Deborah J Hughes Hallett

Interests

Research

Design of curricula and pedagogy for undergraduate mathematics nationally and internationally. Current work in Niger and India. Recently in Pakistan, Brunei, and Colombia. Mathematics and its use in public policy. The role of mathematics in bringing together faculty from countries that may otherwise not have good relations.

Teaching

Mathematics in relation to other fields. How to involve students and practitioners in mathematical thinking. Uses of technology in reaching students.

Courses

Scholarly Contributions

Books

• Hughes Hallett, D. J. (2022). Applied Calculus. Wiley.
• Hughes Hallett, D. J., & Connally, E. (2019). Functions Modeling Change: A Preparation for Calculus. Wiley.
• Hughes Hallett, D. J., Lock, P., & Flath, D. (2018). Applied Calculus. Wiley.
• Hughes Hallett, D. J. (2018). Applied Calculus. Wiley.
• Hughes Hallett, D. J. (2020). Calculus: Multi Variable. Wiley.
• Hughes Hallett, D. J. (2020). Calculus: Single Variable. Wiley.
• Hughes Hallett, D. J., Connally, E., & Lozano, G. (2019). Precalculus: Functions Modeling Change. Wiley.
  More info

  Text emphasizing understanding in the context of modeling. Supports instructors who want to emphasize meaning in addition to manipulation.
• Hughes Hallett, D. J., Gleason, A., Lock, P., & Flath, D. (2019). Applied Calculus. Wiley.
  More info

  Text for college calculus courses focusing on reasoning and application in economics and the life sciences.
• Hughes Hallett, D. J., McCallum, W., Spiegeler, A., & Kalaycioglu, S. (2015). Algebra: Form and Function. Wiley.
  More info

  Text for high school and college focusing on algebraic structure.

Chapters

• Hughes Hallett, D. J. (2021). Policing and the Issue of Racial Profiling. In Mathematics for Social Justice. MAA Press.
• Hallett, D. (2006). The importance of a story line: Functions as models of change. In Functions as Models of Change. Mathematical Association of America. doi:10.5948/UPO9781614443025.051
  More info

  If students are to remember what they learn, the courses they take must tell a coherent story. This story provides a framework onto which they can hang their newly acquired knowledge. Without such a framework, teachers find themselves having to repeat material. Precalculus courses often run the risk of not being memorable because they are defined as the skills needed in calculus rather than telling a coherent story. Thus, the first decision in designing a new precalculus course is to choose the story it will tell. The central theme we chose for our precalculus course is how functions can be used to model change. This theme provides a framework into which all the prerequisite material for calculus naturally fit (functions, graphing, algebra, trigonometry, numerical approximation), while at the same time illuminating a central concept of calculus—the rate of change [1]. Choosing a family of functions to represent a real situation requires students to think about the qualitative behavior of different types of functions. A good way to decide, for example, whether an exponential function fits a particular set of data is to look at a plot. The shape of the plot suggests the family; the values of the parameters are then determined from the data. We have found that introducing the rate of change as the slope of a line is an excellent springboard for comparing the behavior of linear and exponential functions (absolute versus relative rate of change), and for introducing the concepts of increasing, decreasing, and concavity.
• Hallett, D. (2006). What have we learned from calculus reform? The road to conceptual understanding. In What have we learned from Calculus Reform?. Mathematical Association of America. doi:10.5948/UPO9781614443025.008
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  Goals. In order to evaluate the impact of calculus reform, we first need to recall its goals. Although different people may phrase it differently, everyone involved would agree that they were trying to improve the teaching of calculus. Some would say they wanted more student involvement; others would say they wanted to take advantage of technology; others would say they wanted to emphasize problem solving and modeling. Most would agree that they wanted to improve conceptual understanding. What has been the impact of this effort?. Background to calculus reform: Rationale for change. The teaching of calculus came under scrutiny in the 1980s for several reasons. One was concern over the students' apparent lack of understanding of the subject, especially when asked to use it in an unfamiliar situation. Faculty outside mathematics frequently complained that students could not apply the concepts they had been taught. In some instances, ideas were being used in other fields in ways that were sufficiently different from the way they are used in mathematics that it was not surprising that students did not make the connection. For example, the minimization of average cost was done symbolically in mathematics, if at all, whereas it is usually done graphically in economics. However, students also had difficulty recognizing mathematical ideas that were presented the same way as in mathematics. A small difference in notation or the absence of familiar clues-such as “largest” or “smallest” in an optimization problem-easily threw students off. This striking difficulty in transferring knowledge between fields suggested that students' understanding was not sufficiently robust.

