Teaching Reflection // Discovering STEAM at the NGA: A Mini-Lesson on Fractions in Art

This post is part of a series written by Live It Learn It’s Experiential Learning Fellows. During their year-long fellowship with LILI, Fellows are planning their own experience-driven mini-units that include both classroom and field components. In these posts, Fellows will reflect on the experience of planning and leading a Live It Learn It-style unit of study.

In today’s post we’re highlighting a teaching reflection from Marissa Werner on her Mini-Lesson. Ms. Werner is a 4th grade teacher at H.D. Cooke Elementary School in DC’s Ward 1.

As a part of my Experiential Learning Fellowship, I wanted to plan a trip that would allow my students access to experiences we cannot have in our own classroom, as well as support the learning we do in our classroom daily. I chose a trip that would bolster their ability to look closely and think deeply, to communicate their thoughts clearly, and to provide access to a new experience that would broaden their understanding of the world around them. However, I still felt the pressure of a “testing grade” teacher to make sure that the time out of the classroom would not only support their 21st century skills and global competencies, but also help my students understand more deeply the math content we are exploring.

I spent a few months planning a trip to the National Building Museum to visit the Evicted exhibit, in an effort to continue our learning around a powerful topic in a context that would be new to them. During the fall, we studied a thematic unit on migration, which ranged from learning about Early American colonialism as forced migration, to gentrification and rising housing costs in D.C. Tackling a really challenging topic through the lens of math and data has been really powerful, but I struggled to find a way to make the Evicted exhibit developmentally appropriate for fourth graders.

Around the same time, I was feeling pressure to be sure that my students stay on track with our scope and sequence. I became really interested in the idea of making math more playful for my students after reading Jo Boaler’s book, Mathematical Mindsets, and felt compelled to plan an experiential learning trip focusing on these ideas. After spending hours searching online for the right museum to go to in D.C.,  I came across the National Gallery of Art’s Learning Resources for teachers. I was thrilled to find the NGA had a lesson on fractions and money based on Wayne Theibauld’s artwork, Cakes. The timing was perfect, as I was about to launch our unit on fractions with the hope of teaching it in a way that honored students’ prior knowledge, allowed me to understand their misconceptions, and led students to be inquisitive and excited about fractions.

Preparing for the Mini-Unit

Before planning out the mini-unit, I decided to go to the NGA with a learner’s mindset and look and see if I could find any other examples of fractional relationships, parts of a set, equal parts, or any other math concept that I’d be teaching in the next unit. Sure enough, there was no shortage of art that could be connected to these ideas! I chose five works of art, all different sizes and scales. In looking at each piece, I asked myself the following questions:

  • Where is the fractional relationship?
  • How else could I partition it?
  • What might it be like if the object needed to be shared with more or fewer people?
  • What would it have been like if the artist changed the piece to show equal parts?

Most of the artwork I found showed parts of a set — a concept that is challenging for many fourth graders (fractions don’t always refer to parts of one whole object, but objects in a set).  Before leaving the museum, I took photos and drafted questions about each piece that I wanted students to focus on.

I created a Fractions at NGA Questions Packet with a scavenger hunt feel, knowing that would motivate my students. I also wanted students to have the opportunity to think creatively and express their reasoning in different ways, so I included a sketching/modeling component to most of the questions. One of my main goals for the trip was for students to begin to see fractional relationships everywhere, so I included a blank page that encouraged students to sketch and describe any additional fractions they found on their own.

Students reasoning with fractions and sketching what it would be like if the artist had made the cake in eighths for 15 friends instead.

My desire was to keep the Pre and Post-Lessons really simple (“low-floor, high-ceiling”) so that all of my students could access the activity, but have the space to be creative and thoughtful.  I decided to use the See, Think, Wonder thinking routine from Project Zero since we utilize it often in our classroom. I projected an image of Yitzchok Moully’s Apples & Honey, and without probing for mathematical answers, I asked students to write down what they saw, thought, and wondered about the piece. I was not at all surprised to find that students never mentioned noticing fractions, equal parts, or any other math idea. In my head, I hoped that after going on the Field Experience, students would see the piece in a new way.

