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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.
An even later development was the application of CBM to middle-secondary areas: Espin and colleagues at the University of Minnesota developed a line of research addressing vocabulary and comprehension (with the maze) and by Tindal and colleagues at the University of Oregon developed a line of research on concept-based teaching and learning. [3]
Ma and Kelly (2006) mention the necessity of establishing a link between the meaning and form of a word by various strategies, e.g., “direct memorization,” which is a strategy of deliberate vocabulary teaching. In vocabulary teaching programs, it is also necessary to consider the frequency of the words (Nation, 2006b).
Most theories of concept learning are based on the storage of exemplars and avoid summarization or overt abstraction of any kind. In machine learning, this theory can be applied in training computer programs. [2] Concept learning: Inferring a Boolean-valued function from training examples of its input and output.
Instructional scaffolding is the support given to a student by an instructor throughout the learning process. This support is specifically tailored to each student; this instructional approach allows students to experience student-centered learning, which tends to facilitate more efficient learning than teacher-centered learning.
Further, basic concepts centered on time, space, and mathematics are first required to demonstrate and teach probable theories that accurately describe universal phenomenon such as nature, planets, species, and the world around us.
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]
In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.
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