Juliana Belding

APR

13

2017

1:50PM

Calculus Applied! Gauging and Supporting Student Beliefs about the Relevance of Calculus to Other Disciplines

Millions of students take calculus each year, usually as a prerequisite for another discipline or career. Yet the exposure students get to applications of calculus is often limited, leading to a potential disconnect.

So what are student beliefs about calculus’ relevance to these other areas? And what sort of course experiences might help students better see the potential relevance of calculus to other fields?

In this talk, I’ll share about my ongoing attempts to answer these questions. I’ll discuss “Calculus Applied!”, a series of interactive modules that feature practitioners from fields such as mathematical biology, economics, physics and medical imaging discussing problems in their fields and how calculus plays a role. These will launch as a massive open online course (MOOC) this summer 2017.

I’ll also talk about their pilot use in Calculus classes at Harvard College and Boston College and share results from a survey designed to measure student beliefs about the relevance of calculus and math to fields outside mathematics.

## Past talks

R. James Milgram

MAR

05

2015

4:30PM

The implications of common core for college and graduate education

A key part of the federal government’s requirement for any state to apply for Race to the Top (RttT) money in 2010 was that the state agree to “implement policies that exempt from remedial courses and place into credit-bearing college courses students who meet the consortium-adopted achievement standard . . . for those assessments,” and to basically agree to adopt the Common Core Standards (CC).

Given the very low level of the mathematics required in CC, this has profound consequences not only for the first year mathematics offerings of a public university such as Ohio State, but for the entire undergraduate curriculum. Indeed, according to the main writers for the CC mathematics standards, their definition of college readiness is “a student who has passed Algebra II.” But their description of Algebra II is a weak one, with critical topics missing and, overall, significantly below the level that was expected previously.

On the other hand, CC was advertised by its supporters and the current administration as more rigorous than any state’s then current standards, and as the way we will strengthen our Science, Technology, Engineering, and Mathematics (STEM) pipeline. We will show that these claims are simply not true, and were never the real intent of CC. Then we discuss the long term consequences of the almost universal adoption of CC by the states.

R. J. Milgram is emeritus professor of mathematics at Stanford University. He has served on the board of directors for the National Institute for Education Sciences, the NASA Advisory Council, and the Achieve Mathematics Advisory Panel. He was the sole expert in mathematics itself among the original members of the Common Core Validation Committee. From 2002 to 2005, Professor Milgram headed a project funded by the U.S. Department of Education that identified and described the key mathematics that K-8 teachers need to know. He also helped to direct a project partially funded by the Thomas B. Fordham Foundation that evaluated state mathematics assessments. He was one of the four main authors of the 1997 – 2010 California Mathematics Standards, as well as one of the two main authors of the California Mathematics Framework. He was also one of the main advisors for the mathematics standards previous to Common Core in Florida, Georgia, Massachusetts , Michigan, Minnesota, New Mexico, and Texas. Among many other honors, he held the Gauss Professorship at the University of Goettingen, the Regent's Professorship at the University of New Mexico, and Distinguished Visiting Professorships at the Chinese Academy of Sciences in Beijing and at the University of Lille. R. J. Milgram has published over 100 research papers in mathematics and four books, as well as serving as an editor of many others. He currently works on questions in robotics and protein folding. He received his undergraduate and master's degrees in mathematics from the University of Chicago, and a Ph.D. in mathematics from the University of Minnesota.

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Eric Schulz

MAR

26

2015

3:00PM

Eric Schulz
in
CH240

Sticky mathmatics

Interactive visualizations of mathematics are powerful tools that impact student learning and their understanding of concepts that stick with them for a long time. We will explore content and interactive visualizations that have been developed for precalculus and calculus with an eye towards ways they can be used to impact teaching and learning.

Eric Mazur

APR

02

2015

11:00AM

Eric Mazur
in
CH240

Assessment: The Silent Killer of Learning

Why is it that stellar students sometimes fail in the workplace while dropouts succeed? One reason is that most, if not all, of our current assessment practices are inauthentic. Just as the lecture focuses on the delivery of information to students, so does assessment often focus on having students regurgitate that same information back to the instructor. Consequently, assessment fails to focus on the skills that are relevant in life in the 21st century. Assessment has been called the "hidden curriculum" as it is an important driver of students’ study habits. Unless we rethink our approach to assessment, it will be very difficult to produce a meaningful change in education.

Eric Mazur

APR

02

2015

3:00PM

Eric Mazur
in
CH240

Focus on Math Instructions: Confessions of a Converted Lecturer

I thought I was a good teacher until I discovered my students were just memorizing information rather than learning to understand the material. Who was to blame? The students? The material? I will explain how I came to the agonizing conclusion that the culprit was neither of these. It was my teaching that caused students to fail! I will show how I have adjusted my approach to teaching and how it has improved my students’ performance significantly.

