Opportunities to Learn Fractions-as-Quotients in 6th Grade Elementary Mathematics Textbooks

This study analyzed 11 sixth-grade mathematics textbooks published under the 2015 revised national curriculum to examine opportunities to learn for understanding fractions-as-quotients, from the perspective of units coordination and partitioning operations. The analysis revealed that some textbooks provided opportunities for students to explore partitioning strategies independently, and the use of partition lines and partitive auxiliary marks varied across materials. Elements such as promoting distributive reasoning, counting unit fractions, and representing the relationship between the whole and each share were included in most textbooks, though with differing presentations. These features indicate that the textbooks contain implicit opportunities to support distributive partitioning operations and the construction of the quantitative structure of fractions-as-quotients. However, these opportunities may remain latent if not actively realized in classroom instruction. Therefore, this study suggests that such opportunities must be closely aligned with teachers’ instructional strategies. Future textbook development should focus on refining visual representations and activity design to better promote exploratory learning experiences and support students’ conceptual understanding of fractions-as-quotients.