Journals/Publications

• Hughes Hallett, D. J. (2016). Connections: Mathematical, Interdisciplinary, Personal, Electronic. Proceedings of the Canadian Mathematics Education Study Group.
• Hughes Hallett, D. J. (2014). Pictures and Proofs: Which Come First?. Oberwolfach Mathematisches Forschungsinstitut Report 56/2014.
• Hallett, D. (2013). Foreword. Enhancing Mathematics Understanding through Visualization: The Role of Dynamical Software. doi:10.4018/978-1-4666-4050-4
• Ganter, S. L., Lewis, D. J., & Hughes-Hallett, D. (1998). Calculus reform [1]. Science, 279(5359), 2019-2020.
• Hughes-Hallett, D. (1998). Interdisciplinary Activities in Mathematics and Science in the United States. ZDM - International Journal on Mathematics Education, 30(4), 116-118.
  More info

  Abstract: This paper outlines the need for interdisciplinary efforts in mathematics and science at university level in the US. It summarizes the different types of activities currently taking place. They are spread along a spectrum from minimal coordination to complete integration; each having different advantages and disadvantages. Examples of each type or activity are briefly described.

Presentations

• Hughes Hallett, D. J. (2025, March).

  AI and Data Science Labs

  . Online seminar. Online: MAA.
• Hughes Hallett, D. J. (2024, April). Workshop on Teaching & Learning Assistants in the Classroom
  . Mecha workshop. Tucson: CUES.
• Hughes Hallett, D. J. (2022, November). Active Learning across the Mathematics Curriculum. Provost's Workshop. Charlotte: UNC Charlotte.
• Hughes Hallett, D. J. (2023, January). AP Precalculus:  Why? What? Who For?
  . MEAD. TUSD: CRR.
• Hughes Hallett, D. J. (2023, October). AI in Health Care. Meeting of AI working group. Harvard School of Public Health: Harvard Student Group on AI.
• Hughes Hallett, D. J. (2021, February). Mathematics and Climate Change. Mathematics Instruction Colloquium.
• Hughes Hallett, D. J. (2022). Quantitative Methods for Policy Decisons: The Covid Travel Ban. Workshop for Spanish EngineersReal Colegio Complutense.
• Hughes Hallett, D. J. (2022, Aoril). Engaging Students. JMM. Zoom: AMS.
• Hughes Hallett, D. J. (2022, April). Data Driven. AMATYC and MAA. Phoenix: ArizMATYC.
• Hughes Hallett, D. J. (2022, February). Data Driven: Visualizing the Future. SIMIODE Expo Keynote.
• Hughes Hallett, D. J. (2022, January). Climate Change for Everyone. MEAD 2022.
• Hughes Hallett, D. J. (2022, June). AI: The Good, the Bad, and the Challenging. Joyful Jamboree. Zoom: Texas State University.
• Hughes Hallett, D. J. (2022, June). Climate Change and the Labor Market. Industry Presentation. Zoom: Forvia.
• Hughes Hallett, D. J. (2022, November). The Glass Ceiling: Keynote. Arizona Symposium for Women in Mathematics. Prescott: Embry Riddle.
• Hughes Hallett, D. J. (2022, November). Window into Data Science (PD for middle and high school teachers). Seminar. Cambridge: Teachers as Scholars.
• Hughes Hallett, D. J. (2022, Spring). Corruption. Carr Center for Human Rights.
• Hughes Hallett, D. J. (2021, August). Interactive Classroom. MathFest.
• Hughes Hallett, D. J. (2021, August). Two Faces of Algorithms. MathFest.
• Hughes Hallett, D. J. (2021, December). Does Data Belong in Mathematics. PD for High School teachers at Needham HS.
• Hughes Hallett, D. J. (2021, Fall). Does Data Have a Place in a Calculus Course?. Florida Interntional University (FIU) Colloquium.
• Hughes Hallett, D. J. (2021, Feb). Following the Covid Trail in Calculus. T^3 ConferenceTI.
• Hughes Hallett, D. J. (2021, Jan). Climate Change in Calculus. JMMAMS-MAA.
• Hughes Hallett, D. J. (2021, Jan). Covid in Differential Equations. JMM. Zoom: AMS-MAA.
• Hughes Hallett, D. J. (2021, Jan). How the Pandemic Can Help us Teach Logarithms. MEADCRR.
• Hughes Hallett, D. J. (2021, Jan). Modeling with Data Using a Spreadsheet. JMMAMS-MAA.
• Hughes Hallett, D. J. (2021, January). Sea Level Rise and its Costs. JMMAMS-MAA.
• Hughes Hallett, D. J. (2021, January). Unlocking the Differential Equations in Covid Data. JMM-21.
• Hughes Hallett, D. J. (2021, November). Big Ideas of Algebra. Teachers as Scholars (PD for high school teachers).
• Hughes Hallett, D. J. (2021, October). Extracting Meaning from Data. Stanford Online High School.
• Hughes Hallett, D. J. (2021, Spring and Fall). Professional Development Workshops for College Faculty. Organized by Wiley.
• Hughes Hallett, D. J. (2021, Spring). Does Data Have a Place in a Calculus Course? Climate Change and Pandemics. Saudi Arabian Mathematics Society: Special Lecture.
• Hughes Hallett, D. J. (2021, Summer). When Should Students Learn About Data? Now!. Canadian Mathematics Society.
• Hughes Hallett, D. J. (2020, February). Higher Order Thinking Skills (HOTS) in Mathematics. Faculty Professional Development Workshop. Coral Gables Florida: Wiley.
  More info