Krista Maxson

APR

09

2015

3:00PM

College Credit Plus and the Flipped Classroom

This presentation will outline the process used at Shawnee State University to create four college-level mathematics courses in the flipped format for use in offering dual enrollment courses (now College Credit Plus-CCP) at local high schools. Included will be an overview of College Credit Plus with an emphasis placed on the role of Institutions of Higher Education. Eight faculty in the department of Mathematical Sciences at Shawnee State University worked with 20 high school teachers to create content and resources for college algebra, trigonometry, calculus and statistics. Fifteen of the high school teachers completed nine semester hours of graduate mathematics over the summer and are offering the courses at their high school mentored by faculty in the department. The report will highlight what worked as well as lessons learned. This effort was supported financially by a Straight-A-Fund (Ohio Department of Education) grant.

Jessica Ellis

APR

23

2015

3:00PM

The features of successful college calculus programs: An overview of the CSPCC project’s main findings

Calculus I has been pointed to as a major contributing factor in students’ decisions to not pursue STEM (Science, Technology, Engineering, and Mathematics) disciplines, despite years of research and innovations focused on improving calculus instruction. Motivated by this, the MAA has worked with researchers in mathematics and mathematics education to examine the current state of Calculus I programs across the country, identify institutions with more successful Calculus I programs, and conduct case studies at these institutions to understand the factors contributing to their success. In this talk I will highlight the major findings from the Characteristics of Successful Programs in College Calculus (CSPCC) project, many of which will be featured in a monograph to be published later this year. First I will draw on the survey data to discuss the current state of Calculus I across the country, particularly drawing attention to what this data tells us about the students who persist in their STEM disciplines after taking Calculus I and those that don’t. Second, I will summarize the key findings from our case studies, paying special attention to the preparation of graduate students involved in the teaching of Calculus I. Time permitting, I will also discuss our current work on a follow-up grant in which we are investigating the precalculus/calculus sequence.

Angela K. Kubena

MAY

21

2015

3:00PM

"Michigan Mathematics": Successes, Challenges, and Many Moving Parts

In the early 1990s the Michigan math department implemented substantial changes to its calculus program, including adoption of a more conceptual focus, incorporation of cooperative learning in the classroom, and implementation of an extensive instructor training program. Called “Michigan Math,” this continues today, and results on a nationally normed test of calculus learning showed students in Michigan’s standard calculus I course outperforming students at many other institutions. In this talk, we describe some of the history, key characteristics, successes, and challenges of the undergraduate math program at Michigan in general, and of the calculus and instructor training programs in particular.

Matt Thomas

AUG

05

2015

12:40PM

Measuring Conceptual Understanding in Calculus

Measuring conceptual knowledge in calculus is a difficult but important task. It has implications for appropriate course placement, for formative and summative assessment during a course, and can play a role in comparing the effects of different instructional techniques. In this talk, I will describe work analyzing the recently developed Calculus Concept Inventory. Challenges in developing an instrument include assessing content validity, internal structure validity, and reliability. I will discuss the importance of each of these for an instrument, and the results that we have seen in our investigations of the Calculus Concept Inventory.

Emma Smith Zbarsky

OCT

15

2015

1:50PM

Open Source Resources, Sines of the Future

We shall discuss a variety of open source resources that have been created for teaching calculus as well as the implementation currently in place at the Wentworth Institute of Technology. We will provide example problems created by the author together with the cognitive science research behind their design and presentation using Quadbase and OpenStaxTutor. We shall also consider the use of WebWork and the National Problem Library to standardize and localize our courses.

Yvonne Lai

OCT

29

2015

1:50PM

Yvonne Lai
in
CH240

Knowledge and tasks connecting elementary, secondary, and disciplinary mathematics

A well-prepared teacher should be able to help her students see mathematics as ideas that develop over time. Mathematics courses designed specifically for prospective secondary teachers aim for prospective teachers to see and find connections across elementary, secondary, and disciplinary mathematics, and beyond that to be able to use those connections in their future teaching. While there is broad agreement with these aims, there is also little consensus around how to carry them out. Two challenges in meeting these aims are identifying content that lends itself to such connections and designing tasks that can be used to engage with that content. In this talk, I will propose a few examples of content and tasks, and discuss what may make them useful. I will then invite the audience to contribute ways they have used their teaching to meet the challenge of identifying content and designing tasks for the purpose of connecting elementary, secondary, and disciplinary mathematics.

