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A class that is not a set (informally in Zermelo–Fraenkel) is called a proper class, and a class that is a set is sometimes called a small class. For instance, the class of all ordinal numbers , and the class of all sets, are proper classes in many formal systems.
The Harkness method is in use at many American boarding schools and colleges and encourages discussion in classes. The style is related to the Socratic method.Developed at Phillips Exeter Academy, [1] the method's name comes from the oil magnate and philanthropist Edward Harkness, who presented the school with a monetary gift in 1930.
Class discussions: This technique is used in all of the methods described above. It is one of the most important distinctions of constructivist teaching methods. [6] Campus wikis: These provide learners with a platform for curating helpful learning resources. [7] Constructivist approaches can also be used in online learning.
Discussions can be conducted with any class size, although it is typically more effective in smaller group settings. This environment allows for instructor guidance of the learning experience. Discussion requires the learners to think critically on the subject matter and use logic to evaluate their and others' positions.
Different levels of mathematics are taught at different ages and in somewhat different sequences in different countries. Sometimes a class may be taught at an earlier age than typical as a special or honors class. Elementary mathematics in most countries is taught similarly, though there are differences.
The Principles and Standards for School Mathematics was developed by the NCTM. The NCTM's stated intent was to improve mathematics education. The contents were based on surveys of existing curriculum materials, curricula and policies from many countries, educational research publications, and government agencies such as the U.S. National Science Foundation. [3]
Direct instruction (DI) is the explicit teaching of a skill set using lectures or demonstrations of the material to students. A particular subset, denoted by capitalization as Direct Instruction, refers to the approach developed by Siegfried Engelmann and Wesley C. Becker that was first implemented in the 1960s.
It is hoped that communication skills will be developed; exercises aimed at this goal are embedded throughout the curriculum, through the use of group and whole class discussions, the use of writing to present and clarify mathematical solutions; in some IEP classes, formal oral presentations are required. [7]