Education Commons^™

Real-World Modelling To Increase Mathematical Creativity, Robert Weinhandl, Zsolt Lavicza

Journal of Humanistic Mathematics

Modelling could be characterised as one of the core activities in mathematics education. However, when learning and teaching mathematics, mathematical modelling is mostly used to apply and deepen mathematical knowledge and competencies. Our educational study aims to explore how mathematical modelling, using real objects and high-quality mathematical technologies, could be utilised to acquire mathematical knowledge and competencies, and how learners could creatively use their existing knowledge. To discover the potential of mathematical modelling using real objects and high-quality mathematical technologies to acquire mathematical knowledge and competencies, and to stimulate learners' creativity, first, we combined cognitive and creative spirals and mathematical …

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 …

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 …

The Graduate Student Blues, Marion D. Cohen

Journal of Humanistic Mathematics

This is a memoir about my rather unconventional path to a mathematics Ph.D. There were difficulties, due partly to university politics, partly to my youth and immaturity, and partly to the thesis material itself – it was, in the words of some of my fellow students, “not what’s being done now”. I had written the thesis entirely on my own, without help from my Master’s thesis advisor or any other professor at my school. This is not the usual procedure of course. Nobody in my department could understand the thesis or was willing to vouch for it. There followed three …