Marilyn Carlson

OCT

30

2015

3:00PM

A Research-Based Approach for Improving Precalculus Teaching and Learning

The function concept is a central idea of precalculus and beginning calculus and is used for modeling in the sciences and engineering, yet many students complete courses in precalculus and calculus with weak understandings of this concept. Students who are unable to construct meaningful function formulas to relate two varying quantities have little chance of responding to novel applied problems, or understanding key ideas of calculus such as derivative, accumulation and the Fundamental Theorem of Calculus. I will share data that reveals how students might construct these and other critical reasoning abilities and understandings for learning calculus. I will share the research developed Pathways Precalculus student materials and teacher resources that provide the context for this research, and are resulting in large gains in student learning of the function concept and other foundational ideas for learning calculus. Results from using Pathways materials at 5 large universities will be shared and contrasted with other popular approaches to teaching precalculus mathematics.

Vilma Mesa

MAY

18

2016

1:50PM

Vilma Mesa
in
CH240

The National Study of Calculus I: Insights, Lessons Learned, and Future Directions

Understanding how colleges manage to keep students in the Calculus I track is an issue of national importance and the impetus behind a national study of Calculus I in the United States sponsored by the Mathematical Association of America (MAA) and funded by the National Science Foundation (DRL REESE #0910240, PIs David Bressoud, Chris Rasmussen, Vilma Mesa, and Michael Pearson). The study titled Characteristics of Successful Programs in College Calculus I (CSPCC) took place between 2009 and 2015 and included a large-scale survey of Calculus I programs followed up by case-studies of 18 postsecondary programs that were identified as successful. Success was defined by a combination of student variables: persistence in calculus as marked by stated intention to take Calculus II (a proxy for persistence in a STEM major); affective changes, including enjoyment of math, confidence in mathematical ability, interest to continue studying math; and passing rates. In this talk, I will present major findings that cut across the various institutions, regarding teaching and teachers, coordination, and placement policies, and specific findings pertaining the various types of institutions in the study. I will also describe some of the lessons we learned, and some of the ongoing questions we are pursuing.

Andrew Hacker

SEP

16

2016

12:00PM

Queens College, City University of New York

On the math myth

Why do we inflict algebra, geometry, trigonometry, and even calculus on all young Americans, regardless of their interests or aptitudes? asks American political scientist and public intellectual Andrew Hacker. His 2012 New York Times op-ed questioning common core mathematics requirements became one of the paper’s most widely circulated articles.

Though Hacker honors mathematics as a calling and extols its glories and its goals, he argues in The Math Myth and Other STEM Delusions (2015) that mandating it for everyone prevents other talents from being developed.

Daniel Otero

NOV

18

2016

1:50PM

Teaching Undergraduates (Trigonometry) with Primary Historical Sources

The author is one of a team of seven principal investigators on a five-year NSF-funded project called Transforming Instruction in Undergraduate Mathematics via Primary Historical Sources (TRIUMPHS), which is designing and site-testing curricular materials for teaching standard topics in the university mathematics curriculum via the use of primary historical sources. Recently, he made use of a Primary Source Project (of his creation) with precalculus students who are about to do a traditional unit in trigonometry. At this talk, the goals and rationale for the work of TRIUMPHS and the particular experiences of the author with the trigonometry project will be shared and discussed. Attendees will also be invited to work through a portion of the trigonometry project.

Ben Braun

JAN

25

2017

12:30PM

University of Kentucky

Active Learning in Postsecondary Mathematics

A growing number of college math courses include active learning components. What does this look like in practice? What is the right balance to strike between active learning and direct instruction? What are common challenges for departments and faculty implementing active learning? What outcomes should we expect as a result of active learning? In this talk, we will provide some context for current interest in active learning and discuss some answers to these and related questions.

Eddie Fuller

APR

11

2017

12:40PM

Making RUME: Building Research In Undergraduate Mathematics Education capacity in a mathematics department

In 1999 the provost of West Virginia University, in response to low success rates in college algebra and calculus, proposed the creation of a new Institute for Math Learning to investigate and implement new course structures in a hybrid ‘emporium’ model. As a part of this initiative, several tenure line faculty were hired to implement and manage these courses with an interest in pedagogical and educational research in the mathematics realm. Over time, this group of faculty grew to be primarily focused on Research in Undergraduate Mathematics Education (RUME) leading to a discussion of how faculty are rewarded for productivity and what strategic directions would be important of the department. A decision was made to incorporate this area into our PhD program as a major area and our promotion and tenure documents revised to be more inclusive. In this talk the mechanics of this process will be discussed and some of the outcomes from the process presented along with some long term goals and lessons learned.