Annotated Bibliography

Teaching Fractions through Multi-Modal Approaches

Amanda Wheeler and Taylor Faille

Life And Work Skills (LAWS) Program (aged 15-19), Chateauguay Valley Regional High School (Quebec, Canada)
Grade 11 (aged 16-17), Chateauguay Valley Regional High School (Quebec, Canada)
Grade 7 (aged 12-13), Comox Valley School District (British Columbia, Canada)

Rationale

There are many mathematical strands that can be infused with the arts, nature, and physical embodiment to improve student learning, engagement, and retention of skills. In deciding the direction to begin on our project, we wanted to pick a mathematics topic that can be conventionally difficult for some students. Additionally, as our teaching assignments differ greatly from each other (Faille teaches high school math and Wheeler provides K-7 numeracy support to her district), we also wanted to choose a mathematics topic that is applicable to a wide range of grade levels. The decision to settle into the topic of fractions came around mutually.

The basis of this initial research had two main targets. The first goal was to gain a deeper understanding of the impact that art integrated fractions teaching can have on students' learning and overall experience of mathematics. To achieve this, we sought academic research and journals which demonstrated impact. The second goal was to begin ideating about the many ways in which the arts can be integrated into fractional concepts. Much of this research was conducted through watching videos and gathering resources such as lesson plans online.

Our project is going to have us designing a series of activities that integrate aspects of the arts, integration with nature, and authentic embodiment of the fractional skills. As we are working with varying grade levels, we are interested in how these activities can be developed in an open-ended enough way to provide extension opportunities whilst also allowing entry for all students.

Annotated Bibliography

        Adler, I. (1998). The role of continued fractions in phyllotaxis. Journal of Algebra, 205, 227–243

Adler uses points on a cylinder to explain why leaf patterns follow number rules known as continued fractions. He proves that the angle between leaves (the divergence) determines which spiral patterns are visible to the eye. He also identifies "points of close return", which are leaves that line up closely to each other which also shows how they naturally match the Fibonacci sequence

        Azaryahu, L., Broza, O., Cohen, S., Hershkovitz, S., & Adi-Japha, E. (2024). Development of creative thinking via fractions and rhythm. Thinking Skills and Creativity, 52, Article 101514. https://doi.org/10.1016/j.tsc.2024.101514

The researchers looked at the connection between learning fractions and learning rhythm in music. By breaking students into groups receiving separate teaching and comparing these groups to a control that is only taught the fractional concepts, student achievement is assessed. Success was measured for both musical and mathematical concepts. There was a notable enhancement in student performance in the groups of students who engaged in a creative way when compared to those in the control group. This serves as further evidence of the efficacy of creativity in mathematics. Music is something that so many humans enjoy and could prove to be an engaging tool to use when teaching fractions.

        Chahine, I. C. (2013). The impact of using multiple modalities on students’ acquisition of fractional knowledge: An international study in embodied mathematics across semiotic cultures. The Journal of Mathematical Behavior, 32(3), 434–449. https://doi.org/10.1016/j.jmathb.2013.04.004

The researcher investigated how an embodied approach to teaching fractions impacted the understanding students had of various outcomes. The findings were that the 5th grade students who were exposed to multiple modalities of learning including hands on manipulatives, gestures, and movement performed stronger in a post assessment than their peers who utilized a more traditional pencil and paper style of learning. For the purpose of our work, we can use this research as further evidence of the efficacy of utilizing embodied math in fractional learning. We could also look at the activities that were performed to gain inspiration for our own project.

        Goral, M. B., & Wiest, L. R. (2007). An Arts-Based Approach to Teaching Fractions. Teaching Children Mathematics, 14(2), 74–80. http://www.jstor.org/stable/41199065

The authors write about an arts-based approach to teaching fraction concepts through poetry, physical movement, and music. The fractional concept being addressed with these grade 4 and 5 students in the USA is part-whole relationships and equivalence. This foundational understanding is often a difficult one to master which is why an integrated approach was taken. This was not a formal data collecting research enterprise, but they did note that they observed the students demonstrating strong engagement and improved reasoning through the lessons. For our project, it would be interesting to look at a multimodal approach to fractional learning as it seems the more branches and connections that can be developed, the more concrete student understanding will become.

