Geometry has been an educational tool to teach deductive rea

Geometry has been an educational tool to teach deductive reasoning for hundreds of years. Explain why. In the last few decades K-12 geometric instruction has moved from deduction and proof to analytic computation (e.g. find the measure of an angle). Many believe the proofs and reasoning skills are not directly applicable. How should geometry be taught in K-12 schools?

Solution

Solution:

the following five basic characteristics capture the essence of mathematics that is important for K–12 mathematics teaching:

These characteristics are not independent of each other. For example, without definitions, there would be no reasoning, and without reasoning there would be no coherence to speak of. If they are listed separately, it is only because they provide easy references in any discussion.

Concept knowledge is a set of relationships. Theory holds that a wide variety of examples and non-examples must be provided for students to develop concept knowledge. To explain the importance of “best” examples and “concept cards” in concept-based lessons. Best examples are simple and communicate only essential features of the concept, without extraneous or confusing information.Examples containing more than essential features do not help students focus on the concept. In addition, concept knowledge manifests itself in an ability to generalize the concept away from a given context. So, nonessential information should be minimized. Pulling only vital information from a context is particularly important for students, since. Concept cards help students refine concept knowledge by moving beyond “best” examples to feature both examples and non-examples . after which students must practice classifying provided specimens. Finally, students state a general description of the concept.

Learners pass sequentially through levels for each geometry idea they learn and learners can be at different levels for different concepts. K-12 research shows that when instructors teach at a level different from the level of students, teachers and students literally do not understand each other. In addition, instructors must monitor the levels of thinking exhibited by students because \"students may move back and forth between levels quite a few times while they are in transition from one level to the next\" . The instructor who is aware of this sequence and of strategies to address the disparity in thinking levels can ensure that spatial thinking develops

Although it may seem that a student should have experienced success in high school geometry and thus, would have moved into the upper levels . that students regress after finishing high school geometry. Without constant effort to maintain a high level, students do not retain level 2 and/or 3 thinking.