## Marches . . . Napolean to and from Moscow . . . . Students to Calculus

In a recent video conference call involving me and my colleague, Corban Harwood, Mathematics, George Fox University, Newberg OR USA, and others, I noted he had a copy of Charle Minard's marvelous map of Napoleon's Russian campaign hanging on his wall. I too have a copy framed and mounted in my home (and now only, since I am Emeritus) office. Perhaps some of you do as well. It is a marveloous piece of graphics, telling a somber story of Napolean's diminishing forces as he marched into Russia and then retreated home. We show this graphic here.

For some background from Wikipedia we read, "Charles Joseph Minard 27 March 1781 – 24 October 1870) was a French civil engineer recognized for his significant contribution in the field of information graphics in civil engineering and statistics. Minard was, among other things, noted for his representation of numerical data on geographic maps, especially his flow maps." Wikipedia contributors. "Charles Joseph Minard." *Wikipedia, The Free Encyclopedia*. Wikipedia, The Free Encyclopedia, 25 Jan. 2019. Accessed 26 Feb. 2019.

Corban then sent me the following information and graphic which I thought was equally (perhaps more relevant to us here at SIMIODE) as interesting. He said, "Here is the graphic I mentioned which reminded me of Napolean's march. This is from the 2016 MAA/NCTM report on the state of Calculus. I used it on Saturday during a pane at Linfield College: *Philosophical Challenges and Opportunities for the Mathematical Sciences *to discuss the conflict between the student/parent/teacher view of accelerated math curriculum in HS to a math professors view of its outcome at the university level. A 2006 study at Rutgers found that only 5% of incoming students who had taken Calculus in HS were placed in advanced math courses." We present it here to contrast the graphics, but also to allow it to convey the flow to calculus.

What Corban's citation, "A 2006 study at Rutgers found that only 5% of incoming students who had taken Calculus in HS were placed in advanced math courses." suggests is that of those students who took Calculus in high school the result was not really to place out AND take advanced math courses. If not that then what? Interesting issue.

Corban Harwood@ onBrian,

I think the more apt comparison is students to and from STEM majors, with Calculus being the gateway. In leading the panel discussion at the Oregon Academy of Sciences meeting last Saturday, I found this topic quite cathartic. Awareness of the issue was increased across the board, eliciting questions from professors and prompting students to share their own experiences.

Here is a citation of the report.

--Bressoud, David Ed. The Role of Calculus in the Transition from High School to College Mathematics. Report of the workshop held at the MAA Carriage House Washington, DC, March 17–19, 2016. Mathematical Association of America, 2017.

Here is the introduction to the section of the report containing this graphic:

"College calculus is the STEM (Science, Technology, Engineering, Mathematics) gatekeeper. For many students, it is the most difficult course they face if they are interested in pursuing a STEM career. While success in college calculus can open the door, failure is a major impediment to continuing to a STEM or pre-med major. The goal of the Factors Influencing College Success in Mathematics (FICSMath) project has been to investigate the factors that contribute to students’ success in their first college calculus course, with a special focus on students’ mathematics experiences during high school. With this in mind, our team has carried out a study encompassing a large, nationally representative sample of 134 U.S. 2-year colleges, 4-year colleges, and universities. Within these institutions, we collected detailed data from 10,437 introductory calculus students of 336 college calculus instructors. At the end of the semester, instructors reported the final grades of each student. Both a canonical dataset and an extensive codebook have been made available to team members at several institutions, along with their collaborators and graduate students, so that a wide range of research questions could be, and is going to be, investigated. This background chapter presents seven of the most interesting studies generated from the FICSMath project (which relate to students’ high school mathematics coursework, including calculus), often using excerpts from papers that we have published."

--Factors Influencing Success in Introductory College Calculus. Philip M. Sadler and Gerhard Sonnert, Science Education Department, Harvard-Smithsonian Center for Astrophysics, Cambridge, MA.

Here is a summary from another section of the MAA/NCTM Report:

"What the members of the mathematical community—especially those in the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM)—have known for a long time is that the pump that is pushing more students into more advanced mathematics ever earlier is not just ineffective: It is counter-productive. Too many students are moving too fast through preliminary courses so that they can get calculus onto their high school transcripts. The result is that even if they are able to pass high school calculus, they have established an inadequate foundation on which to build the mathematical knowledge required for a STEM career. Nothing demonstrates this more eloquently than the fact that from the high school class of 1992, one-third of those who took calculus in high school then enrolled in precalculus when they got to college, and from the high school class of 2004, one in six of those who passed calculus in high school then took remedial mathematics in college."

--Background to the MAA/NCTM Statement on Calculus. David Bressoud , Dane Camp , Daniel Teague

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