        Lovemore, T. S., Robertson, S.-A., & Graven, M. (2021). Enriching the teaching of fractions through integrating mathematics and music. South African Journal of Childhood Education, 11(1), Article a899. https://doi.org/10.4102/sajce.v11i1.899

Lovemore, Robertson, and Graven (2021) describe an action research study that integrates music note values into Grade 5 fraction lessons to address learning challenges in South Africa. By employing multiple sensory representations and the American note-naming system, the authors demonstrate how musical rhythms can clarify concepts like equivalence and the inverse order relationship of unit fractions. The study concludes that this integrated approach fosters a deeper conceptual understanding of fractions while simultaneously increasing student motivation and confidence in mathematics

        Maclean, Lauren. (2020, September 12). Mentoring Nature Connections: Fraction Nature Walk [Video]. YouTube. https://www.youtube.com/watch?v=IJwQ-PQk6Ms

This video brings students on a nature walk and allows them the freedom to find fractions in leaves. Whether it's color differences or broken leaves. The small project is to set up a fraction clothes line, where a leaf that represents a half, would go half way on the clothes line. There is an element of environmental care in this video as well. The teacher introduces ratios/proportions by teaching students when it is okay to take a piece of nature and when it must be left, if you can find 7 samples, then you may take 1, if not you must leave it. Other options for observing include a technology component, such as taking pictures, or an artistic component such as sketching. I would love to use this as an example with my group as we have a trail through a forest on campus, therefore we could easily do this project to help students understand fractions while appreciating nature, if weather permits (we currently have a lot of snow!), this could be done and incorporated into this project. Something similar may also be done that accommodates the season of winter.

        Marotta, Barbara. (2022, February 3). If You Were a Fraction by Trisha Speed Shaskan [Video]. YouTube. https://www.youtube.com/watch?v=PL7Vc-v8Lus

This is a read aloud of the book “If You Were a Fraction” by Trisha Speed Shaskan. A use of everyday items (such as food) and animal characters to demonstrate fractions through literature and illustrations. Perhaps a good introductory tool to a fractions unit.

        Narsh's art. (2021, January 21). Fun Fraction Art [Video]. YouTube. https://www.youtube.com/watch?v=PS-wYCuM8Gk

This video demonstrates an art options to better understand fractions. Students cut pieces of shaped paper into smaller symmetrical pieces where each piece represents a fraction of a whole. With these smaller pieces of paper, the students glue them onto a square to create a colorful symmetrical design. Once the whole class has made their piece, they are put together as a sort of quilt. This would be an activity we would like to integrate into our classes to show the connection between visual arts and fractions.

        Richmond, H. (2021). Fraction action: An embodied approach to teaching fractions (Curriculum unit). Charlotte Teachers Institute.

This resource is a multi lesson unit that puts into action how embodied learning through movement can occur within the learning of fractional content. The lessons are designed for grade 3-5. The author suggests utilizing strategies like human number lines, walking research, and kinesthetic modelling in the teaching. There is an emphasis on making movement a natural part of this teaching and not just a token for motivation. There is no research data connected to this unit which can aid in deciding whether these choices would be impactful in a classroom, however, it does provide great ideas on how to integrate movement. This resource provides clear, concrete examples.

        Scaptura, C., Suh, J., & Mahaffey, G. (2007). Masterpieces to mathematics: Using art to teach fraction, decimal, and percent equivalents. Mathematics Teaching in the Middle School, 13(1), 24–28.

This is a journal article where middle school students created visual artwork to explore the connections between fractions, decimals and percentage. There is an emphasis placed on representational fluency and also is supportive of students who are English language learners. This is a fantastic source of an idea of how to integrate artwork and fractions.

Next Steps

With the goal of utilizing these lessons within our teaching roles, we have decided upon the following timeline for completion to ensure this is achieved.

We want to develop around 4 activities that effectively integrate fractional thinking with the arts, nature, or kinesthetic movement (or a combination of them). We will each work on and develop two.

February 20th - Each have 1 activity developed and ready to use

February 27th - Each completed 1 activity in classes

March 6th - Reflect and include first activity into presentation, and develop a 2nd lesson each

March 13th - Lesson 2 completed in class(s)

March 20th - Reflect and include the second activity into the presentation. Video recording done

March 24- Must be handed in by