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Zieffler et al. (2008) suggest three types of tasks that have been used in studies of students' informal inferential reasoning and its development. Estimate and draw a graph of a population based on a sample; Compare two or more samples of data to infer whether there is a real difference between the populations from which they were sampled
[3] [4] Display questions bear similarities to closed questions in terms of their requirement for short and limited answers and they can be classified under convergent questions. On the other hand, referential questions and open questions are similar in their requirement for long, often varied, answers, and can be grouped under divergent questions.
Popular in inquiry education, divergent questions allow students to explore different avenues and create many different variations and alternative answers or scenarios. Correctness may be based on logical projections, may be contextual, or arrived at through basic knowledge, conjecture, inference, projection, creation, intuition, or imagination.
Logical reasoning happens by inferring a conclusion from a set of premises. [3] Premises and conclusions are normally seen as propositions. A proposition is a statement that makes a claim about what is the case. In this regard, propositions act as truth-bearers: they are either true or false. [18] [19] [3] For example, the sentence "The water ...
Each logic operator can be used in an assertion about variables and operations, showing a basic rule of inference. Examples: The column-14 operator (OR), shows Addition rule: when p=T (the hypothesis selects the first two lines of the table), we see (at column-14) that p∨q=T.
Therefore, this sample approximately matches the population; If the population is, say, a large number of balls which are black or white but in an unknown proportion, and one takes a large sample and finds they are all white, then it is likely, using this statistical syllogism, that the population is all or nearly all white.
For example, oxygen is necessary for fire. But one cannot assume that everywhere there is oxygen, there is fire. A condition X is sufficient for Y if X, by itself, is enough to bring about Y. For example, riding the bus is a sufficient mode of transportation to get to work.
A study conducted in 1985 showed that over 90% of the mistakes subjects made were actually answers to other questions with a common multiplicand. [3] That is, questions such as 4 x 6 = 24 and 3 x 8 = 24 were very likely to promote errors (8 x 4 = 24) due to associative interference. [3]