With respect to the implementation of instruction, models of development can
serve as a filter for analyzing and characterizing students’ responses. In our teaching
experiments (Jones et al., 2001), we have found that filtering students’ responses
using a model of development helps teachers to build a much richer knowledge base
than they would without such a filter. In particular, a model helps teachers to frame
questions and written tasks that accommodate the diversity of reasoning reflected in
a group or class. Such accommodation and sensitivity by the teacher may enable
children to develop more mature levels of reasoning. For example, a teacher who
was aware from earlier group work that one student was reasoning about the
dimensions of the sampling process in an integrated way (Level 5; see Chapter 13)
might use that student’s response as a focal point for a formative or summative
discussion on the dimensions of the sampling. Alternatively, the teacher might use
the response of a student who was using transitional reasoning (Level 2; see Chapter
13) on the dimensions of sampling as a means of focusing on the need for
completeness and connections.
With respect to the implementation of instruction, models of development can
serve as a filter for analyzing and characterizing students’ responses. In our teaching
experiments (Jones et al., 2001), we have found that filtering students’ responses
using a model of development helps teachers to build a much richer knowledge base
than they would without such a filter. In particular, a model helps teachers to frame
questions and written tasks that accommodate the diversity of reasoning reflected in
a group or class. Such accommodation and sensitivity by the teacher may enable
children to develop more mature levels of reasoning. For example, a teacher who
was aware from earlier group work that one student was reasoning about the
dimensions of the sampling process in an integrated way (Level 5; see Chapter 13)
might use that student’s response as a focal point for a formative or summative
discussion on the dimensions of the sampling. Alternatively, the teacher might use
the response of a student who was using transitional reasoning (Level 2; see Chapter
13) on the dimensions of sampling as a means of focusing on the need for
completeness and connections.
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