This paper reports on a study examining teachers' perceptions of students they observed in an animated episode and who were engaged in the work of making conjectures in a geometry classroom.
The descriptions of students were collected from conversations around the animated story, The Square; however, the ways in which participants described students are arguably relevant to teachers' work of supporting students in making conjectures in other geometric contexts.
Interestingly, we again see participants describing more students in terms of the resources that they use to make conjectures and less description of students in terms of the conjectures that are shared or students' strategies for making conjectures.
As teachers frame conjecturing tasks as primarily about the resources that students use, we see that the operations that students use to make conjectures and the conjectures that students arrive at could be underspecified and undervalued in classrooms.
In response to the first phase of work, working independently to make conjectures, teachers were concerned with the task resources that students use to make conjectures - in particular, teachers were concerned with how students misused task resources and what additional resources they might benefit from using.
Decades of experimental study have shown that when human subjects play games, especially games that ideally call for use of Bayes's rule in making conjectures about other players' beliefs, we should expect significant heterogeneity in strategic responses.
Most people would have a hard time explaining the present state of the art world, much less making conjectures about where it will be in 10-20 years. 10-20 years
To further describe what making conjectures involves in the high school geometry classroom, we propose a set of instructional norms to underpin the interaction among teacher and students around conjectures (see Table 1).
The study reported on here explores one of the sources of increased complexity of teachers' work as they support students to engage in making conjectures: What teachers perceive in students' work as they are engaged in making conjectures.
The particular topics that we're discussing here are very close to Prof Hawking's heart and, in many cases, he's made conjectures or worked in these subjects so it is an assessment of where we stand today".
The participants' comments highlighted above inform the question of how teachers perceive students as they are engaged in making conjectures.
