Digital Commons Network^™

Tribute To Gene Chase, Calvin Jongsma

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Gene’s academic work was always one of service to God, his students, and his colleagues, and his intellectual passion was to promote the development of Christian perspectives on various aspects of the field. His contributions to the ACMS have been much appreciated and, God willing, may still bear fruit into the future.

Incorporating Perspectival Elements In A Discrete Mathematics Course, Calvin Jongsma

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Discrete mathematics is a vast field that can be explored along many different paths. Opening with a unit on logic and proof and then taking up some additional core topics (induction, set theory, combinatorics, relations, Boolean algebra, graph theory) allows one to bring in a wealth of relevant material on history, philosophy, axiomatics, and abstraction in very natural ways. This talk looks at how my 2019 textbook on discrete mathematics, focused in this way, came to be, and it highlights the various perspectival elements the book includes.

Generations Of Reason: A Family’S Search For Meaning In Post-Newtonian England (Book Review), Calvin Jongsma

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Reviewed Title: Generations of Reason: A Family's Search for Meaning in Post-Newtonian England by Joan L. Richards. New Haven, CT: Yale University Press, 2021. 456 pp. ISBN: 9780300255492.

Richard Whately's Revitalization Of Syllogistic Logic, Calvin Jongsma

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This is an expanded version of the first chapter Richard Whately’s Revitalization of Syllogistic Logic in Aristotle’s Syllogism and the Creation of Modern Logic edited by Lukas M. Verburgt and Matteo Cosci (Bloomsbury, 2023). Drawing upon the author’s 1982 Ph. D. dissertation (https://digitalcollections.dordt.edu/faculty_work/230/ ) and more current scholarship, this essay traces the critical historical background to Whately’s work in more detail than could be done in the published version.

The History Of Mathematics: A Source-Based Approach, Volume Ii (Book Review), Calvin Jongsma

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Reviewed Title: The History of Mathematics: A Source-Based Approach, Volume II by June Barrow-Green, Jeremy Gray, and Robin Wilson. Providence, Rhode Island: MAA Press, an imprint of the American Mathematical Society, 2022. 687 pp. ISBN: 978-1-4704-4382-5

The New Era In American Mathematics, 1920-1950 (Book Review), Calvin Jongsma

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Reviewed Title: The New Era in American Mathematics, 1920-1950 by Karen Hunger Parshall. Princeton University Press, 2022. 640 pages. ISBN: 9780691197555.

Classroom And Computational Investigations Of Camel Up, Thomas J. Clark

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Camel Up is a popular board game in which players score points by betting on camels which move randomly via a dice mechanic. The game is available both as a board game [1], as well as an IOS App [2]. Because of the random nature of the camels it is generally difficult to play optimally, but one can nevertheless develop various strategies. Probabilistic knowledge proves helpful in assigning relative value to potential game choices. We discuss how this game can be used to motivate and provide context for learning about the concepts of conditional probability and expected value. Also we …

For The Love Of Mathematical Research: A Conversation With Undergraduate Research Students, Mike Janssen

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"One of my passions as a professor is creating opportunities for students to ask questions about mathematics."

Posting about students' perspectives on mathematics research from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

https://inallthings.org/for-the-love-of-mathematical-research-a-conversation-with-undergraduate-research-students/

The Continuous, The Discrete And The Infinitesimal In Philosophy And Mathematics (Book Review), Calvin Jongsma

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Reviewed Title: The Continuous, the Discrete and the Infinitesimal in Philosophy and Mathematics by John L. Bell. Springer, 2019. 313 pp. ISBN: 9783030187064.

The History Of Mathematics: A Source-Based Approach, Volume 1 (Book Review), Calvin Jongsma

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Reviewed Title: The History of Mathematics: A Source-based Approach, Volume 1 by June Barrow-Green, Jeremy Gray, and Robin Wilson. Providence : American Mathematical Society, 2019. 488 pp. ISBN: 9781470443528.

