Group Members: Vannessa Smythe & Nicole Fulton
Title: Multiplication Through Art, Play, and Place
Level: Grades 3/4
Mathematical Focus- Developing conceptual understanding of multiplication as:
- Equal groups
- Repeated addition
- Visual and spatial representations of number relationships
- Communicating mathematical thinking through oral, written, and artistic forms
Pedagogical Approaches- Embodied learning
- Arts-based pedagogy
- Play-based learning
- Outdoor and place-based learning
- Multiple modes of representation and expression
Research Context and Classroom ImplementationThis lesson sequence will be implemented in a Grade 3 classroom where students are beginning formal instruction in multiplication. The lessons will be embedded within regular mathematics instruction and designed to support students in developing conceptual understanding of multiplication through embodied, visual, and artistic experiences.
In addition to a post-assessment, student work samples, photographs of representations, and anecdotal observations will be collected throughout the lesson sequence. Particular attention will be paid to how students use multiple modes of representation, including physical actions, visual models, oral explanations, and artistic expression, to communicate their mathematical thinking.
Planned Lesson Sequence (5 Lessons Total)- Stamping Multiplication Art
- Students use manipulatives (e.g., Lego bricks) to create stamped artwork
- Each stamp represents a consistent group size (e.g., groups of 2, 4, 6, or 10)
- Students design an artistic composition using color and repetition
- Students orally explain or write the corresponding multiplication sentence
2. Indigenous-Inspired Dot Art Multiplication
- Students create dot art designs (e.g., flowers or circular forms)
- Each section or petal contains a fixed number of dots (e.g., 25 or 50)
- The number of sections represents the number of equal groups
- Students communicate the associated multiplication equation orally or in writing
- Learning is framed within a respectful discussion of Indigenous art practices
3. Outdoor Multiplication Sculpture
- Students collect natural materials (e.g., twigs, stones, pinecones)
- Materials are organized into consistent groups (e.g., bundles of five)
- Students create an outdoor artwork or structure using repeated groups
- Students explain or document the multiplication represented in their work
Lesson 4 – To Be Developed
- Additional arts-based or play-based multiplication experience
- Focus on student collaboration and mathematical communication
Lesson 5 – To Be Developed
- Culminating multiplication representation or reflection
- Opportunity for student choice and creative expression
Draft Annotated Bibliography
Alibali, M. W., & Nathan, M. J. (2012). Embodiment in mathematics teaching and learning: Evidence from learners' and teachers' gestures. Journal of the Learning Sciences, 21(2), 247–286.
https://doi.org/10.1080/10508406.2011.611446This study explores how learners’ and teachers’ gestures contribute to mathematical thinking and demonstrates that physical movement is closely linked to understanding mathematical ideas. The authors show that gestures support reasoning about quantity, structure, and relationships by allowing learners to externalize their thinking in space. This article supports our project by highlighting how bodily movement and embodied actions can reinforce ideas of grouping, repetition, and spatial arrangement that underpin multiplication, complementing visual and art-based approaches.
Boaler, Jo, Chen, L., Williams, C., & Cordero, M. (2016). Seeing as understanding: The importance of visual mathematics for our brain and learning. Journal of Applied & Computational Mathematics, 5(5), 1–6.
This article draws on neuroscience and classroom research to show that many mathematical concepts are stored in visual and sensory-motor memory systems, meaning that mathematical thinking relies heavily on visual, spatial, and embodied brain pathways even when working with symbols. This research is particularly helpful for Grade 3/4 multiplication instruction, as it supports providing students with opportunities to use visual representations, manipulatives, and to develop their own gestures and physical actions to build conceptual understanding of multiplication before formal symbolic procedures.
Brezovnik, A. (2017). The benefits of fine art integration into mathematics in primary school. CEPS Journal, 5(3), 11–32.
https://doi.org/10.26529/cepsj.125This study investigates the effects of integrating fine art into mathematics instruction at the primary school level and found that students who learned mathematics through art achieved higher results than those taught through traditional methods. The author argues that art integration supports visual imagination, motivation, and creative mathematical thinking by helping students engage with mathematical ideas in more meaningful and expressive ways. This article supports our project by providing empirical evidence that art-based approaches enhance mathematical understanding and student engagement, strengthening the rationale for using visual and creative activities as a foundation for mathematics instruction.
Cartwright, K. (2024). Interpreting young children's multiplicative strategies through their drawn representations. Mathematics Education Research Journal, 36(2), 367–397.
https://doi.org/10.1007/s13394-023-00450-4This study examines how young children express their understanding of multiplication through their drawn representations. The author shows that children use drawings to reveal strategies such as grouping, repeated addition, and structuring quantities, even when they do not yet use formal mathematical language. This article supports our project by demonstrating that drawing and visual representation are powerful tools for making multiplicative thinking visible, reinforcing the value of art-based activities as a way to support and interpret students’ understanding of multiplication.
Furner, J., Powers, J., & Brown, S. (2021). Studying Mayan culture in the elementary classroom: Integrating mathematics, visual arts and technology through an authentic multi-leveled curriculum. International Journal of Whole Schooling, 17(1), 1.
This practitioner-focused article describes an interdisciplinary unit in which elementary students learned mathematical concepts through the study of Mayan culture using visual arts and hands-on materials. Students represented numerical systems, grouping, and repeated quantities through artistic designs, symbols, and manipulatives, helping them make sense of structure and quantity visually. This article supports our project by showing how visual art and cultural design can be used to model grouping, arrays, and repeated addition, making multiplication more concrete and accessible for elementary students.
