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This may lead to questions that they cannot answer with their present ideas or reasoning patterns. In the second phase the concept is introduced and explained. Here the teacher is more active, and learning is achieved by explanation. Finally, in the third phase, the concept is applied to new situations and its range of applicability is extended.
Word problem from the Līlāvatī (12th century), with its English translation and solution. In science education, a word problem is a mathematical exercise (such as in a textbook, worksheet, or exam) where significant background information on the problem is presented in ordinary language rather than in mathematical notation.
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen or retracing any lines.
Critical thinking is the process of analyzing available facts, evidence, observations, and arguments to make sound conclusions or informed choices. It involves recognizing underlying assumptions, providing justifications for ideas and actions, evaluating these justifications through comparisons with varying perspectives, and assessing their rationality and potential consequences. [1]
Double counting – counting events or occurrences more than once in probabilistic reasoning, which leads to the sum of the probabilities of all cases exceeding unity. Equivocation – using a term with more than one meaning in a statement without specifying which meaning is intended. [21]
[5] [6] One central aspect is that this support is not restricted to a specific reasoner but that any rational person would find the conclusion convincing based on the premises. [6] [1] This way, logical reasoning plays a role in expanding knowledge. [7] The main discipline studying logical reasoning is called logic.