Measurement (Book Review), Calvin Jongsma

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Reviewed Title: Measurement by Paul Lockhart. Cambridge, MA: Harvard University Press, 2012. 407 pp. ISBN: 9780674057555.

Arithmetic (Book Review), Calvin Jongsma

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Reviewed Title: Arithmetic by Paul Lockhart. Cambridge, MA: Harvard University Press, 2017. 223 pp. ISBN: 9780674972230.

A Mathematician's Lament: How School Cheats Us Out Of Our Most Fascinating And Imaginative Art Form (Book Review), Calvin Jongsma

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Reviewed Title: A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form by Paul Lockhart. New York: Bellevue Literary Press, 2009. 144 pp. ISBN: 9781934137178.

Comparing Powers Of Edge Ideals, Mike Janssen, Thomas Kamp, Jason Vander Woude

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Given a nontrivial homogeneous ideal I ⊆ k[x1, x2, . . . ,xd], a problem of great recent interest has been the comparison of the rth ordinary power of I and the mth symbolic power I(m). This comparison has been undertaken directly via an exploration of which exponents m and r guarantee the subset containment I(m) ⊆ Ir and asymptotically via a computation of the resurgence ρ(I), a number for which any m/r > ρ(I) guarantees I(m) ⊆ Ir. Recently, a third quantity, the symbolic defect, was introduced; as It ⊆ I(t), the symbolic defect is the minimal number of generators …

Finding Meaning In A Multivariable World: A Conceptual Approach To An Algebra-Based Second Course In Statistics, Karen Mcgaughey, Beth Chance, Nathan L. Tintle, Soma Roy, Todd Swanson, Jill Vander Stoep

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Although the teaching of the first course in statistics has improved dramatically in recent years, there has been less focus on a similarly conceptual-based second course aimed at non-majors. We present a curriculum for the second course, designed to expand statistical literacy across disciplines, which focuses on conceptual understanding of multivariable relationships through data visualization, study design, the role of confounding variables, reduction of unexplained variation, and simulation-based inference, rather than the mathematically-based discourse often used in the second course. Our curriculum uses a student-centered pedagogical approach, utilizing guided discovery activities based on real-world case studies, facilitated by student-focused technology …

Start A Math Teacher Circle: Connect K-12 Teachers With Engaging, Approachable, And Meaningful Mathematical Problems, Tom Clark, Mike Janssen, Amanda Harsy, Dave Klanderman, Mandi Maxwell, Sharon Robbert

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Many K-12 math teachers are not ready to teach from a conceptual and inquiry-oriented perspective because they have an algorithmic understanding of mathematics. One solution is to create a math teacher circle (MTC), which provides conceptual and inquiry-based learning activities and builds professionalism among the teachers. In this paper, we describe the origins of two such MTCs, highlighting the process of identifying leadership team members, submitting the grant proposal for seed money, and hosting launch events, intensive summer workshops, and monthly meetings during the academic year. We also share opportunities for professional development for college and university faculty, including research …

Abstraction And Infinity (Book Review), Calvin Jongsma

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Reviewed Title: Abstraction and Infinity by Paolo Mancosu, Oxford University Press, 2017. 222 pp. ISBN: 9780198746829.

Sourcebook In The Mathematics Of Medieval Europe And North Africa (Book Review), Calvin Jongsma

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Reviewed Title: Sourcebook in the Mathematics of Medieval Europe and North Africa, by Victor J. Katz. Menso Folkerts, Barnabas Hughes, Roi Wagner, and J. Lennart Berggren, Eds., Princeton University Press, Princeton, 2016. 574 pp. ISBN: 9780691156859.

Finding Fibonacci: The Quest To Rediscover The Forgotten Mathematical Genius Who Changed The World (Book Review), Calvin Jongsma

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Reviewed Title: Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World by Keith Devlin. Princeton, NJ: Princeton University Press, 2017. 256 pp. ISBN: 9780691174860.

