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Full-Text Articles in Education
More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway
More Than Free Textbooks: Labor And Pedagogy In Implementing Open Resources In A Trigonometry Course, Caleb Holloway
Journal of Humanistic Mathematics
This paper reports the implementation of open educational resources (OER) in a university trigonometry class, with an emphasis on the pedagogical considerations and academic labor involved. To date these two matters have been underreported in the literature on OER. I provide an account of the work involved both in choosing an open textbook and in creating hundreds of accompanying homework exercises for an online learning platform. I also present the pedagogical lens that informed this implementation, discuss how it informed my adoption of an open textbook, and provide specific examples of how it guided the creation of these exercises. Based …
Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos
Mathematics Education As Dystopia: A Future Beyond, Peter Appelbaum, Charoula Stathopoulou, Constantinos Xenofontos
Journal of Humanistic Mathematics
We argue that scholars and practitioners of mathematics education need to find new directions through recognition of its dystopic characteristics, and embrace these characteristics as both the source of challenges and method of response. This contrasts with the generally utopic approach of most scholarship in the field. We offer critical ethnomathematics education as a model, since it has its own origins in lingering dystopic legacies. A perpetual hopelessness and disempowerment is one implicit curriculum of contemporary mathematics education, where the mathematics one learns might help to describe things, yet hardly assists in transforming the reification of power and agency in …
Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie
Middle School Students Generating Mathematical Problems From A Real-Life Situation, David Coffland, Ying Xie
Journal of Humanistic Mathematics
In this study, we examined the effect of different presentation formats of a realistic situation on students’ mathematical problem-posing behavior. We divided thirty-six middle school students into two groups, gave them a pretest, and then showed them a realistic, problem-posing situation in Artifact or Video format. We used Silver’s core dimensions of creativity, namely fluency, flexibility, and originality, to measure participants’ problem-posing activity. The results for the fluency measures showed that the Artifact group wrote more questions than the Video group but the same number of mathematics problems. The Video group posed problems in more mathematical domains than the Artifact …
Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou
Students Studying Students And Reasoning About Reasoning: A Qualitative Analysis, Salvatore J. Petrilli, Grant Clark, Nicholas Demarco, Jack Esposito, Brianne Giuliano, Sara Greiss, Emily Harris, Alessia Merritts, Kyle Murray, Mateusz Piekut, Brian Seidl, Scott Shannon, Nicole Silva, Christina Sullivan, Brittany Willoughby, Yile Zhou
Journal of Humanistic Mathematics
In this work, a faculty member takes a journey along with students as they enhance their understanding of how people solve mathematical problems through a mainly qualitative statistical project. Student authors of this paper registered for a problem solving seminar led by the faculty author, and then created and analyzed self-built assessment tools to explore problem solving techniques. Here we share our findings and recommendations, which we hope will inspire others to explore novel pedagogical techniques in the teaching of mathematical problem solving. We incorporate into our presentation ur voices, reflecting on how we and others solve problems.
Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge
Mathematics Out Of Nothing: Talking About Powerful Mathematical Ideas With Children, Matthew Oldridge
Journal of Humanistic Mathematics
Parents and educators have powerful opportunities to introduce children to big mathematical ideas, when those ideas become necessary. Children are capable and curious. They don’t need to be sheltered from big mathematical ideas. Bring out mathematical ideas when kids are ready, or when they are needed. This article describes one such instance, when I helped my six-year-old son move beyond zero in the negative direction when subtracting.
