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The use of multiple representations supports and requires tasks that involve decision-making and other problem-solving skills. [2] [3] [4] The choice of which representation to use, the task of making representations given other representations, and the understanding of how changes in one representation affect others are examples of such mathematically sophisticated activities.
The difference is that tiles cannot be locked together. They remain as separate pieces, which in many teaching scenarios, may be more ideal. These three types of mathematical manipulatives can be used to teach the same concepts. It is critical that students learn math concepts using a variety of tools.
A lesson plan is a teacher's detailed description of the course of instruction or "learning trajectory" for a lesson. A daily lesson plan is developed by a teacher to guide class learning. Details will vary depending on the preference of the teacher, subject being covered, and the needs of the students .
In that province, test scores in grades three and grade six math declined between 2009 and 2013, and "some contend that the math curriculum rather than teacher education is to blame for the lower scores because it places more emphasis on real-world concepts and applications than on rote learning". [5]
In many cases, however, educational professionals did not understand mathematics as well as their critics. This became apparent with the publication of the book Knowing and Teaching Elementary Mathematics (1999) by Liping Ma. The author gave evidence that even though most Chinese teachers had only 11 or 12 years of formal education, they ...
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