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Articles 121 - 150 of 152
Full-Text Articles in Education
Reflections On Math Students’ Circles: Two Personal Stories From Colorado, Diana White, Lori Ziegelmeier
Reflections On Math Students’ Circles: Two Personal Stories From Colorado, Diana White, Lori Ziegelmeier
Journal of Humanistic Mathematics
Math Students’ Circles provide an opportunity for mathematicians to work in their communities to engage young students in mathematics as a human, aesthetic, and social endeavor. Sometimes referred to simply as Math Circles, these venues give mathematicians experience in introducing children to topics not typically seen in school curricula in an exciting, hands-on format. This article explores two Math Students’ Circles (MSCs) in the state of Colorado from the point of view of two pre-tenure faculty members. One participated in MSCs for four years while working on her Ph.D. in mathematics, the other started an MSC as an offshoot of …
On Similarities And Differences Between Proving And Problem Solving, Milos Savic
On Similarities And Differences Between Proving And Problem Solving, Milos Savic
Journal of Humanistic Mathematics
A link between proving and problem solving has been established in the literature [5, 21]. In this paper, I discuss similarities and differences between proving and problem solving using the Multidimensional Problem-Solving Framework created by Carlson and Bloom [2] with Livescribepen data from a previous study [13]. I focus on two participants’ proving processes: Dr. G, a topologist, and L, a mathematics graduate student. Many similarities between the framework and the proving processes of Dr. G and L were revealed, but there were also some differences. In addition, there were some distinct differences between the proving actions of the …
Attitudes And Experiences In Liberal Arts Mathematics, Jennifer Clinkenbeard
Attitudes And Experiences In Liberal Arts Mathematics, Jennifer Clinkenbeard
Journal of Humanistic Mathematics
For many university students, the last formal experience in a mathematics classroom is a single semester “general education” mathematics class. Traditionally, students in this type of class often hold negative attitudes towards mathematics. Here I study a sample of students from this population (49 students at a large, urban, comprehensive public university enrolled in a “math for liberal arts majors” course) to research whether a positive experience in a freshman-level general education mathematics course correlates with a positive change in the students’ attitude towards mathematics in general. I also explore which specific aspects of such a course contribute most to …
E-Brock Bugs©: An Epistemic Mathematics Computer Game, Laura Broley, Chantal Buteau, Eric Muller
E-Brock Bugs©: An Epistemic Mathematics Computer Game, Laura Broley, Chantal Buteau, Eric Muller
Journal of Humanistic Mathematics
Devlin in [7] argues that video games are an ideal medium for the teaching and learning of mathematics, though he points out that very few ’good’ mathematics video games exist. Building on a probabilistic board game developed in the 1980s, we created a mathematics computer game, E-Brock Bugs. The design of the game carefully follows Devlin’s principles of a good mathematics video game, including a well-developed storyline, the selection of an in-game avatar, and an environment where mathematics arises in a natural and meaningful way. As a result, we argue that E-Brock Bugs is an epistemic computer game [1]; …
On Mathematics And Culture: Insights From An International School, M. Sencer Corlu, Burcu Alapala
On Mathematics And Culture: Insights From An International School, M. Sencer Corlu, Burcu Alapala
Journal of Humanistic Mathematics
We explore the factors that influence the relationship between mathematics and culture in the international school context. First, we share some thoughts about international schools in general and the international mathematics curriculum implemented at the middle grades level at our school in particular. Second, we present some interesting snapshots from our culturally-diverse mathematics classrooms.