  Session for faculty in mathematics and science on how--and why--we should work to increase our students' higher order thinking skills.
• Hughes Hallett, D. J. (2020, February). Keynote Address: Skills and Concepts: Rivals or Partners. Qatar Math Day. Qatar: Ministry of Education.
• Hughes Hallett, D. J. (2020, January). Measles for All Ages. MEAD.
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  Session on role of mathematics in getting students to understand the impact of measles and vaccination.
• Hughes Hallett, D. J. (2020, March). Keynote: Thinking outward and Teaching Backward: Skill and Understanding in Mathematics. Conference on Academic Support. Miami: Florida International University.
• Hughes Hallett, D. J. (2019, April). Quantative Intuition. CUES Mapping Educational Challenges Interdisciplinary WorkshopCenter for Univrsity Education Scholarship.
• Hughes Hallett, D. J. (2019, January). Who Gets to Draw the Lines?. MEAD. Tucson: CRR.
• Hughes Hallett, D. J. (2019, July). Role of Data in Public Policy: Race and Policing, International Criminal Court. Conference for Spanish Graduate studentsReal Colegio Complutense.
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  To show graduate students from engineering how their statistical skills can be used to address social problems
• Hughes Hallett, D. J. (2019, July). Women in Mathematics and Science. Asian University for Women Bangladesh. Zoon: Asian University for Women (Bangladesh).
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  Discussion of many roles of mathematicians and scientists in public and academic life.
• Hughes Hallett, D. J. (2019, Novermber). Teaching Backward: Techniques for Student Centered Teaching. Professional Development. Online webinar and blog: Wiley.
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  Techniques for developing effective and student friendly courses.
• Hughes Hallett, D. J. (2019, October). Silos and Spiders: What Measles Tells Us about Policy and Education. Science and Diplomacy ConferenceUA.
  More info

  This talk considered contributions to the measles tragedy from policy, education, public health, development, and political will. One significant contributor is the lack of coordination between education and public health. This lack of coordination is an unsurprising consequence of the silo-ed design of our educational systems.
• Hughes Hallett, D. J. (2018, April). Prerequisites and Corequisites: What is in Our Future?. MAA-AMATYC Southwest Section. Pima CC: MAA-AMATYC.
• Hughes Hallett, D. J. (2018, January). Prequisites Past and Future. JMM. SanDiego: AMS and MAA.
• Hughes Hallett, D. J. (2018, January). Prequisites: Past and Future. Joint Mathemtics Meetings. San Diego: AMS-MAA.
• Hughes Hallett, D. J. (2018, March). What is So Fundamental about the Fundamental Theorem of Calculus?. T^3: Teachers Teaching With Technology. San Antonio, Texas: Texas Instruments.
• Hughes Hallett, D. J. (2018, May). Keynote: What Makes Algebra So Hard?. Changing the Culture. Vancouver Canada: Pacific Institute of Mathematical Sciences.
• Hughes Hallett, D. J. (2018, November). What Makes Algebra So Hard?. Seminar for Teachers. Cambridge MA: Teachers as Scholars.
• Hughes Hallett, D. J. (2018, October). From Silos to Spiders: New Approaches to Teaching. Good Practices in Higher Education: TransAtlantic Perspective. Cambridge MA: Real Colegio Computense (Coalition of Spanish Universities).
• Hughes Hallett, D. J. (2017, December). Serving Underprepared Students. National Meeting of Canadian Mathematical Society. Waterloo, Canada: Canadian Mathematical Society.
• Hughes Hallett, D. J. (2017, December). The Internet and Globalization. National Meeting of Canadian Mathematical Society. Waterloo, Canada: Canadian Mathematical Society.
• Hughes Hallett, D. J. (2017, March). Statistics at the Supreme Court: Arizona Redistricting. Conference: Teachers Teaching with Technology. Chicago: Texas Instruments.
• Hughes Hallett, D. J. (2017, March). What's Natural about e and pi? (Or: What is Natural about Base e and Radians?). Conference: Teachers Teaching with Technology. Chicago: Texas Instruments.
• Hughes Hallett, D. J. (2017, November). How Much Difference Do Alternative Teaching Methods Really Make?. Reimagining Calculus Education. Hoboken, NJ: Steven's Institute of Technology.
• Hughes Hallett, D. J. (2017, October). Quantiative Pipeline. Faculty Research Seminar. Cambridge MA: Harvard Kennedy School.
• Hughes Hallett, D. J. (2016, February). Co-Chair Workshop on Critical Issues in Math Ed: Observing, evaluating and improving teaching. MSRI, Berkeley.
• Hughes Hallett, D. J. (2016, February). Logarithms: Yesterday, Today, and Tomorrow. Teachers Teaching with Technology.
• Hughes Hallett, D. J. (2016, February). Numbers in the News: Race and the Law. Teachers Teaching with Technology.
• Hughes Hallett, D. J. (2016, February). The Perils of Chikungunya and of (a)(b)(c). Teachers Teaching with Technology.
  More info

