A 15-16 year old teenager, Alexander Muench, created this graph using only equations and inequalities supported on the Desmos Graphing Calculator. (https://www.desmos.com/calculator/zx7cbldsuw)
Meaningful Relevance
Project based instruction/learning (PBL) refers to a teaching strategy that centers student's own inquiry and exploration skills as the driving force of the classroom. In order to have a high-quality PBL classroom, teachers should present lessons and problems that are "rooted in purposeful and authentic experiences generated by students asking relevant questions" (De Vivo). In the case of the Desmos Art Project, the teacher should present the task of making a graph and give them choice in the content of the art. Allowing students to choose the content of their art will make it more relevant to their interest and gives them more autonomy to promote their motivation consistent with the Self-Determination Theory of motivation (Cook and Artino). Every child loves to play and "art making and play... come from similar pleasure-seeking centers in our human psyche" (Anderson 33). Desmos allows students to combine the play of art with the systems of math.
Gaps in Knowledge
The earlier De Vivo quote referenced the idea that students should be asking relevant questions. It is important that these questions come from the student's own curiosity versus any external reason. Reiser and Dempsey refer to this as epistemic curiosity and perceptual curiosity. The curiosity that comes from within about the need to know how or why something is verses the reflexive curiosity peaked without any additional thinking. Making pictures on a graphing calculator that is only meant to graph a couple of lines and curves is hard. The question students should be asking themselves in every PBL lesson is, "what do I need to know to solve this problem?" The Desmos art project pushes students towards thinking about how they can modify equations they already know and what kinds of equations do they not know to form certain lines or curves. Teachers should intentionally design their problems in ways that push students towards the intended learning outcome. A graphics teacher can utilize this problem to teach bezier curves. A calculus teacher can utilize this problem to teach integrals. An algebra teacher can utilize this problem to teach inequalities. Regardless, students will be required to fill in that knowledge while they work towards their end goal of creating art.
Satisfying Outcomes
Completing any problem can be satisfying. Creating art is uniquely one of the few things we do out of pleasure versus out of a need to live. So much of schoolwork is only relevant until you turn it in or take the test. Art is meant to be consumed and engaged with long after its completion and, a lot of the times, is meant to promote feelings of joy. The satisfying outcome in this case is the function of "carrying aesthetic pleasure" and getting information feedback (Anderson and Dempsey and Reiser). The Desmos platform lets you do all of this and makes it easy to share with others just by copying a link. Easy sharing options allows students to see other's success and anticipate their own success. Teachers should design their PBL problems in ways that promote this satisfying outcome of solving the problem. The satisfaction needs to come from the completion of the problem versus from any external reward. You can also achieve satisfaction through surprising outcomes that students believe they can achieve. Reiser and Dempsey say that it is important for students to have "positive expectancies for success" to avoid helplessness. In the case of the desmos art project they should be able to see the awesome drawings and anticipate that they will be able to create something cool as well. I will end on the most satisfying outcome of doing art in Desmos: a fully animated video using only the desmos calculator by Youtuber JohnDoesStuff.
References
Anderson, T. (2004). Why and How We Make Art, with Implications for Art Education. Arts
Education Policy Review, 105(5), 31–38.
Cook, D. A., & Artino, A. R. (2016). Motivation to learn: an overview of contemporary
theories. Medical Education, 50(10), 997–1014. https://doi-org.oclc.
fullsail.edu/10.1111/medu.13074
De Vivo, K. (2022). A New Research Base for Rigorous Project-Based Learning. Phi Delta
Kappan, 103(5), 36–41.
Reiser, Robert A., and John V. Dempsey. Trends and Issues in Instructional Design and
Technology. Pearson, 2018.
Hi, thank you for post. I like the Van Gogh art reference in conjunction with how you’re referencing calculations and the human psyche. Van Gogh, as in the era of abstract art does play with a subconscious, lower levels of color such as blue and purple and yellow suggest an undertone. And the swirls and circular drawings suggest movement within the picture instead of stagnation. Im unsure of how the reference of “what I can think of to solve this problem“ can help much in a Van Gogh painting reference or a mathematical may calculated fractal system because it’s meant to be more of pondering and to make you question something instead of solve. It however plays into the hum…
Hi, thank you for post. I like the Van Gogh art reference in conjunction with how you’re referencing calculations and the human psyche. Van Gogh, as in the era of abstract art does play with a subconscious, lower levels of color such as blue and purple and yellow suggest an undertone. And the swirls and circular drawings suggest movement within the picture instead of stagnation. Im unsure of how the reference of “what I can think of to solve this problem“ can help much in a Van Gogh painting reference or a mathematical may calculated fractal system because it’s meant to be more of pondering and to make you question something instead of solve. It however plays into the hum…
Facilitating Meaningful Relevance
Creating opportunities to combine a problem-based model (PBL), including the use of art materials with the rules and logic of mathematical principles is a relevant and proactive way of engendering students' interest in math. The element of surprise often piques curiosity, creating art through mathematical formulas is a surprising twist to the more traditional methods of working problems. As Desmos, Baldomero (June 18), demonstrates, using math to create visual illustrations embeds the relevance of math to art and vice versa. Incorporating problem-based learning engages students who are otherwise disengaged from the process of writing out algorithms or sifting through story problems. Students motivated by highly stimulating activities find it is engaging to combine art materi…
This study highlights the benefits of teaching math through Art. The study emphasizes that teaching math through art incorporates the following learner engagement principles; Meaningful Relevance, Gaps in Knowledge, Satisfying Outcomes. Teaching art through math also encompasses elements of mindfulness and contemplative pedagogy. Inviting the contemplative simply includes the natural human capacity for knowing through silence, looking inward, pondering deeply, beholding, witnessing the contents of our consciousness…. These approaches cultivate an inner technology of knowing….” (Chick 2010) Including art in the curriculum allows for the learner engagement principle called beholding. Beholding is a way of incorporating mindfulness and contemplative practice into the classroom. You stand in front of [artworks], hold them in your hands, look them in the eye, aw…
IDT5120 Blog Post #3
YOU CAN LEARN THROUGH ARTS AND CRAFTS: Project Based Instruction in Desmos Brandon Baldomero Jun 18
Facilitating Meaningful Relevance Creating opportunities to combine a problem-based model (PBL), including the use of art materials with the rules and logic of mathematical principles is a relevant and proactive way of engendering students' interest in math. The element of surprise often piques curiosity, creating art through mathematical formulas is a surprising twist to the more traditional methods of working problems. As Desmos, Baldomero (June 18), demonstrates, using math to create visual illustrations embeds the relevance of math to art and vice versa. Incorporating problem-based learning engages students who are otherwise disengaged from the process of writing out algorithms or sifting through story…