How Can Mathematics Students Learn To Play?, Christopher K. Storm, Holly Zullo
How Can Mathematics Students Learn To Play?, Christopher K. Storm, Holly Zullo
Journal of Humanistic Mathematics
When we teach mathematics, we strive to teach students to think like mathematicians. In this paper we discuss one particular mathematical habit of mind that students do not naturally display. More specifically our study of voting patterns in data collected from classroom voting questions indicates that the undergraduate students who were in the classes using these questions did not understand the significance of counterexamples to statements, or lacked the ability to construct them, or both. Searching for counterexamples to disprove statements is a natural habit of mind for professional mathematicians. In this paper we give examples, and make some recommendations. …
The Case Of The Missing Speedometer: The First Day Of Calculus, Marion D. Cohen
The Case Of The Missing Speedometer: The First Day Of Calculus, Marion D. Cohen
Journal of Humanistic Mathematics
This article describes the way I've been teaching the first day of Calc I, my single-variable Calculus class. By the end of the hour students have (A) dictated difference quotients for me to write on the board, (B) dictated one example of the limit of difference-quotients definition of derivative of a function at a point, and (C) calculated a few derivatives. The more rigorous definitions of function, of operations on functions, and of limits can wait until later. This approach has been very successful, and students have said they "get it this time around."
Recreational Mathematics – Only For Fun?, Lovisa Sumpter
Recreational Mathematics – Only For Fun?, Lovisa Sumpter
Journal of Humanistic Mathematics
In this paper, I explore recreational mathematics from two perspectives. I first study how the concept appears in educational policy documents such as standards, syllabi, and curricula from a selection of countries to see if and in what way recreational mathematics can play a part in school mathematics. I find that recreational mathematics can be a central part, as in the case of India, but also completely invisible, as in the standards from USA. In the second part of the report, I take an educational historical approach. I observe that throughout history, recreational mathematics has been an important tool for …
Improving Project Success In An Online Mathematics Course, David Shoenthal
Improving Project Success In An Online Mathematics Course, David Shoenthal
Journal of Humanistic Mathematics
With more mathematics courses migrating to online environments, it is important to know whether these courses are comparable to their face-to-face counterparts. To that end, in two different years, I taught an online and a face-to-face section of the same finite mathematics course. After analyzing the data regarding differences in the two sections for the first year, I incorporated changes intended to improve the consistency of project success between the two sections as well as the overall success of the class projects in the online section. My main tool was mimicking the interaction of group members and providing immediate instructor …
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
On The Persistence And Attrition Of Women In Mathematics, Katrina Piatek-Jimenez
Journal of Humanistic Mathematics
The purpose of this study was to investigate what motivates women to choose mathematics as an undergraduate major and to further explore what shapes their future career goals, paying particular attention to their undergraduate experiences and their perceptions of the role of gender in these decisions. A series of semi-structured, individual interviews were conducted with twelve undergraduate women mathematics majors who were attending either a large public university or a small liberal arts college. This study found that strong mathematical identities and enjoyment of mathematics heavily influenced their decisions to major in mathematics. At the career selection stage, these women …
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
The Discipline Of History And The “Modern Consensus In The Historiography Of Mathematics”, Michael N. Fried
Journal of Humanistic Mathematics
Teachers and students of mathematics often view history of mathematics as just mathematics as they know it, but in another form. This view is based on a misunderstanding of the nature of history of mathematics and the kind of knowledge it attempts to acquire. Unfortunately, it can also lead to a deep sense of disappointment with the history of mathematics itself, and, ultimately, a misunderstanding of the historical nature of mathematics. This kind of misunderstanding and the disappointment following from it--both raised to the level of resentment--run through the paper "A Critique of the Modern Consensus in the Historiography of …
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 …
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Benjamin Banneker's Original Handwritten Document: Observations And Study Of The Cicada, Janet E. Barber, Asamoah Nkwanta
Journal of Humanistic Mathematics
Benjamin Banneker, farmer, mathematician, astronomer, and scientist, is known for his mathematical puzzles, ephemeris calculations, almanacs, his wooden clock, land surveying work, and famous letter on human rights. However, as a naturalist, his scientific and systematic observations of the cicadas are less known. In this paper we publicize Banneker’s naturalistic study of the seventeen-year periodic cycle of the cicada and make available the original handwritten document of his observations. We also introduce the audience of this journal to an intriguing natural problem involving prime numbers.
