Education Commons^™

Drawing Parallels In Art Science For Collaborative Learning: A Case Study, Karen Westland

The STEAM Journal

This research paper explores drawing as a tool to facilitate interdisciplinary practice. Outlined is the personal experience of PhD researcher [name removed] in their physics/craft research project, combined with thoughts and opinions from collaborators gathered through group discursive interviews. Interdisciplinary projects face interpersonal and conceptually ambiguous challenges which can be addressed through adopting drawing techniques for educational purposes. Findings highlight that drawing can assist across a breadth of applications as a learning tool for everyone, regardless of drawing ability, to improve the functionality of collaborative projects. Specifically, drawing combined with other communication techniques develops a performative communicative approach that enriches …

Supporting Mathematic Achievement For Students With Learning Disabilities Through Enhanced Anchored Instruction, Wendie Lappin Castillo

The STEAM Journal

Difficulties in mathematical learning are common and significant.The struggle has increased exponentially with the Common Core State Standards in effect. Students with or without learning or mathematical disabilities may respond to continued failure by withdrawing their effort, carrying low self-esteem, and/or displaying avoidance behaviors. Enhanced anchored instruction is designed to provide students the opportunity to construct knowledge and design solutions to problems collaboratively. The approach of enhanced anchored instruction attempts to guide students to become more active in learning through the use of technology. Enhanced anchored instruction provides students the opportunity to work through problems attached to a visual anchor. …

Possible Adventures In Impossible Figures, Knarik Tunyan

The STEAM Journal

This interdisciplinary article aims to engage student into stepping outside traditional disciplinary boundaries by combining the arts, math, and programming. First, we explore a geometric pattern in the Penrose triangle. Then using the fundamental concepts of geometry, we find geometric relationship, calculate the vertices coordinates, and digitally reconstruct the Penrose triangle using coding. Students are encouraged to further explore this topic by finding another pattern, creating modifications of the Penrose triangle by changing measurements, or considering other impossible figures.

Visual Arts Enhance Instruction In Observation And Analysis Of Microscopic Forms In Developmental And Cell Biology, Max Ezin, Christina Noravian, Amira Mahomed, Adam Lyle, Aveleen Gill, Tamira Elul

The STEAM Journal

Two important skills for scientists in developmental and cell biology, as well as in fields such as neurobiology, histology and pathology, are: 1) observation of features and details in microscopic images of cells, and 2) quantification of cellular features observed in microscopic images. However, current training in developmental and cell biology does not emphasize observation and quantitative analysis of microscopic images, and it is unclear how best to teach students these skills. Here, we describe our experiences applying visual artistic approaches to instruct undergraduate and graduate students in how to observe and analyze cellular forms in microscopic images. At Loyola …

Music In Steam: Beyond Notes, Hao Huang

The STEAM Journal

Given current debates about STEAM, it would be well to remember that more than five centuries before STEM was conceived, the original Renaissance man, Leonardo da Vinci, wrote in one of his notebooks that "To develop a complete mind, study the science of art, study the art of science. Learn how to see. Realize that everything connects to everything else." (Spong 2006) A discussion of the effectiveness of teaching music and its accompanying technology in conjunction with math and the science education follows. .Given the recent shift from in-classroom teaching to online instruction compelled by the Covid 19 pandemic, an …

Picking Up Steam: The Role Of Languages And Linguistics, Keith Mason

The STEAM Journal

Languages and linguistics are powerful skills that enhance STEAM curricula and careers. A variety of approaches and methods to language teaching and learning inform educators how to proceed with the enhancement of STEAM programs. Linguistics, the science of language, can help STEAM students, especially within the science and mathematics components, because of its reliance on hypothesis formulation for scientific inquiry and data collection and analysis. Language, an important aspect of the human experience, elevates or picks up the STEAM experience.

Extending Power Series Methods For The Hodgkin-Huxley Equations, Including Sensitive Dependence, James S. Sochacki

CODEE Journal

A neural cell or neuron is the basic building block of the brain and transmits information to other neurons. This paper demonstrates the complicated dynamics of the neuron through a numerical study of the Hodgkin-Huxley differential equations that model the ionic mechanisms of the neuron: slight changes in parameter values and inputted electrical impulses can lead to very different (unexpected) results. The methods and ideas developed for the ordinary differential equations are extended to partial differential equations for Hodgkin-Huxley networks of neurons in one, two and three dimensions.

Specifications-Based Grading Reduces Anxiety For Students Of Ordinary Differential Equations, Mel Henriksen, Jakob Kotas, Mami Wentworth

CODEE Journal

Specifications-based grading (SBG) is an assessment scheme in which student grades are based on demonstrated understanding of known specifications which are tied to course learning outcomes. Typically with SBG, students are given multiple opportunities to demonstrate such understanding. In undergraduate-level introductory ordinary differential equations courses at two institutions, SBG has been found to markedly decrease students’ self-reported anxiety related to the course as compared to traditionally graded courses.

