Abstract
This study examined how the levels-of-sophistication framework supports pre-service mathematics teachers’ professional noticing of students’ reasoning about length measurement. Three pre-service teachers were asked to analyse students’ written solutions in the tasks that reflected different characteristics of students’ reasoning before and after participating in an intervention based on the “Levels of Sophistication in Students’ Reasoning about Length” (Battista, 2006) conceptual framework The findings indicated that the levels-of-sophistication framework enabled the pre-service teachers to give their full attention to students’ mathematical understanding and to provide proper instruction to support students’ learning and hence, it had a significant role in the improvement of the professional noticing skills of these pre-service teachers. Thus, it is suggested that the levels-of-sophistication framework can be used to support pre-service teachers’ professional noticing skills and to better prepare them to teach length measurement based on students’ reasoning.
Highlights
Understanding the mathematical thinking of students is crucial for selecting and designing instructional tasks, understanding students’ reasoning, assessing students’ learning progress, and recognizing and remedying students’ learning difficulties (Battista, 2017)
This study examined how the levels-of-sophistication framework supports pre-service mathematics teachers’ professional noticing of students’ reasoning about length measurement
Three pre-service teachers were asked to analyse students’ written solutions in the tasks that reflected different characteristics of students’ reasoning before and after participating in an intervention based on the “Levels of Sophistication in Students’ Reasoning about Length” (Battista, 2006) conceptual framework The findings indicated that the levels-of-sophistication framework enabled the pre-service teachers to give their full attention to students’ mathematical understanding and to provide proper instruction to support students’ learning and it had a significant role in the improvement of the professional noticing skills of these pre-service teachers
Summary
Understanding the mathematical thinking of students is crucial for selecting and designing instructional tasks, understanding students’ reasoning, assessing students’ learning progress, and recognizing and remedying students’ learning difficulties (Battista, 2017). Teachers should pay attention to the events that occur in the classroom and notice the instances that provide opportunities for student learning, and they should elicit students’ thinking through questioning in order to eliminate students’ misconceptions and difficulties. These practices can be signs of teachers’ noticing skills (Jacobs et al, 2011). Teachers who are able to notice students’ thinking can create tasks that direct students’ attention to appropriate learning opportunities (Mason, 2011). Teachers should be able to identify students’ thinking through students’ explanations, justifications, and questions, and they should be able to interpret them, and make instructional moves based on this recognition (Luna et al, 2009)
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