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Liberal Arts Inspired Mathematics: A Report Or How To Bring Cultural And Humanistic Aspects Of Mathematics To The Classroom As Effective Teaching And Learning Tools, Anders K H Bengtsson
Journal of Humanistic Mathematics
This is the report of a project on ways of teaching university-level mathematics in a humanistic way. The main part of the project recounted here involved a journey to the United States during the fall term of 2012 to visit several liberal arts colleges in order to study and discuss mathematics teaching. Several themes that came up during my conversations at these colleges are discussed in the text: the invisibility of mathematics in everyday life, the role of calculus in American mathematics curricula, the "is algebra necessary?'' discussion, teaching mathematics as a language, the transfer problem in learning, and the …
My Mathematics, Karen Morgan Ivy
My Mathematics, Karen Morgan Ivy
Journal of Humanistic Mathematics
This poem reflects a personal kaleidoscopic perspective into a world of actively engaging others in teaching and learning mathematics.
Selling Mathematics: Service & Quality, Jon Jacobsen
Selling Mathematics: Service & Quality, Jon Jacobsen
Journal of Humanistic Mathematics
Is there a difference between teaching mathematics and selling mathematics? The author presents his personal experience on the topic and reflects on how this perspective can be used to improve public perception of and engagement with mathematics.
Math Stories: Learning And Doing Mathematics Through Fiction Writing, Frederick Chen, Janna Raley
Math Stories: Learning And Doing Mathematics Through Fiction Writing, Frederick Chen, Janna Raley
Journal of Humanistic Mathematics
In this paper, we advocate the writing of mathematical fiction (i) as an aid for students in learning mathematics, and (ii) to engage students in doing mathematics.
Cultural Immersion And Mathematics Teacher Education: Explorations In Morocco And South Africa, Kori L.H. Maxwell, Iman C. Chahine
Cultural Immersion And Mathematics Teacher Education: Explorations In Morocco And South Africa, Kori L.H. Maxwell, Iman C. Chahine
Journal of Humanistic Mathematics
This article examines the first author's personal experiences as a mathematics educator studying ethnomathematics and indigenous knowledge systems (IKS) through immersion in indigenous cultures. In describing these encounters, we highlight the importance and impact of cultural immersion experiences on educators' perspectives regarding the nature of mathematical knowledge. We argue that cultural immersion not only builds a well-rounded individual, but also provides educators with the necessary tools to maintain relevance in the diverse and constantly evolving landscape that is the classroom. Insights gained from this study have direct implications in our teaching practices as they remind us to be mindful of …
Dnr-Based Curricula: The Case Of Complex Numbers, Guershon Harel
Dnr-Based Curricula: The Case Of Complex Numbers, Guershon Harel
Journal of Humanistic Mathematics
DNR is a research-based framework which seeks to understand fundamental problems of mathematics learning and teaching. This paper discusses DNR with a particular reference to a curricular unit on complex numbers. Originally designed for college-bound high school students, the unit is structured to progress along a path that roughly parallels the development of complex numbers in the history of mathematics. We have tested the unit in three teaching experiments with inservice and prospective secondary mathematics teachers. The results from these experiments demonstrate the ways of thinking afforded and targeted by the unit. The correspondence between these ways of thinking and …
At The Gate Of Discovery, Jan Nordgreen
At The Gate Of Discovery, Jan Nordgreen
Journal of Humanistic Mathematics
This is the story of how a mathematical problem was discovered. Although it was never solved, it gave great joy to the discoverer.
Developing A Healthy Scepticism About Technology In Mathematics Teaching, Peter J. Rowlett
Developing A Healthy Scepticism About Technology In Mathematics Teaching, Peter J. Rowlett
Journal of Humanistic Mathematics
A reflective account is presented of experiences which took place alongside a research project and caused a change in approach to be more sceptical about implementation of learning technology. A critical evaluation is given of a previous e-assessment research project, undertaken from a position of naive enthusiasm for learning technology. Experiences of teaching classes and designing assessment tasks lead to doubts regarding the extent to which the previous project encouraged deep learning and contributed to graduate skills development. Investigations of the benefits of another technology – in-class response systems – lead to revelations about learning technology: its enthusiastic introduction in …
Incorporating Pólya’S Problem Solving Method In Remedial Math, Shenglan Yuan
Incorporating Pólya’S Problem Solving Method In Remedial Math, Shenglan Yuan
Journal of Humanistic Mathematics
György Pólya’s problem solving method has influenced generations of mathematicians and non-mathematicians alike. Though almost all math teachers have come across Pólya’s problem solving method, his ideas are not regularly implemented in the classroom. Few studies have examined the effectiveness of his approach in teaching remedial math. In this article we revisit this once well-known teaching method and show how it can be used in basic skills math classes to ease student fears of math, and potentially change their common misconceptions of the subject.
