Picturing mathematics anew: murals illuminate new learning pathways
As William & Mary continues celebrating the Year of the Arts throughout 2024, the School of Education has unveiled its third annual mural, which highlights the power of integrating art with mathematics instruction. While mathematics remains at the core, the murals creatively showcase the interconnectedness of mathematics with other disciplines, serving as dynamic lenses through which mathematical concepts can be explored. This integration enriches learning and fosters a more holistic understanding of mathematics. Each mural, brought to life by students in the M2 Summer Math Camp, is part of a multiyear NSF-funded research project led by the Provost’s Distinguished Associate Professor Gladys Krause.
The goal of this project is to explore how creativity can enhance mathematics education, moving beyond rote memorization to foster a deeper understanding of mathematical concepts, for both students and teachers. Collaborating with former ESL teacher Caroline Finchum, a current graduate student in the School of Education, and artist Maria Emilia Borja ‘11, Krause’s research aims to reimagine mathematical instruction by integrating art and analyzing the intersection of creativity, mathematics and language.
The First Mural: Recontextualizing Math Through Word Problems and Language
All the M2 Project participants are multilingual immigrant students; languages spoken in the classroom include Spanish, Pashto, Farsi and English. Each mural serves as the culmination of their learning throughout the school year, and the first mural was completed in the summer of 2022.
A significant focus centered on word problems, particularly those involving fractions and proportions. The project also emphasized the role of language in the learning process, with students practicing and integrating multiple languages into their mathematical discussions and the mural's design.
The students’ excitement and joy in the process immediately became apparent. At the end of the first day, Krause remembers one student saying, “This is not a math camp. We’re having too much fun today!” As Krause explained, the student's remark underscored to her how students had already absorbed the pervasive notion that mathematics must be difficult if it is to be learned effectively. This moment highlighted the opportunity provided by the camp to break away from traditional associations of mathematics with struggle, and affirm that mathematics can, and should, be joyful, engaging and accessible for all learners.
The mural’s creation was not without its challenges. Initially, the plan was to project an image onto the
wall for the students to paint over. However, limited space necessitated abandoning that plan in place of a grid system to translate a smaller image onto the large 21’ x 9’ mural space. This adaptation became a major learning focus, with students engaging more deeply than expected with the mathematical concepts of scaling, area and proportion to enlarge their designs.
A key challenge for the instructors involved rethinking their approach to mathematical problem-solving, a central focus of this research study. Krause argues that encouraging diverse methods of solving problems enriches understanding: "If we can consider multiple ways of approaching a problem, our understanding deepens. A problem that allows only one method of solution rarely deepens mathematical understanding and usually doesn’t belong in the classroom." For teachers and teacher educators, this project emphasizes the value of designing problems that foster multiple solution strategies. By integrating students' languages and experiences into the problem-solving process and embracing varied approaches to solutions, the project challenges conventional notions of mathematics instruction, highlighting the role of creativity in deepening student understanding and engagement.
The Second Mural: Exploring Geometry and Tessellations
Building on the success of the first mural, the second project, completed in 2023, focused on geometry and tessellations — ways of covering a surface with polygons that fit together like puzzle pieces — and again emphasized the importance of language and culture through student contributions. This time the researchers intentionally integrated the grid system into the creative process, allowing students to explore complex geometric concepts in a hands-on and visual manner.
One of the notable achievements during the second year was the students’ increased independence and initiative. They creatively improvised tools, using available materials such as a piece of wire and a shoelace, to trace precise circles on the wall. This type of hands-on problem-solving not only deepened their comprehension of geometric concepts, but also fostered a sense of ownership over both the artistic and mathematical aspects of the project. During the design of the mural, students were also invited to write poems.
“Language has always been a key component of the work I do in mathematics,” Krause explained, “and this year we decided to work on poems to identify patterns in rhymes and rhythms as a way of sharing the beauty of mathematics.” This interdisciplinary approach reinforced the interconnectedness of mathematics, language and culture, making the learning experience more relevant and meaningful to the students. By engaging with both artistic and linguistic elements, students could see mathematics not as an isolated subject but as a dynamic and integral part of their world, thereby enhancing their motivation and deepening their understanding.
The Third Mural: Mastery of Mathematical Concepts and Creative Autonomy
The third mural project, completed in 2024, was fully student driven. Students demonstrated new levels of autonomy and mastery, both artistically and mathematically. This mural, which spans multiple walls and extends over doors, presented more complex challenges in terms of proportion
and design.
A major focus of the third mural was the creation of colors, with students devising their own formulas to mix precise shades. This process involved a deep engagement with mathematical concepts such as ratios and scaling that people apply readily in the context of cooking recipes, but which might be less familiar in the context of mixing paints. For example, students had to translate a color formula that was sufficient for a small area into one that could cover a large section of the wall. This required them to develop new units of measurement, such as “mega drops,” and to apply these concepts in a practical context.
Krause elaborates: “Now they are starting to think about what ‘mega drops’ means, not just at this particular scale, but how they can apply it to different contexts. Can they do this when they’re cooking? Can they do this when they’re measuring something? And right there, this new world of mathematics, this new understanding, changes completely.”
The theme of recipes emerged naturally as students discussed food and its connections to family and culture. This led to the mural incorporating depictions of the students’ favorite foods and recipes, further deepening the integration of math, language and cultural expression. The project culminated in a family gathering where parents shared their own recipes, highlighting the strong community that had developed around the mural project. Krause expressed deep gratitude for the cooperation and trust of the parents and families over the past three years, noting that their contributions made her research possible.
The students’ ability to take complete control of the project from start to finish demonstrates the success of the teaching methods developed through Krause’s research. This success also illustrates the potential for these methods to be applied in other educational settings, which is the next phase of her project.
Celebrating Art, Community and Learning
The M2 Summer Math Camp murals are more than just artistic projects; they are powerful tools for transforming mathematics education. By integrating multiple contexts into mathematics instruction, these projects have helped students see the relevance of mathematics to their lives, fostered a deeper understanding of complex concepts, and built a strong, supportive community among students, educators and families.
As William & Mary continues its Year of the Arts celebration, the mural projects demonstrate the power of creativity, collaboration and community in education. They also highlight the potential to reshape mathematical instruction in K–12 classrooms, particularly for multilingual learners, by embracing interdisciplinary approaches that make learning more engaging and meaningful.
