Rather than just understanding and applying individual concepts, students understand the relationship among concepts. Case studies in business, for example, fit this level. The level of difficulty can be controlled for novices to experts by the number of issues presented in the cases requiring analysis. Likewise, this process to control difficulty can be used for any mathematics problem-solving scenario based on level of expertise of learners.
For example, at elementary levels, students are introduced to analysis when a few extraneous facts are included in a problem, which are not needed to solve it. At an analysis level, students are able to appreciate that some problems do not have a unique solution and there is more than one way to defend a position or solution method, as in a case study. Memorization and recitation fall within the knowledge level.
Teachers might rely on a lecture method and assigned readings. They are transmitters of knowledge. Such tests rely on one-right answer. When writing, students tend to parrot back what the teacher has said. However, the ability to recite information that has been memorized does not mean that students know what they are saying.
Memorization does not come easy for learners, but some memorization is involved in mathematics. For example, read by Margaret Groves Every teacher should have some knowledge on how students learn and be able to connect research to what they do in the classroom. In the , the Deans for Impact provide a valuable summary of cognitive science research on how learning takes place.
Likewise, the Centre for Education Statistics and Evaluation in New South Wales, Australia elaborates on research that teachers really need to understand about cognitive load theory: To save your place, write down or.
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