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Throughout the problem-solving process students use objects to develop understanding, conveying understanding and meaning through gestures. [9] Problem solvers use gestures to connect their thoughts to the manipulatives with which they are familiar, and changing a manipulative's shape affects how a student connects with it and uses it to solve ...
Best problem-solving practices include meta-cognition (managing memory and attention), grouping problems by type and conceptual connections (e.g. "river crossing problems"), moving between more general and abstract problems and particular, simpler examples, and collaboration with other club members, with current online communities, and with ...
The role of instructional text is to define and describe the problem solving procedures whereas how to apply these procedures is shown through worked examples. [2] Students can learn from step-by-step approach of worked examples which later can be helpful to them in solving similar problems on their own. [3] Novices, however, often find it ...
This is only likely to happen in classrooms that emphasize rich problem solving and the exchange of many approaches to mathematical situations, and that give attention to and value students’ mathematical reasoning". [5] To demonstrate this approach, Small provides an example of students learning to add 47 and 38.
Fluid intelligence is the ability to solve novel reasoning problems and is correlated with a number of important skills such as comprehension, problem-solving, and learning. [4] Crystallized intelligence, on the other hand, involves the ability to deduce secondary relational abstractions by applying previously learned primary relational ...
For example, geometry has its origins in the calculation of distances and areas in the real world, and algebra started with methods of solving problems in arithmetic. Abstraction is an ongoing process in mathematics and the historical development of many mathematical topics exhibits a progression from the concrete to the abstract.
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.
One of the popular examples in computer science is the mathematical models of various machines, an example is the deterministic finite automaton (DFA) which is defined as an abstract mathematical concept, but due to the deterministic nature of a DFA, it is implementable in hardware and software for solving various specific problems. For example ...