Leading the Field Experience

For the Field Experience, I was fortunate enough to have all fourth graders come on the trip, averaging about 7 students per group. I encouraged my colleagues to allow students to grapple with the challenging questions, and to spend time thinking about the relationship between art and math in front of them. I listened to students in various groups having really interesting conversations about what they saw and what it meant to them. At the same time, I heard shouts of excitement as students called out for teachers and friends to come look at a work of art, or a pattern in the floor or ceiling that they found showing a fraction. Students were very intrigued with one another’s thoughts and observations, while focusing on their own sketches of what they saw. 

Student finds different pieces of art that show a fractional relationship and takes the time to accurately count the parts of a whole.
“These aren’t fifths because they aren’t equal parts. They need to be all the same size.” -Keyry

In-Classroom Reflection

The Pre and Post-Lessons were both really telling of what students learned in the classroom before and after visiting the museum. For the Post-Lesson, I wanted there to be room for students to debate and discuss what they thought, so I divided them into small groups. I was thrilled with their responses after the trip! Many students attempted to describe the fractions they saw. Others included mathematical ideas like arrays, rows, and columns. This showed me that even if the content of our trip wasn’t arrays, at least some students were beginning to look for and notice mathematics in art.

The Post-Lesson was really useful in helping me understand student misconceptions. Although the trip did not re-mediate all misunderstandings about fractions or identifying fractional units, it showed me some major areas of growth that I could plan lessons around (of which I may not have found until much later in the unit). For example, I realized that a common misunderstanding was that students describe “fourths” by writing ¼ instead of 4/4. When identifying a numerator, like 8 apples in a set that included 8 apples and 1 honey jar, many students wrote the fraction as 8/8 instead of 8/9, showing a misunderstanding about the relationship between the numerator and the denominator. It was great to learn so much about what my students already know and what they need support on in such a fun way that didn’t feel punitive to them.

I anticipate feeling a similar challenge to what I felt when beginning this process when I plan my next mini-unit. I feel a tension between my belief that students learn from experiences and the pressure to stick to the academic content to be prepared for obligatory standardized tests. I want to deepen my understanding of the resources around D.C. that can help students find joy in learning about mathematics while experiencing something they would not normally have access to. I feel that this is a major issue of equity where we put so much pressure on our students in Title I schools to prepare urgently for PARCC, while their more affluent peers may be given more time and flexibility to learn in ways that are more engaging and more fruitful in the long run.

“This is an array! But it’s also 64 equal parts so that’s a fraction.” -Ydelis (students are allowed to walk on these interactive sculptures!)

I would encourage any teacher considering planning a mini-unit to really prepare the experience thoughtfully, especially if your scope and sequence limits the amount of days you can spend outside of your classroom. Looking back, I spent too much time trying to plan a trip that I loved the idea of, but unfortunately was not developmentally appropriate for my students. Ask yourself the following when planning your own trip:

  • Will students have the opportunity to experience things they don’t have access to in the classroom?
  • Will they have the opportunity to express themselves in multiple ways, and perhaps in ways that are not typically used in your classroom?
  • Will it allow students the chance to ask questions and pursue their own curiosities?
  • Will you be able to connect the learning, thinking, or understandings to other learning?
  • Will the kids feel excited or joyful?

If you answered “Yes!” to the above questions, then you should do it! Even if it doesn’t connect directly with the standard you are working on that week, or if you have to spend more time drawing a connection to a text or a math concept, it will be worth your students’ increased excitement and interest in all learning.

If you take photos and post them on social media, be sure to tag us @liveitlearnitdc or #LILIpad. We’d love to hear how you connected fractions and art in your classroom!

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