The International Conference On Creative Mathematical Sciences Communication: Online Event (Cmsc'20) And Cmsc'21, Frances Rosamond

Journal of Humanistic Mathematics

You are warmly invited to register now for the 5th International Conference on Creative Mathematical Sciences Communication (CMSC’21) which will be held at Adam Mickiewicz University in Poznań, Poland, 2–6 July, 2021.

The International Conference on Creative Mathematical Sciences Communication (CMSC) is a unique gathering of computer scientists and mathematicians, teachers, musicians, dancers, dramatists, game designers, educators and communicators of all sorts.

Due to the pandemic, the in-person event scheduled for 2020 has been post- poned and a short CMSC Online Event was organized as a “teaser” or trailer in order to feel the spirit of the full 5th CMSC …

Changes And Deltas, Jim Wolper

Journal of Humanistic Mathematics

Lecturing about Mathematics is like playing Jazz.

The Human Face Of Mathematics: Reuben Hersh (1927-2020) In Memoriam, Elena Anne Corie Marchisotto

Journal of Humanistic Mathematics

Reuben Hersh (1927-2020) celebrated mathematics as a human endeavor, historically evolved and intelligible only in a social context. It is therefore appropriate to remember him in the Journal of Humanistic Mathematics. There have been many tributes to Reuben, which commemorate his life and impressive mathematical and philosophical achievements. This memoriam to Reuben instead focuses on showing how his humanistic philosophy was so indicative of the person he was.

Three Creativity-Fostering Projects Implemented In A Statistics Class, Margaret Adams

Journal of Humanistic Mathematics

Undergraduates in an introductory statistics class at a rural Southeastern college were assigned three creativity-fostering projects: statistics vocabulary crossword puzzle, word wall, and graffiti art poster. Given math anxiety, fear of failure, and lack of enthusiasm, it seemed imperative to spark interest and involvement. Rhodes 4P’s model (1961) served as the framework for this intrinsic case study involving 62 students. Independent thinking and research, peer collaboration, and use of art supplies within this model (person, press, process and product) generated remarkable learning outcomes. Grading rubrics focused on originality, quality and statistics content. Projects were classified into three qualitative categories ranging …

Creative Assignments In Upper Level Undergraduate Courses Inspired By Mentoring Undergraduate Research Projects, Malgorzata A. Marciniak

Journal of Humanistic Mathematics

This article describes methods and approaches for incorporating creative projects in undergraduate mathematics courses for students of engineering and computer science in an urban community college. The topics and the grading rubrics of the projects go way beyond standard homework questions and contain elements of finding own project, incorporating historical background, inventing own questions and exercises, or demonstrating experiments to illustrate some aspects of the project. After analyzing challenges and outcomes of these projects, I identified several skills which help students be successful, including the skills of creativity. These skills are writing, oral presentation, math skills, and collaboration skills. I …

What Would The Nautilus Say? Unleashing Creativity In Mathematics!, Megan E. Selbach-Allen, Cathy A. Williams, Jo Boaler

Journal of Humanistic Mathematics

While the nautilus shell is often represented in popular culture as an example of a golden spiral, according to many mathematicians it is not. In this paper we examine multiple arguments for and against considering the nautilus as a “golden” spiral and offer a semi-structured task that is accessible to middle school students and beyond to begin their own investigation. Our hope is that asking, what would the nautilus say, can serve as a starting point for children and adults alike to push against the walls we so often draw around mathematical questions and begin to see where their creativity …

Tactivities: Fostering Creativity Through Tactile Learning Activities, Angie Hodge-Zickerman, Eric Stade, Cindy S. York, Janice Rech

Journal of Humanistic Mathematics

As mathematics teachers, we hope our students will approach problems with a spirit of creativity. One way to both model and encourage this spirit – and, at the same time, to keep ourselves from getting bored – is through creative approaches to problem design. In this paper, we discuss ``TACTivities'' – mathematical activities with a tactile component – as a creative outlet for those of us who teach mathematics, and as a resource for stimulating creative thinking in our students. We use examples, such as our ``derivative fridge magnets'' TACTivity, to illustrate the main ideas. We emphasize that TACTivities can …

Going Beyond Promoting: Preparing Students To Creatively Solve Future Problems, Kristin M. Arney, Kayla K. Blyman, Jennifer D. Cepeda, Scott A. Lynch, Michael J. Prokos, Scott Warnke

Journal of Humanistic Mathematics

While we cannot know what problems the future will bring, we can be almost certain that solving them will require creativity. In this article we describe how our course, a first-year undergraduate mathematics course, supports creative problem solving. Creative problem solving cannot be learned through a single experience, so we provide our students with a blend of experiences. We discuss how the course structure enables creative problem solving through class instruction, during class activities, during out of class assessments, and during in class assessments. We believe this course structure increases student comfort with solving open-ended and ill-defined problems similar to …

Does Your Course Effectively Promote Creativity? Introducing The Mathematical Problem Solving Creativity Rubric, Kayla K. Blyman, Kristin M. Arney, Bryan Adams, Tara A. Hudson

Journal of Humanistic Mathematics

As believers in the power of blending the creative with the quantitative, we design our courses with an eye towards developing creative problem solvers. However, when it comes time to evaluate our course's success in developing creative problem solvers we come away with a plethora of qualitative evidence and yet we are left hungry for the quantitative evidence we desire as mathematicians.

