Abstract
Inside the discipline, mathematical work consists of the interplay between stating and refining conjectures and attempting to prove those conjectures. However, the mathematical practices of conjecturing and proving are traditionally separated in high school geometry classrooms, despite some research showing that students can successfully navigate the interplay between the two. In this manuscript, we share perspectives from secondary mathematics teachers regarding what conjecturing and proving look like in geometry classrooms and possible rationales for why they are separated. We document that from the teachers’ perspective, the activities of conjecturing and proving have different goals, draw on different resources, and require different actions from students. In teachers’ eyes, these differences necessitate the separation of conjecturing and proving. By understanding teachers’ perspectives on the activities of conjecturing and proving, we can better consider the constraints of the classroom environment and possibly design activities in which conjecturing and proving could be reunited to allow students a more authentic mathematical experience.
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Notes
In this manuscript, we use normal and normally to mean that something accords with instructional norms.
We use figure to refer to the mathematical concept about which properties are ascribed, or the object of semiosis. We use diagram to refer to the graphical artifact transacted in semiosis (see also Herbst et al. 2017, Chapter 2).
The animations designed as part of this research project, including The Square, can be viewed as part of the original collection in LessonSketch (www.lessonsketch.org).
All names used here are pseudonyms.
It is worth noting for international readers that in the USA geometry is taught in a single course of high school studies that students take in their 9th or 10th grade; experienced geometry teachers are teachers with experience teaching this course.
Each session was attended by at least two members of the research team. A facilitator ensured the smooth running of the session and the comfort of the participants. A provocateur ensured that the conversation would yield data that would inform research questions, at times pressing participants to say more on topics in ways that are not generally allowed in conversation. For more information on the design of the focus groups please, see Nachlieli and Herbst (2010), also Nachlieli (2011).
All animated students’ names are Greek letters.
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Acknowledgements
The authors acknowledge the support of the National Science Foundation through the Grant ESI-0353285 to Patricio Herbst. All opinions are those of the authors and do not necessarily represent the views of the Foundation.
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Aaron, W.R., Herbst, P.G. The teacher’s perspective on the separation between conjecturing and proving in high school geometry classrooms. J Math Teacher Educ 22, 231–256 (2019). https://doi.org/10.1007/s10857-017-9392-0
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DOI: https://doi.org/10.1007/s10857-017-9392-0