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Symmetry And Measuring: Ways To Teach The Foundations Of Mathematics Inspired By Yupiaq Elders, Jerry Lipka, Barbara Adams, Monica Wong, David Koester, Karen Francois
Journal of Humanistic Mathematics
Evident in human prehistory and across immense cultural variation in human activities, symmetry has been perceived and utilized as an integrative and guiding principle. In our long-term collaborative work with Indigenous Knowledge holders, particularly Yupiaq Eskimos of Alaska and Carolinian Islanders in Micronesia, we were struck by the centrality of symmetry and measuring as a comparison-of-quantities, and the practical and conceptual role of qukaq [center] and ayagneq [a place to begin]. They applied fundamental mathematical principles associated with symmetry and measuring in their everyday activities and in making artifacts. Inspired by their example, this paper explores the question: Could symmetry …
The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli
The Mathematics Orientation Seminar: A Tool For Diversity And Retention In The First Year Of College, Salvatore J. Petrilli
Journal of Humanistic Mathematics
In this article I describe Adelphi University's Mathematics Orientation Seminar, a new course that was introduced into the mathematics major to help students find their passion in mathematics and to strengthen the educational community within our department. I discuss quantitative and qualitative results of surveys among students in the Mathematics Orientation Seminar in Fall 2016 and Fall 2017, which suggest that this might be a useful course for other institutions to utilize within any major. Finally, I explore faculty perspectives and describe what I believe to be the final version of this course.
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Dramathizing Functions: Building Connections Between Mathematics And Arts, Gunhan Caglayan
Journal of Humanistic Mathematics
This article focuses on connections between mathematics and performance arts (drama). More specifically we offer an exposition of a segment of college algebra mathematics (an introduction to functions), with an approach primarily emphasizing the aesthetic aspects of mathematical learning, teaching, and performing.
What If?: Mathematics, Creative Writing, And Play, Emily Clader
What If?: Mathematics, Creative Writing, And Play, Emily Clader
Journal of Humanistic Mathematics
Mathematics can inform creative writing by suggesting structures for it to follow, as well as by providing the imaginative impetus for common rules to be broken. In a workshop co-taught by the author, a class of sixth-grade students explored this interplay as they produced fractal-inspired poetry and geometry-inspired fiction. This article describes the form and results of the workshop in the context of a broader discussion of the influence of mathematics upon literature.
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
The Role Of Sequence In The Experience Of Mathematical Beauty, Leslie Dietiker
Journal of Humanistic Mathematics
In this article, I analyze the aesthetic dimensions of a sequence of mathematical events found in an unusual first grade lesson in order to demonstrate how sequencing may affect an individual’s experience of mathematical beauty. By approaching aesthetic as a sense or felt quality of an experience in context (Sinclair, 2001, 2011), this analysis explains how sequence can affect the way mathematical objects or actions are experienced by an individual. Thus, rather than questioning whether or in what ways a set of mathematical objects are beautiful or not, this paper addresses under what conditions is the mathematics in play beautiful. …
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
What Is So Negative About Negative Exponents?, Geoffrey D. Dietz
Journal of Humanistic Mathematics
While teaching college-level mathematics (from College Algebra to Calculus to Abstract Algebra), I have observed that students are often uncomfortable using negative exponents in calculations. I believe the fault partially lies in the manner in which negative exponents are taught in Algebra 1 or Algebra 2 courses, especially in rigid instructions always to write answers using only positive exponents. After reviewing a sample of algebra texts used in the United States over the last two centuries, it appears that while attitudes toward negative exponents have varied from author to author over time, the current trend is to declare explicitly that …
Changing The Order Of Mathematics Test Items: Helping Or Hindering Student Performance?, Kristin T. Kennedy, Allison G. Butler
Changing The Order Of Mathematics Test Items: Helping Or Hindering Student Performance?, Kristin T. Kennedy, Allison G. Butler
Journal of Humanistic Mathematics
This paper recounts an experiment by a mathematics professor who primarily teaches mathematics majors. The main question explored is whether the ordering of the questions makes a difference as to how students perform in a test. More specifically we focus here on the following research questions:\ (1) Does arranging a math test with easy-to-hard items versus hard-to-easy items impact student performance? and (2) If so, does item order impact male and female mathematics majors and non-majors in unique ways? We examine data collected over multiple semesters with several different classes. We find that for most of the mathematics students who …
A Mathematician Weighs In On The Evolution Debate, Kris H. Green
A Mathematician Weighs In On The Evolution Debate, Kris H. Green
Journal of Humanistic Mathematics
There are a variety of reasons underlying the lack of public acceptance for the theory of evolution in the United States. An overlooked cause is related to problems with the mathematics curriculum in the K-12 setting. In this essay, we examine this relationship and propose changes to the mathematics curriculum that could improve mathematical thinking while also providing a basis for understanding theories, like evolution, that are poorly understood.