Математическая грамотность. Минск: рикз, 2020. 252 с
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2-ex pisa
| Change and Relationships
89. The natural and designed worlds display a multitude of temporary and permanent relationships among objects and circumstances, where changes occur within systems of interrelated objects or in circumstances where the elements influence one another. In many cases these changes occur over time, and in other cases changes in one object or quantity are related to changes in another. Some of these situations involve discrete change; others change continuously. Some relationships are of a permanent, or invariant, nature. Being more literate about change and relationships involves understanding fundamental types of change and recognising when they occur in order to use suitable mathematical models to describe and predict change. Mathematically this means modelling the change and the relationships with appropriate functions and equations, as well as creating, interpreting and translating among symbolic and graphical representations of relationships. 90. Change and relationships is evident in such diverse settings as growth of organisms, music, seasonal change and cycles, weather patterns, employment levels and economic conditions. Aspects of the traditional mathematical content of functions and algebra, including algebraic expressions, equations and inequalities, tabular and graphical representations, are central in describing, modelling and interpreting change phenomena. Computational tools provide a means to visualise and interact with change and relationships. Recognising how and when a computational device can augment and complement mathematical concepts is an important computational thinking skill. 91. Representations of data and relationships described using statistics are also used to portray and interpret change and relationships, and a firm grounding in the basics of number and units is also essential to defining and interpreting change and relationships. Some interesting relationships arise from geometric measurement, such as the way that changes in perimeter of a family of shapes might relate to changes in area, or the relationships among lengths of the sides of triangles. 92. Growth phenomena: Understanding the dangers of flu pandemics and bacterial outbreaks, as well as the threat of climate change, demand that people think not only in terms of linear relationships but recognise that such phenomena need non-linear (often exponential but also other) models. Linear relationships are common and are easy to recognise and understand but to assume linearity can be dangerous. A good example of linearity and one probably used by everyone is estimating the distance travelled in various amounts of time while traveling at a given speed. Such an application provides a reasonable estimate as long as the speed stays relatively constant. But with flu epidemics, for example, such a linear approach would grossly underestimate the number of people sick in 5 days after the initial outbreak. Here is where a basic understanding of non-linear (including quadratic and exponential) growth and how rapidly infections can spread given that the rate of change increases from day to day is critical. The spread of the Zika infection is an important example of exponential growth; recognising it as such helped medical personnel to understand the inherent threat and the need for fast action. 93. Identifying growth phenomena as a focal point of the change and relationships content category is not to signal that there is an expectation that participating students should have studied 189 the exponential function and certainly the items will not require knowledge of the exponential function. Instead, the expectation is that there will be items that expect students to (a) recognise that not all growth is linear, (b) that non-linear growth has particular and profound implications on how we understand certain situations, and (c) appreciate the intuitive meaning of “exponential growth” as an extremely rapid rate of growth, for example in the earthquake scale, every increase by 1 unit on the Richter scale does not mean a proportional increase in its effect, but rather by 10, 100, and 1000 times etc. жүктеу/скачать 7,1 Mb. Достарыңызбен бөлісу:
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