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Advances in Social Sciences Research Journal – Vol. 11, No. 1

Publication Date: January 25, 2024

DOI:10.14738/assrj.111.16349.

Baez, R., Sanchez, H., & Pllana, D. (2024). Creativity in High School Through Drawing with Polynomials. Advances in Social Sciences

Research Journal, 11(1). 318-332.

Services for Science and Education – United Kingdom

Creativity in High School Through Drawing with Polynomials

Rudy Baez

Jose Marti STEM Academy High School Union City NJ

Henry Sanchez

Jose Marti STEM Academy High School Union City NJ

Duli Pllana

Jose Marti STEM Academy High School Union City NJ

ABSTRACT

High school math projects center on solving real-world examples in a wide variety

of situations that require a creative skill set. Creativity in high school mathematics

takes place in a subtle form. In contrast, creativity presents itself conspicuously in

art. Therefore, this paper will explore the utilization of polynomial equations in

drawing various figures as part of algebra class projects. Additionally, these

projects incorporate integrated digital tools in mathematics. The paper will analyze

three algebraic projects: the first project involves drawing a bird, the second project

focuses on drawing a butterfly, and the third project entails drawing a bat using

polynomial equations with the technological tool Desmos. All three projects are

products of student work that encompass figures requiring up to forty polynomial

equations. The students' impressive work demonstrates the power of mathematics

in pushing the boundaries of other subjects. As digital technology becomes

increasingly integral, mathematical tools are positioned as universal tools for the

future and are poised to rival artists in producing visual art. This raises the

intriguing question: can a mathematician create better art with mathematical

equations through digital technology than an artist?

Keywords: The bird, butterfly, bat, projects, drawing, creativity, math, art, the teacher,

students, group work

INTRODUCTION

Generally, the presence of creativity in high schools within any school district is limited,

whereas the domain of art offers a broader scope for creative expression. Integrating

mathematics with artistic elements during high school projects could lead to the creation of

innovative artworks. For instance, a project assigned to an algebra class could involve drawing

a figure—any image or photography that captures the students' interest—by employing

polynomial and parametric equations and algebraic strategies taught in their classes. Students

could showcase their work using various versions of PowerPoint or Google Slides.

The cooperative nature of PowerPoint projects is thus motivating and provides a stimulating

environment for students (Apple and Kikuchi, 2007). Additionally, students could utilize

technological tools; while various software options are available, Desmos stands out as an easy-

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Baez, R., Sanchez, H., & Pllana, D. (2024). Creativity in High School Through Drawing with Polynomials. Advances in Social Sciences Research Journal,

11(1). 318-332.

URL: http://dx.doi.org/10.14738/assrj.111.16349

to-use and effective choice. Desmos is (free access) faster at graphing, thus providing

immediate feedback to the students who can see the function change in real-time as they modify

parameters (King, 2017). By modeling a chosen image and scrutinizing it through the lens of

mathematical equations, students can creatively bridge the realms of math and art—

transforming mathematical projects into artistic expressions—using the technological prowess

of Desmos.

Mathematics and art share a profound relationship, particularly in the exploration of patterns

and the graphical interpretation of mathematical examples and concepts. The relationship

between math and art is a complex and multifaceted one, but there is evidence to suggest that

mathematical principles play a fundamental role in creative expression (Ekbote, 2023).

Experimenting with diverse mathematical equations within the Cartesian system produces a

range of graphs, each showcasing distinct and often unpredictable shapes. Through the

utilization of digital technology, students can combine various polynomials through trial and

error, thereby giving rise to imaginative and unforeseen shapes.

Digital technology boasts extensive applications, particularly when Internet access is

considered. Integrating technology into mathematics education facilitates collaboration among

teachers and enables both students and educators to expand their knowledge base. For

instance, teachers can discover various activities aligned with their topics, employing them to

reinforce their understanding. Teachers can assign homework and projects through websites,

fostering communication with students to address any lingering questions.

Students can leverage a range of applications such as Desmos, Geogebra, Wolfram Calculator,

and various online calculators as mathematical tools to solve problems and graph functions

spanning linear, quadratic, cubic, rational, exponential, logarithmic, trigonometric, parametric,

piecewise-defined, mathematical animations, and more. Desmos is proficient in foundational

computations, and can also be adapted for various graph-related and non-graph-related

functionalities. These encompass calculating partial sums, estimating function roots,

determining definite integral values, and even finding the greatest common factors within a list

of integers (Math Valute, n.d.)

Students from a technology-focused urban high school in New Jersey utilized the technological

tool app, Desmos, to successfully complete a project within their Algebra 2 classes. This

approach facilitates the development of student understanding of the connections between

elements, not simply the application of steps and formulas (Ives, n.d.). The project entailed

creating a figure from scratch using familiar mathematical equations. Students opted for

various figures including butterflies, bugs, Mickey Mouse, bats, birds, and more. The focus of

this paper lies in the examination of three innovative projects from distinct groups, involving

the illustration of a bird, a butterfly, and a bat using polynomial equations presented in the form

of piecewise functions and equations.

METHOD

The teacher assigned a group project to the students, tasking them with drawing figures using

mathematical equations through Desmos. They were required to select a figure from a real- world example, analyze its key characteristics, and subsequently render it utilizing polynomial

functions. The underlying concept aimed to manifest the creative essence of mathematics

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Advances in Social Sciences Research Journal (ASSRJ) Vol. 11, Issue 1, January-2024

Services for Science and Education – United Kingdom

through the medium of art. It requires looking at things from multiple angles and being willing

to explore new possibilities (Ammy, 2023).

Figure 1: The figure on the left side depicts a bird that is symmetric with respect to the y axis

and the right side presents polynomial functions describing the shape of the bird (Outer

Hebrides, n.d) - Students work (project The Bird – google slide 3).

For instance, the teacher initiated the process with Figure 1. Displaying a real-world entity on

the left side, the teacher generated two polynomial functions (using Desmos) on the right to

depict the figure. The subsequent step involved assigning a group of students the task of

expanding upon Figure 1. Their objective was to introduce additional polynomial functions

until the figure on the right mirrored the one on the left. The students were guided to present

a minimum of four distinct slides, each featuring equations. Furthermore, each slide was to

incorporate a greater number of equations than the previous one, progressively converging the

figure to closely resemble the real-world counterpart. Ultimately, the selected group—the one

that demonstrated the most exemplary performance, successfully completed the project. They

accomplished the task by employing 39 polynomial equations to bring to life Figures 2 and 3.

The mathematics teacher assigned a project to students, dividing them into groups of four.

Their task was to employ polynomial functions combined with well-defined piecewise

functions, facilitated through the digital prowess of Desmos, to artistically depict the shape of a

bird. The illustration presented in Figure 1 encompassed a real-world example, depicting the

bird on the left side, while juxtaposing it with two polynomial equations on the right side—

these equations served as illustrative examples to guide students in their own projects. It is

worth noting, however, that each individual project was expected to be wholly distinctive—a

product of creative endeavor, never witnessed before.