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Teaching The Complex Numbers: What History And Philosophy Of Mathematics Suggest, Emily R. Grosholz
Journal of Humanistic Mathematics
The narrative about the nineteenth century favored by many philosophers of mathematics strongly influenced by either logic or algebra, is that geometric intuition led real and complex analysis astray until Cauchy and Kronecker in one sense and Dedekind in another guided mathematicians out of the labyrinth through the arithmetization of analysis. Yet the use of geometry in most cases in nineteenth century mathematics was not misleading and was often key to important developments. Thus the geometrization of complex numbers was essential to their acceptance and to the development of complex analysis; geometry provided the canonical examples that led to the …
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 …
Joanne Growney's Poetry-With-Mathematics Blog -- An Appreciation, Gregory E. Coxson
Joanne Growney's Poetry-With-Mathematics Blog -- An Appreciation, Gregory E. Coxson
Journal of Humanistic Mathematics
Now is a good time to work on the boundaries of practice and theory, of art and science. We are seeing a rising tide of interest in these boundaries. Witness the growing Bridges movement, which has been exploring the connections between mathematics and the arts. Similarly, JoAnne Growney's blog, Intersections -- Poetry with Mathematics, explores the connections between mathematics and poetry. Through this review, I aim to give readers a taste of what can be found in Intersections as a way of encouraging others, be they mathematicians, poets, or neither, to visit the blog.
A Workshop To Introduce Concepts Of Moral Math, Sarah Voss
A Workshop To Introduce Concepts Of Moral Math, Sarah Voss
Journal of Humanistic Mathematics
"Moral Math" refers to the study of ideas drawn from mathematics which can positively impact moral decision-making and social behavior. This essay describes a workshop designed to introduce these ideas to interested individuals of varying degrees of mathematical and theological sophistication. Created by a retired minister and former math professor, the workshop details five sets of interactive exercises culled from game theory, theoretical complexity, fuzzy logic, basic algebra, and simple arithmetic. Exercises are user-friendly, interactive, and easily related by analogy to various social issues.
Gaming Your Mathematics Course: The Theory And Practice Of Games For Learning, Kathleen H. Offenholley
Gaming Your Mathematics Course: The Theory And Practice Of Games For Learning, Kathleen H. Offenholley
Journal of Humanistic Mathematics
Learning through play is fundamental to humans and to many other animals. Game Based Learning is an interactive pedagogy that has as its foundation the tenet that games, by their very nature, increase learning through positive emotional experience. This article introduces readers to what games in mathematics classes have the potential to do, including to decrease anxiety, increase motivation, and deepen learning through immersive gaming. The article then connects this theory to practice, providing examples of both computer and non-computer games in introductory middle school, high school and college mathematics. The article analyses how these games work, and makes the …
We Could All Be Having So Much More Fun! A Case For The History Of Mathematics In Education., Louise Anderton, David Wright
We Could All Be Having So Much More Fun! A Case For The History Of Mathematics In Education., Louise Anderton, David Wright
Journal of Humanistic Mathematics
Many students experience mathematics as ahistorical and acultural. We review the philosophical roots of this experience and pose alternatives. We argue that there is evidence that the inclusion of a historical dimension into the teaching of mathematics courses at all levels, combined with an ‘active’ approach to learning, will improve motivation and achievement.
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.
On Doing Mathematics, Sue Vanhattum
On Doing Mathematics, Sue Vanhattum
Journal of Humanistic Mathematics
Who is a mathematician? What does it mean to do mathematics? I discuss my process in solving a math problem, and what it meant to me.