Making And Breaking Mathematical Sense (Book Review), Calvin Jongsma

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Reviewed Title: Making and Breaking Mathematical Sense by Roi Wagner. Princeton, NJ: Princeton University Press, 2017. 236 pp. ISBN: 9780691171715.

Mathematical Justice?, Valorie L. Zonnefeld

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"I’d like to suggest the possibility of guiding students toward more just ways of seeing and being in the world in mathematics class."

Posting about human flourishing through mathematical study­­­­­­­­ from In All Things - an online journal for critical reflection on faith, culture, art, and every ordinary-yet-graced square inch of God’s creation.

http://inallthings.org/mathematical-justice/

Lies, Statistics, Mathematics And The Truth, Nathan L. Tintle

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"Recognizing a key distinction between mathematics and statistics is helpful in understanding how we know if a statement is true."

Posting about deductive and inductive reasoning­­­­­­­­ from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/lies-statistics-mathematics-and-the-truth/

Mathematical Beauty, Mike Janssen

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"With all the brokenness in the world, is the study of the mathematical aspects of Creation worthwhile?"

Posting about ­­­­­­­­the beauty of mathematics from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/mathematical-beauty/

Best Sandbox, Tom Clark

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"Mathematics ought to be for everyone, not just for mathematicians, scientists, and engineers. Mathematics is not only about application; it is part of the created world."

Posting about ­­­­­­­­learning about math through creative play from In All Things - an online hub committed to the claim that the life, death, and resurrection of Jesus Christ has implications for the entire world.

http://inallthings.org/the-best-sandbox/

Weighing Fog: Hands On Modeling For Day 1 Of Differential Equations, Tom Clark

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The first day of many mathematics classes contains formalities and very little mathematics. Here an alternative is presented where modeling is placed as the centerpiece to orient students to the real work of differential equations. Namely, to capture as beautifully and compactly as possible through the process of conjecture and investigation, the deep and interesting aspects of the physical world. A demonstration of the sublimation of dry ice sits at the center of the lesson. Students collaborate in groups to design an experiment that could measure the change in mass of a piece of dry ice that is dropped into …

Specifications Grading In A First Course In Abstract Algebra, Mike Janssen

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Specifications grading offers an alternative to more traditional, points-based grading and assessment structures. In place of partial credit, students are assessed pass/fail on whether or not they have achieved the learning outcomes being assessed on a given piece of work according to certain specifications, with limited opportunities for revision of non-passing work. This talk will describe the learning outcomes and specifications grading system I used in my Fall 2016 abstract algebra course, as well as student responses.

Spot It! Mathematical Structure In A Children's Game, Tom Clark

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"Whenever I lead the Northwest Iowa Math Teachers’ Circle I want to use a problem that is easy to explain, unfolds in many directions, and encourages inquiry. Spot It! is the best session topic I have ever seen for this. All you have to do is play the game for a minute or two, and questions arise spontaneously."

Faith Connections In The Math Classroom, Valorie L. Zonnefeld, Ryan G. Zonnefeld

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Looking for ways to make faith connections in your math classroom? The Zonnefelds present a framework, developed in collaboration with local teachers, that synthesizes faith connections, the TfT framework, and Common Core standards.

Standards-Based Assessment In A Developmental Math Course, Valorie L. Zonnefeld, Michal Huizenga, Aaron Van Beek, Kate Van Weelden

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Learn why we decided to try standards-based instruction in an undergraduate, developmental algebra course and what we learned in the process.

Improving Proof-Writing With Reading Guides, Mike Janssen

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One of the barriers in the transition to advanced mathematics is that the proofs and ideas in even the best mathematics texts must be read more carefully than many students are accustomed to. Yet in order to learn to write proofs well, one must learn how to read proofs well. Borrowing an idea from Lewis Ludwig, I flipped my introduction to proofs (discrete structures) course in Spring 2016 with the use of reading guides. Each day, students were responsible for reading a section of the text and completing a worksheet that highlighted the main points, asked students to create their …