  With many thanks to Joceline Lega:http://www.u.arizona.edu/~lega/CHIK_Site/sourceFiles/CHIK_Poster.pdf
• Hughes Hallett, D. J. (2016, January). College Calculus and the Preparation Gap: Identified Problems and Models for Improvement.. JMM Seattle.
• Hughes Hallett, D. J. (2016, June). Mathematics in the Time of MOOCs. Fields Institute, Canada.
• Hughes Hallett, D. J. (2016, June). Use of Data in Policy Analysis. by invitation of the Ministry of Development, Gilgit-BaltistanUnited Nations.
• Hughes Hallett, D. J. (2016, November). Teaching Mathematics for Today and Tomorrow. Pontificia Universidad Javeriana, Colombia. Bogota: Department of Mathematics (talk given with simultaneous translation to faculty and students).
• Hughes Hallett, D. J. (2016, October). Calculus: Affecting the Lives of Millions. Conference: Reimagining Calculus Education. Hoboken, NJ: Stevens Institute of Technology.
• Hughes Hallett, D. J. (2015, April). Globalizing Our Classrooms. ORMATYC Keynote Speaker.
• Hughes Hallett, D. J. (2015, December). Didactics of Higher Education as a Scientific Discipline. KHDM, Hannover, Germany.
• Hughes Hallett, D. J. (2015, December). Mathematics for the Social Sciences. Wright State Mathematics Department Colloquium.
• Hughes Hallett, D. J. (2015, June). Connections: Mathematical, Interdisciplinary, Personal, Electronic. Canadian Mathematics Education Study Group Keynote.
• Hughes Hallett, D. J. (2015, March). Accumulated Change: Bridging Calculus and Modeling. Teachers Teaching with Teachnology.
• Hughes Hallett, D. J. (2014, April). Flipping and Resequencing in Algebra, Statistics, and Calculus. ORMATIC Annual Conference. Lincoln City, Oregon: ORMATYC (Oregon Two Year Colleges).
• Hughes Hallett, D. J. (2014, April). Role of Basic Skills in Technical Education. Leaders' Forum: World Skills. Bogota, Colombia: SENA.
• Hughes Hallett, D. J. (2014, January). Mathematians in Inservice Teacher Education. Mathematicians and School Mathematics Education. Banff, Canada: BIRS.
• Hughes Hallett, D. J. (2014, May). Globalizing Our Classrooms. CUNY 2014 Mathematics ConferenceCUNY Mathematics Departments.
• Hughes Hallett, D. J. (2014, October). Mathematics and the Social Sciences. CBMS Forum on Mathematics in the First Two Years.

Poster Presentations

• Hughes Hallett, D. J. (2014, December). Pictures and Proofs: Which Come First?. Oberwolfach Workshop on Mathematics in Undergraduate Programs. Germany: MFO.

Reviews

• Hughes Hallett, D. J. (2022. Establishing a New Standard of Care for Calculus Students with Evidence from a Randomized Trial.