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The research mentioned above suggests that 'making conjectures' unfolds in classrooms in two distinct phases: (1) students work privately (individually or in groups) making conjectures and (2) the class publicly discusses those conjectures.
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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.
The teacher then says to the class 'I'll give you some time to make conjectures and then we will see if we can prove some of those conjectures'.
They are out to characterize a very rich mathematical universe, to be sure one in which there are so many things, and of such great variety of structure(s), that one should be able to find, therein, a set-theoretic 'surrogate' for virtually any kind of mathematical object or structure about which one may wish to make conjectures and prove theorems.
Mathematical cognition further extends beyond content knowledge to include a person's ability to reason and think mathematically to evaluate and synthesize information, make conjectures and draw logical conclusions, and apply knowledge to real-world problems and situations (Steen 2001; Wilkins 2000; National Council of Teachers of Mathematics 2000 , 1989.
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 town started making conjectures about the bodies: some said that Cerviño had buried them under his patio; others that he'd cut them into strips and thrown them into the sea.
Foresight processes are often subject to bias due to semantic blurriness when making conjectures or predictions.
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 participants' comments highlighted above inform the question of how teachers perceive students as they are engaged in making conjectures.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com