Holtzman, C., & Susholtz, L. (2011). Object lessons: Teaching math through the visual arts, K-5 (1st ed.). Stenhouse Publishers.
https://doi.org/10.4324/9781003579076This book explores how mathematical understanding develops through visual art, hands-on materials, and meaningful objects. In the sections related to multiplication, students engage in activities such as measuring facial features and then doubling or halving those measurements to create disproportionate portraits, making multiplicative change visible through scaling and design. We draw on this approach in our project by using art-making to explore grouping, scaling, and repeated change, allowing students to represent multiplicative ideas through visual structure and creative expression rather than symbolic calculation alone.
Mageed, I. A. (2025). Phenomenal fractal geometric techniques in mathematics education for Key Stage 2 students: A new paradigm for teaching multiplication tables. https://doi.org/10.20944/preprints202506.2486.v1
This article proposes a visual and pattern-based approach to teaching multiplication in which students generate fractal-like geometric designs from multiplication tables, drawing on constructivist learning theory and insights from brain research on visual pattern recognition. The article is particularly helpful for Grade 3/4 multiplication instruction as it supports using art-based visual representations and pattern exploration to help students see mathematics as a system of meaningful patterns to be explored, rather than a set of rules or facts to be memorized.
Nemirovsky, R., Rasmussen, C., Sweeney, G., & Wawro, M. (2012). When the classroom floor becomes the complex plane: Addition and multiplication as ways of bodily navigation. Journal of the Learning Sciences, 21(2), 287–323.
https://doi.org/10.1080/10508406.2011.611445
This qualitative study looks at how students use body movement, gesture, and space to understand addition and multiplication during a mathematics lesson. The authors show that mathematical ideas are developed through physical actions and interactions with the learning environment, not just through symbols or written procedures. This research directly supports our project by encouraging the use of movement-based activities, such as stomping, stepping, and spatial exploration, to help students build meaning in multiplication rather than focusing only on getting correct answers.
Physical Activity in Mathematics Education: Developing “Grundvorstellungen” of Multiplication by Learning through Physical Activity (Bayer & Rottmann, 2018).
https://tidsskrift.dk/learningtech/article/view/110494This study investigates learning multiplication through physical activity using three purposefully designed movement-based games, Jumping Along the Number Line, Multiplicative Relay Race, and Multiplicative Atomic Game, each targeting different aspects of multiplication as equal groups, supported by pre- and post-assessments to examine conceptual growth. Despite limitations in sample size and duration, the study is particularly helpful for our work, as it emphasizes students’ physical engagement and meaning-making in multiplication, focusing on developing conceptual understanding rather than solely on producing correct answers.
Putrawangsa, S. Visualising Multiplication through Spatial Analogy: Exploring the Role of Embodiment and Spatial Reasoning in Promoting Mathematical Visualisation.
This mixed-methods doctoral study examines multiplication instruction with primary students of a similar age to those in Grades 3/4, focusing on the use of embodied activities, visual representations, and spatial reasoning. The study is particularly helpful for our project as it shows how students leverage interconnected modes such as physical action, gesture, visual models, and talk to develop flexible problem-solving strategies, supporting a smooth transition from concrete experiences to abstract reasoning and enabling students to generalise their understanding across contexts.
Schoevers, E. M., Leseman, P. P. M., & Kroesbergen, E. H. (2020). Enriching mathematics education with visual arts: Effects on elementary school students’ ability in geometry and visual arts. International Journal of Science and Mathematics Education, 18, 1613–1634.
https://doi.org/10.1007/s10763-019-10018-zThis study investigates the impact of integrating visual arts into mathematics instruction and found that art-based approaches strengthened students’ visual–spatial reasoning and mathematical understanding. The authors argue that artistic activities help students recognize structure and patterns, which are central to mathematical thinking. This research supports the use of visual art, such as dot-based designs and creating stamped artwork, as meaningful ways to deepen conceptual understanding in elementary mathematics.
Xu, H., & Ball, R. (2024a). Indigenous mathematics: From mainstream misconceptions to educational enrichment. Canadian Journal of Science, Mathematics and Technology Education, 24(2), 160–175.
https://doi.org/10.1007/s42330-024-00321-5This article challenges the misconception that Indigenous peoples lack sophisticated mathematical knowledge and presents evidence that Indigenous mathematics includes complex reasoning related to patterning, measurement, spatial relationships, and prediction. The authors argue that narrow, Eurocentric definitions of mathematics exclude culturally embedded forms of mathematical thinking and limit what is recognized as legitimate learning. This study supports our project by emphasizing that mathematics is often expressed through visual design, cultural practices, and relational systems, which aligns with using art-based lessons to make multiplication meaningful and culturally responsive for Grade 3/4 students.
Xu, H., & Ball, R. (2024b). Multiple forms of knowing in mathematics: A scoping literature study.
https://doi.org/10.48550/arxiv.2406.16921This scoping study reviews research on ethnomathematics and Indigenous mathematics and shows that mathematical thinking is deeply embedded in cultural, artistic, and land-based practices such as weaving, building, games, and pattern-making. The authors argue that these practices involve important mathematical ideas like patterning, spatial reasoning, and measurement, and that recognizing them challenges narrow, Eurocentric views of mathematics. This study supports our project by justifying the use of art-based, place-based, and outdoor lessons as meaningful ways to teach multiplication to Grade 3/4 students.