Preparing the Next Generation of Students in the Mathematical Sciences to “Think with Data”

By Johanna Hardin, Pomona College, and Nicholas J. Horton, Amherst College

As statisticians in mathematics departments, we have both spent many department meetings, departmental reviews, and water-cooler conversations discussing the merits of various different curricular decisions with respect to the calculus sequence (“Why not take linear algebra before calculus III??”), upper division electives (“But those classes are needed for graduate school!”), and number and order of courses required for the mathematics major/minor. Recently, more of those discussions have related to critical components of the statistics curriculum, and how courses from mathematics ensure that statistics students have a solid quantitative foundation. These kinds of conversations reinforce the fact that there are strong connections between mathematics and statistics, and these connections can and do affect decisions about undergraduate curricula.

More generally, this is an exciting time to be in a quantitative field. The amount of data available is staggering and there is no end to the need for models that harness the deluge of information presented to us every day. Mathematicians, Statisticians, Data Scientists, and Computer Scientists will all play substantial roles in moving quantitative ideas forward in a new data driven age.   To be clear, there are challenges as well as opportunities in what lies ahead, and how we move forward – particularly with respect to training the next generation of mathematical, statistical, and computational scientists – requires deep and careful thought.

The goal of this blog post is to share some of the recent pedagogical ideas in statistics with our mathematician colleagues with whom we – as statisticians – are intimately engaged in building curricula. We hope that the description of the recent developments will open up larger conversations about modernizing both statistics and mathematics curricula.   Many of the ideas below on engaging students in and out of the classroom, connecting courses in sequence or in parallel, and assessing new programs are relevant to all of us as we work to better our own classrooms.

We spent 18 months as part of a committee whose purpose was to revise the American Statistical Association’s Undergraduate Curriculum Guidelines (posted here). These new recommendations provide a flexible structure to ensure that students receive the necessary background and critical and problem solving skills to thrive in our increasingly data-centric world. Through our work on the undergraduate statistics guidelines committee, we were excited by many interesting and innovative ideas our colleagues were implementing in and about their own classrooms. This led us to co-edit a special issue of The American Statistician on Statistics and the Undergraduate Curriculum (December, 2015, including a guest editorial). In this blog post, we briefly describe several of the articles of this special issue, with the goal of familiarizing the readers with some of the issues and innovations that statisticians have implemented in their undergraduate classrooms. Many mathematicians teach introductory and advanced statistics courses, and we believe they have a vested interest in what statisticians can and should know mathematically. Additionally, they are likely interested in additional reflections on and ideas for their own classes. Our hope is that the special issue of TAS can be a valuable resource for those interested in statistics and the mathematical sciences at the undergraduate level.

The issue brought together a set of articles designed to help undergraduate statistics curricula be forward thinking. We begin with an editorial that includes a list of key papers discussing statistics at the undergraduate level. George Cobb provides a particularly provocative article encouraging all of us to “tear down” current curricula and start over. His piece is accompanied by 19 responses from renowned statisticians and education experts across the world. A link to these responses and George’s spirited rejoinder can be found here.

A number of the articles in the issue work to answer the question: “Do our bachelor’s graduates have the needed skills to compute with data?” Chamandy et al. describe problems they have encountered at Google that required sophisticated understanding of theoretical statistics. They describe excellent case studies for advanced undergraduate statistics students, by demonstrating problem solving in context. In another paper, Nolan and Temple Lang report on their summer program, “Explorations in Statistics Research”, which exposed six summer cohorts of students to the process of posing statistical questions and solving real world industry problems. In his paper, Grimshaw provides a framework for adding real data into a course with metrics arranged on two axes: data source and data management. On each axis the data is considered to be good/better/best for developing student skills of computing with data. Each of these responses provides practical examples of pedagogical innovations that statisticians have developed to help their students become more adept at working with real data in more realistic settings.

On the curricular side, many of the articles provide structure for a specific class designed to modernize the curriculum. For example, Hardin et al. and Baumer discuss different approaches to implementing a data science / computational statistics course in the modern era. Their articles provide templates for structuring the course to integrate data science with statistics while simultaneously allowing students opportunities to practice communicating results to a larger audience. Green and Blankenship provide an updated data-focused approach to the traditional Statistical Theory course. Their paper provides multiple great examples for making both Probability and Statistical Theory courses more modern and more interactive. Blades et al. and Khachatryan describe second courses (after introductory statistics), which are well suited to the goal of building students’ skills at making decisions based on data. Blades et al. discuss using design of experiments as a second course in statistics, which can follow introductory statistics combined with any level of mathematics. Khachatryan brings case studies into a time series course to help students engage with the real world connections.

The issue closes with a pair of articles (Chance & Peck and Moore & Kaplan) that address the curriculum from the assessment perspective, providing a framework for basing programmatic decisions. The set of articles will be of particular interest to readers who seek ideas for program evaluation, new approaches to teaching statistics, and to incorporate some new ideas into their existing courses and programs.

We hope that The American Statistician special issue and the extended bibliography of papers in the guest editorial as well as the online discussion provide useful fodder for further review, assessment, and continuous improvement of the undergraduate statistics curriculum. As mathematicians and statisticians we will work together to ensure that the next generation of students is able to take a leadership role by making decisions using data in the increasingly complex world that they will inhabit.

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1 Response to Preparing the Next Generation of Students in the Mathematical Sciences to “Think with Data”

  1. Avatar Samantha says:

    This is a pretty interesting piece. Thanks for writing it. I loved the thought provoking notions you mentioned.

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