In this article we describe the development of the Mathematical Problem Solving Creativity Rubric and its pilot use in a freshman-level Mathematical Modeling and Introduction to Calculus course at the United States Military Academy. We not only come …

A Study Of Problem Posing As A Means To Help Mathematics Teachers Foster Creativity, Deborah Moore-Russo, Amanda A. Simmons, Michael J.D. Tulino

Journal of Humanistic Mathematics

Research suggests that mathematical creativity often results from extended periods of mathematical activity and reflection based on the use of deep and flexible content knowledge [14, 15]. This implies that instruction can influence creativity. However, for teaching to foster creativity in mathematics, there should be purposefully designed instructional tasks. It is doubtful that routine, mechanical exercises would foster creativity. Moreover, mathematical creativity may neither be explicitly promoted, nor fully appreciated, by students when a learning space involves only problem solving, even if the problems are challenging and engaging. For students to get an authentic sense of mathematics and to develop …

Learning To Transform, Transforming To Learn: Children’S Creative Thinking With Fractions, Higinio Dominguez, Sandra Crespo, Tamara Del Valle, Melissa Adams, Megan Coupe, Gustavo Gonzalez, Yordhan Ormazabal

Journal of Humanistic Mathematics

In this paper we contribute an alternative conceptualization of creativity by highlighting movement as creating spatial and temporal dimensions that are important to make sense of creativity in children mathematical thinking. Using data from an international collaboration between two teaching-research teams from the United States and Chile, we trace how children mobilized their social bodies, materials, tools, images, metaphors, languages, and improvisations in order to make sense of the concept of fractions. Based on these findings we offer a number of discussion points that highlight the importance of creating these kinds of learning spaces, the role of tasks in promoting …

Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling

Journal of Humanistic Mathematics

Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in …

Project Based Learning: Are There Any Academic Benefits For The Teacher Or Students?, Michael Aristidou

Journal of Humanistic Mathematics

In this paper, I raise an issue often neglected in Project Based Learning (PBL) literature. What academic benefits, if any, does the teacher or the student gain by adopting PBL pedagogy in college? I argue that PBL by its structure yields little academic benefits for the teacher or the students, and this could affect motivation as well. I present some examples from my personal teaching experience in mathematics. And thus, as I explain, a more “traditional” project-based approach could be better for both teacher and students.

On Not Teaching Addition: A Homeschooling Parent Teaches And Researches Math, Marion D. Cohen

Journal of Humanistic Mathematics

Interactions with the humans in one’s life can have bearings on the way one interacts with one’s work – and vice versa. In particular, the ways in which a math person who is also a parent interacts with their children can correlate with the ways that person interacts with students, colleagues, and with math itself. This article describes some of that correlation in one mathmom’s life. In particular, this mathmom worked toward balancing, both as a mom and as a teacher, her beliefs and feelings with societal mindsets and practices.

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.

College Students’ Images Of Mathematicians And Mathematical Careers, Katrina Piatek-Jimenez, Miranda Nouhan, Michaela Williams

Journal of Humanistic Mathematics

In this paper we report our findings of college students’ images of mathematicians and we reflect on different methodologies used to assess this information. The study reported in this paper was conducted in two stages. During the first stage, we asked 179 college students to “draw a mathematician” and also asked them to list five characteristics and five careers for a mathematician. In the second stage of the study, we conducted four focus group interviews with a total of twelve college students. During the focus group interviews, we showed the students 16 photos of real people and asked them to …

What Gets Checked At The Door? Embracing Students' Complex Mathematical Identities, Jennifer L. Ruef

Journal of Humanistic Mathematics

Identity formation is complex, ongoing, and context specific. To be successful in mathematics classes, students must negotiate and navigate the normative identity of the class--what counts as being "good at math" (Cobb, Gresalfi & Hodge, 2009). Within the constraints of normative identity, students must also negotiate a personal doer-of-math identity: who they are within the context of this particular mathematics class. When students are compelled to suppress key aspects of their identity in order to accommodate the normative identity of the class cognitive bandwidth for learning may be impeded (Steele, 1997). Conversely, when students are guided in braiding individual identity …