by The Open University
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In the opening part of this unit we argued that, as human beings, we are constantly engaging with the world through mechanisms called ‘ways of knowing?, and that three important ways of knowing are language, mathematics and science. Although it may be easy to see what makes language, mathematics and science different from each other, in real-life contexts they are rarely used in isolation. We tried to show this by using shopping as an example of an everyday activity that can involve all three subjects. Very likely, you can think of many other instances where two or more of these ways of knowing come into play.
Spend about ten minutes or so thinking of three activities that you have done recently which involved using at least two of the three ways of knowing ? language, mathematics and science ? within the same activity. Write a brief account of what happened, in particular noting how closely intertwined they were in each case.
Possible examples of activities are:
buying fabric to make a coat (calculating quantities, judging fabric properties such as waterproofness and warmth, talking to the sales assistant);
showing a child how to make a cake (measuring quantities, explaining and instructing, understanding that heat causes chemical changes).
Examples of how these ways of knowing can converge include:
counting aloud, which uses both language and mathematics simultaneously;
heating sugar and fruit to exactly the right temperature to make jam, which combines the use of mathematics (measuring temperature) with science (knowing that a change takes place at a specific temperature).
Almost any activity can be supported by language: talking with a colleague, reading, writing or, indeed, thinking. (The relationship between language and thinking is a topic we will come back to later.)
As well as occurring together, the three ways of knowing have many capacities in common ? they involve:
problem-solving and decision-making;
logical reasoning;
communication;
making connections and recognising common characteristics.
Another feature that language, mathematics and science have in common is that each can be:
either a toolkit that enables us to make sense of and engage with the world; or
an academic discipline ? a refined body of knowledge and of ways of thinking, which can be applied to everyday situations but also extended to relate to many possible situations.
For example, the mathematical concept of square can help us both to recognise any square object and to plan a square building before going on to construct it.
Unfortunately, when subject knowledge becomes more abstract and decontextualised, it can appear irrelevant to everyday life and difficult to understand. This can cause frustration to learners of any age, engendering negative attitudes that they carry with them for the rest of their lives. The importance of context is a theme that will be developed further in this part of the unit, as we argue that the term covers much more than just the physical surroundings in which an activity or a communication takes place.
We now turn our attention to the idea of thinking, arguing that symbols are an essential element in developed thought. Although the focus will be more on the thinking patterns of individuals (i.e. ‘what's in your head?), we will not lose sight of the idea that thinking is not an isolated or decontextualised activity. We also develop the idea of ‘making meaning? and the notion that there is more than one kind of meaning.
An important element of here will be for you to undertake an audit of your own knowledge of language, mathematics and science. This may seem strange, however such audits are aimed partly at exploring the gap between implicit and explicit knowledge, and helping you to articulate some knowledge that you may not have articulated before. If you have encountered Vygotsky's (1978) notion of the Zone of Proximal Development, you will be familiar with the idea that there are always areas of knowledge in which we have some understanding but are not fully confident; and that it is by giving attention to these areas that we extend our knowledge.
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