Математическая грамотность. Минск: рикз, 2020. 252 с
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2-ex pisa
| Uncertainty and Data
102. In science, technology and everyday life, variation and its associated uncertainty is a given. It is a phenomenon at the heart of the theory of probability and statistics. The uncertainty and data content category includes recognising the place of variation in the real world including, having a sense of the quantification of that variation, and acknowledging its uncertainty and error in related inferences. It also includes forming, interpreting and evaluating conclusions drawn in situations where uncertainty is present. The presentation and interpretation of data are key concepts in this category (Moore, 1997 [28] ). 103. Economic predictions, poll results, and weather forecasts all include measures of variation and uncertainty. There is variation in manufacturing processes, test scores and survey findings, and chance is fundamental to many recreational activities enjoyed by individuals. The traditional curricular areas of probability and statistics provide formal means of describing, modelling and interpreting a certain class of phenomena in which variation plays a central role, and for making corresponding stochastic inferences. In addition, knowledge of number and of aspects of algebra such as graphs and symbolic representation contribute to engaging in problem solving in this content category. 104. Conditional decision making: statistics provides a measure of the variation characteristic of much of what people encounter in their daily lives. That measure is the variance. When there is more than one variable, there is variation in each of the variables as well as co-variation characterising the relationships among the variables. These inter-relationships can often be represents in two-way tables that provide the basis for making conditional decisions (inferences). In a two-way table for two dichotomous variables (i.e. two variables with two possibilities each), there are four combinations. The two-way table (analysis of the situation) provides three types of percentages which, in turn, provide estimates of the corresponding probabilities. These include the probabilities of the four joint events, the two marginal, and the conditional probabilities which play the central role in what we have termed conditional decision making. The expectation for the PISA test items is that students will be able to read the relevant data from the table with a deep understanding for the meaning of the data that they are extracting. 105. In the illustrative example Purchasing Decision the student is presented with a summary of customer ratings for a product in an online store. Additionally, the student is provided with more a more detailed analysis of the reviews by the customers who provided 1- and 2-start ratings. This is 191 effect sets up a two way table and the student is asked to demonstrate an understanding of the different probability estimates that the two-way table provides 106. Identifying conditional decisions making as a focal point of the uncertainty and data content category signals that students should be expected to appreciate how the formulation of the analysis in a model impacts the conclusions that can be dawn and that different assumptions/relationships may well result in different conclusions. Content Topics for Guiding the Assessment of Mathematical Literacy of 15-year-old Students 107. To effectively understand and solve contextualised problems involving change and relationships; space and shape; quantity; and uncertainty and data requires drawing upon a variety of mathematical concepts, procedures, facts, and tools at an appropriate level of depth and sophistication. As an assessment of mathematical literacy, PISA strives to assess the levels and types of mathematics that are appropriate for 15-year-old students on a trajectory to become constructive, engaged and reflective 21st century citizens able to make well-founded judgments and decisions. It is also the case that PISA, while not designed or intended to be a curriculum- driven assessment, strives to reflect the mathematics that students have likely had the opportunity to learn by the time they are 15 years old. 108. In the development of the PISA 2012 mathematical literacy framework, with an eye toward developing an assessment that is both forward-thinking yet reflective of the mathematics that 15- year-old students have likely had the opportunity to learn, analyses were conducted of a sample of desired learning outcomes from eleven countries to determine both what is being taught to students in classrooms around the world and what countries deem realistic and important preparation for students as they approach entry into the workplace or admission into a higher education institution. Based on commonalities identified in these analyses, coupled with the judgment of mathematics experts, content deemed appropriate for inclusion in the assessment of mathematical literacy of 15-year-old students on PISA 2012, and continued for PISA 2021, is described below. 109. For PISA 2021 four additional focus topics have been added to the list. The resulting lists is intended to be illustrative of the content topics included in PISA 2021 and not an exhaustive listing: Growth phenomena: Different types of linear and non-linear growth Geometric approximation: Approximating the attributes and properties of irregular or unfamiliar shapes and objects by breaking these shapes and objects up into more familiar shapes and objects for which there are formulae and tools. Computer simulations: Exploring situations (that may include budgeting, planning, population distribution, disease spread, experimental probability, reaction time modelling etc.) in terms of the variables and the impact that these have on the outcome. Conditional decision making: Using basic principles of combinatorics and an understanding of interrelationships between variables to interpret situations and make predictions. Functions: The concept of function, emphasising but not limited to linear functions, their properties, and a variety of descriptions and representations of them. Commonly used representations are verbal, symbolic, tabular and graphical. Algebraic expressions: Verbal interpretation of and manipulation with algebraic expressions, involving numbers, symbols, arithmetic operations, powers and simple roots. Equations and inequalities: Linear and related equations and inequalities, simple second- degree equations, and analytic and non-analytic solution methods. Co-ordinate systems: Representation and description of data, position and relationships. 192 Relationships within and among geometrical objects in two and three dimensions: Static relationships such as algebraic connections among elements of figures (e.g. the Pythagorean theorem as defining the relationship between the lengths of the sides of a right triangle), relative position, similarity and congruence, and dynamic relationships involving transformation and motion of objects, as well as correspondences between two- and three-dimensional objects. Measurement: Quantification of features of and among shapes and objects, such as angle measures, distance, length, perimeter, circumference, area and volume. Numbers and units: Concepts, representations of numbers and number systems (including converting between number systems), including properties of integer and rational numbers, as well as quantities and units referring to phenomena such as time, money, weight, temperature, distance, area and volume, and derived quantities and their numerical description. Arithmetic operations: The nature and properties of these operations and related notational conventions. Percents, ratios and proportions: Numerical description of relative magnitude and the application of proportions and proportional reasoning to solve problems. Counting principles: Simple combinations. Estimation: Purpose-driven approximation of quantities and numerical expressions, including significant digits and rounding. Data collection, representation and interpretation: Nature, genesis and collection of various types of data, and the different ways to analyse, represent and interpret them. Data variability and its description: Concepts such as variability, distribution and central tendency of data sets, and ways to describe and interpret these in quantitative and graphical terms. Samples and sampling: Concepts of sampling and sampling from data populations, including simple inferences based on properties of samples including accuracy and precision. Chance and probability: Notion of random events, random variation and its representation, chance and frequency of events, and basic aspects of the concept of probability and conditional probability. жүктеу/скачать 7,1 Mb. Достарыңызбен бөлісу:
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