By Alfred North Whitehead
Offers the texts of a sequence of lectures added among 1912 and 1928 at the reasons and perform of schooling.
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Extra resources for Aims of Education
The question is: How do we encourage this type of reflection? Providing explicit guidelines for encouraging reflection is difficult, but a critical factor is that teachers recognize and value reflection. When that is the case, teachers establish classroom norms that support reflection. A specific norm that plays a critical role in supporting reflection in the descriptions of classrooms that follow is the expectation that students articulate their thinking. Asking students why their solutions work, why a given solution is like another solution, how they decided to solve the problem as they did, and the like, not only helps to develop students’ ability to articulate their thinking, it encourages them to reflect.
Tasks and tools should be selected to provide a window on students’ thinking, not just so that the teacher can provide more appropriate instruction for specific students, but also so the teacher can construct better models for understanding students’ thinking in general. CONCLUSION For students and teachers, the development of understanding is an ongoing and continuous process and one that should pervade everything that happens in mathematics classrooms. For many years there has been a debate on whether an individual should learn skills with understanding from the outset or whether he or she should acquire a certain level of skill mastery first and then develop an understanding of why skills work the way they do.
What we are proposing is that the development of understanding involves these forms of mental activity in some form. For an idea to be understood, it must be related to other ideas, but there are many ways that ideas might be related. We are not suggesting that relations must be formed in the same way or through the same activities, only that understanding depends on ideas being organized in some productive way that makes them accessible for solving problems. The ability to extend and 24 MATHEMATICS CLASSROOMS THAT PROMOTE UNDERSTANDING apply knowledge is a hallmark of understanding, but this does not imply that all people extend and apply their knowledge in the same way.