Newton and Leibniz in their invention of calculus. The exploration of this topic is intended to show students that mathematics is a human invention. Suggestions are made to help teachers incorporate the mathematics and the history into their own lessons.

### Nancy C. Miller

For many women, traditional calculus courses have usually not been encouraging places.

### Harley Flanders

The student preparing for science or engineering should enter college with the technical skills needed in calculus. Particularly, he must know how to set up and solve problems and get accurate, answers. Now the typical realistic calculus problem involves only a little of the ideas of calculus per se but a lot of high school algebra and geometry.

### Carl B. Allendoerfer

Calculus is frequently taught at the wrong time, by the wrong people, and in the wrong way. It is high time we gave this matter our urgent attention.

### Jeffrey M. Rabin

A problem that can help high school students develop the concept of instantaneous velocity and connect it with the slope of a tangent line to the graph of position versus time. It also gives a method for determining the tangent line to the graph of a polynomial function at any point without using calculus. It encourages problem solving and multiple solutions.

### W. H. Tyler

The title of this paper may have various psychological reactions on the reader, according to his mental attitude and experience. To some it will perhaps seem as reasonable as teaching Greek in the kindergarten. A generation ago, when some of us were young, calculus was an ultimate goal of college mathematics, to be attained only after prolonged and painful servitude in the regions of college algebra and conic sections. The idea of teaching it even to college freshmen would have seemed heterodox, if indeed anybody had been so radical as to propose it. When finally reached it appealed only to the algebraically minded with its marvelous intricacies of partial fractions and reduction formulas. Excursions into geometry relieved the perplexities of some, to be sure, but the fact that calculus should be anything but an end in itself was more or less effectually disguised.