Математическая грамотность. Минск: рикз, 2020. 252 с
particular supports reasoning about the
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2-ex pisa
| Using models in general and mathematical models in particular supports reasoning about the
real-world applications of mathematics envisaged in this framework by encouraging students to focus on the most significant elements of the situations and in so doing to reduce the problem to its essence. Understanding variation as the heart of statistics 72. In statistics accounting for variability is one, if not the central, defining element around which the discipline is based. In today’s world people often deal with these types of situations by merely ignoring the variation and as a result suggesting sweeping generalisations which are often misleading, if not wrong, and as a result very dangerous. Bias in the social science sense is usually created by not accounting for the sources and magnitudes of the variability in the trait under discussion. 184 73. Statistics is essentially about accounting for or modelling variation as measured by the variance or in the case of multiple variables the covariance matrix. This provides a probabilistic environment in which to understand various phenomena as well as to make critical decisions. Statistics is in many ways a search for patterns in a highly variable context: trying to find the single defining “truth” in the midst of a great deal of random noise. “Truth” is set in quotes as it is not the nature of truth that mathematics can deliver but an estimate of truth set in a probabilistic context, accompanied by an estimate of the error contained in the process. Ultimately, the decision maker is left with the dilemma of never knowing for certain what the truth is. The estimate that has been developed is, at best a range of possible values – the better the process, for example, the larger the sample of data, the narrower the range of possible values, although a range cannot be avoided. Some aspects of this have been present in previous PISA cycles, the growing significance contributes to the increased stress in this framework. 74. Understanding variation as a central feature of statistics supports reasoning about the real- world applications of mathematics envisaged in this framework in that students are encouraged to engage with data based arguments with awareness of the limitations of the conclusions that can be drawn. Problem solving 75. The definition of mathematical literacy refers to an individual’s capacity to formulate, employ, and interpret (and evaluate) mathematics. These three words, formulate, employ and interpret, provide a useful and meaningful structure for organising the mathematical processes that describe what individuals do to connect the context of a problem with the mathematics and solve the problem. Items in the 2021 PISA mathematics test will be assigned to either mathematical reasoning or one of three mathematical processes: Formulating situations mathematically; Employing mathematical concepts, facts, procedures and reasoning; and Interpreting, applying and evaluating mathematical outcomes. 76. It is important for both policy makers and those engaged more closely in the day-to-day education of students to know how effectively students are able to engage in each of these elements of the problem solving model/cycle. Formulating indicates how effectively students are able to recognise and identify opportunities to use mathematics in problem situations and then provide the necessary mathematical structure needed to formulate that contextualised problem in a mathematical form. Employing refers to how well students are able to perform computations and manipulations and apply the concepts and facts that they know to arrive at a mathematical solution to a problem formulated mathematically. жүктеу/скачать 7,1 Mb. Достарыңызбен бөлісу:
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