Teaching fraction operations for conceptual understanding is a challenging task. For the topic of fraction division especially, teachers need support because teachers find this difficult to teach and elementary and middle school students struggle to learn this concept. Well-structured professional development can assist teachers in exploring their own understanding as well as how to incorporate multiple representations in their instruction. This naturalistic inquiry study investigated fourth to sixth grade teachers’ invented real-world problems and pictorial representations for fraction division. The teachers completed a written assessment focused on conceptual understanding of fraction operations through multiple representations at the beginning and conclusion of a weeklong professional development experience. The questions on the assessment were taken or modified from prior research studies. The results in this paper focus specifically on a task in which the teachers had to develop a real world story problem for 2½ ÷ ¾ and solve the problem by drawing a pictorial representation. The teachers showed statistically significant improvement on developing appropriate real-world problems and using pictorial representations to solve their problems. Implications for teachers’ usage of multiple representations are discussed along with needed structures for professional development targeted on fractions.
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