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    Conceptualizing "homework" in flipped mathematics classes
    (National Taiwan Normal University, 2017) de Araujo, Zandra; Otten, Samuel; Birişçi, Salih
    Flipped instruction is becoming more common in the United States, particularly in mathematics classes. One of the defining characteristics of this increasingly popular instructional format is the homework teachers assign. In contrast to traditional mathematics classes in which homework consists of problem sets, homework in flipped classes often takes the form of an instructional video. This paper presents a framework for flipped mathematics homework that categorizes types of homework and also draws on technology literature and mathematics education literature to discern quality for each type. For each category of homework, we provide illustrative examples from a study of flipped mathematics implementations. We show how the quality of instructional videos can vary and that, in addition to instructional videos, teachers also assigned videos to motivate subsequent in-class work on mathematics tasks. We close with directions for future work.
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    Mathematics teachers' motivations for, conceptions of, and experiences with flipped instruction
    (Pergamon-Elsevier Science Ltd, 2017) de Araujo, Zandra; Otten, Samuel; Birişçi, Salih
    Flipped instruction in school mathematics has been occurring more frequently. This study investigated two teachers' motivations for, conceptions of, and experiences with flipped mathematics instruction. We found that the teachers were motivated to flip based on colleagues' recommendations and potential benefits for students. The teachers discussed changes to their instruction as a result of transitioning to flipped instruction and we interpreted those changes in terms of how teachers perceived the interactions among students, mathematics content, and themselves. Although the teachers viewed many of these changes as beneficial, some presented new challenges as they navigated their changing role in the classroom.
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    Teacher-created videos in a flipped mathematics class: digital curriculum materials or lesson enactments?
    (Springer Heidelberg, 2017) de Araujo, Zandra; Otten, Samuel; Birişçi, Salih
    The rise of digital resources has had profound effects on mathematics curricula and there has been a concurrent increase in teachers flipping their instruction-that is, assigning instructional videos or multimedia for students to watch as homework and completing problem or exercise sets in class rather than vice versa. These changes have created a need to better understand not only the features and learning affordances of these videos but also the phenomena of instructional videos taking the place of textbooks altogether. Drawing on an enacted mathematics curriculum framework, this article reports on a study of a mathematics teacher who implemented flipped instruction and created her own instructional videos and multimedia resources as replacements of printed textbooks. We examined the relationship between the teacher's printed textbook and the digital curriculum materials she used with her flipped mathematics classroom. We also explored her role in creating the digital curriculum materials and the ways in which those materials were used in-class. The case reveals similarities between the new material design and conventional textbooks and it also illustrates the teacher's simultaneous work designing and enacting digital curriculum materials. The broad issue of considering videos as curriculum materials rather than only as instructional representations is discussed.