1.6 Do, talk and record triad

The do–talk–record triad (DTR) is a description of what is likely to take place in collaborative mathematics classrooms. It is concerned with observable events, and with the learner rather than the teacher, though many teaching insights flow from it. Although the order of the triad suggests that it should be followed in a particular sequence, this is not necessarily the case. Sometimes talking comes before doing or recording before talking. It also takes time for a learner to move
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1.2.3 Process

Mathematical processes are different from content in that they overarch the subject and are not thought of as hierarchical. A list of processes could contain:

  • problem-solving (including investigating);

  • mathematical modelling;

  • reasoning;

  • communicating;

  • making connections (including applying mathematics); and

  • using tools.

Each of the six processes liste
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Learning outcomes

After studying this unit, you should:

  • understand some current issues in mathematics education, such as the relationship of mathematics content to mathematics processes.

  • understand a variety of approaches to the teaching of mathematics such as 'do-talk-record'

  • be able to approach mathematical problems and tasks in a flexible way.


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1.6.5 RSS

RSS (‘Really Simple Syndication’ or ‘Rich Site Summary’) newsfeeds supply headlines, links, and article summaries from various websites. By using RSS ‘feedreader’ software you can gather together a range of feeds and read them in one place: they come to you, rather than you having to go out and look for breaking news. The range of RSS feeds on offer is growing daily. There is probably a feed to cover all aspects of your life where you might need the latest information, and you may
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1.3.9 Summary

There is a lot of information available on maths and statistics via the internet. Try the activities below to start exploring what is available.

Activity

1.1.4 Evaluating information

How well does the following statement describe your approach to evaluating the information that you use?

When I come across a new piece of information (e.g. a website, newspaper article) I consider the quality of the information, and based on that I decide whether or not to use it.

  • 5 – This is an excellent match; this is exactly what I do


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Acknowledgements

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Grateful acknowledgement is made to the following sources for permission to reproduce material in this unit:

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References

Anderson, R.C. (2002) Ray's story [online], http://www.interfaceinc.com/getting_there/ Ray.html (Accessed 31 November 2002).
Arnstein, S.R. (1969) ‘Ladder of citizen participation’, Journal of the American Institute of Planners, vol. 35, pp. 216–24.
Bromley, S. (2001). Governing the European Union, London, Sage.

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4.2.1 Eco-efficiency = money in the bank

Business can profit from taking the environment into account (generally called eco-efficiency). Poor environmental performance is seen as a reflection of poor business practice in general. Eco-efficiency promotes the economic benefits of energy and materials savings, at the same time being first to market with new technologies or products. Since business sustainability lobbies promoted eco-efficiency in the early 1990s, the creed has gained rapid acceptance, and with good cause. There
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2.2 Vibrant civil societies and a networked globe

One thing is common to all three attempts to find a route to a sustainable economy and society: in different ways they all assume that people will get actively involved in making human societies more sustainable. But this transformation will not take place through the corporate world's promises, by local protectionism, a return to ‘strong states’ or the publication of numerous indicators. Any of the three positions outlined above requires interactions and feedbacks created by a vibrant
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3.2 The past temperature of the planet

Measuring the concentration of lead in the ice is called a direct measurement: the ice sample is melted and the water produced contains a very small but readily measured quantity of lead dust. A very accurate set of scales would be needed to measure it, but it is a directly measured quantity. There are also many indirect measurements that can be made using proxy data. The concept for using proxies is both simple and brilliant: one measured property allows inference about other states o
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1.1 What is the carbon footprint and why is it important?

The carbon footprint is the annual amount of greenhouse gas emissions, mainly carbon dioxide, that result from the activities of an individual or a group of people, especially their use of energy and transport and consumption of goods and services. It's measured as the mass, in kilograms or tonnes per year, either of carbon dioxide (CO2) emissions alone, or of the carbon dioxide equivalent (CO2e) effect of other greenhouse gas emissions.


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5.3 The rebound effect

When individuals or organisations implement energy efficiency improvements, they usually save money as well as saving energy. However, if the money saved is then spent on higher standards of service, or additional energy-consuming activities that would not have otherwise been undertaken, then some or all of the energy savings may be eliminated. This tendency is sometimes known as the ‘rebound effect’. For example, if householders install improved insulation or a more efficient heating boi
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2.2 Economic valuation: towards ecological economics

The blue whale could have supplied indefinitely a sustainable yield of 6000 individuals a year.

This is one of the earliest references to sustainability in the literature, taken from the 1971 edition of the science journal Nature (cited in Senge et al., 2006, p. 45). Here, the blue whale is given instrumental value – a means of measuring not the survival of the blue whale for its intrinsic v
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7 Some philosophical issues

In this unit we have considered global issues that have implications for our health and the health of future generations. This places our own lives in a different context and also indicates the uncertainties that surround the future. Whilst some environmental changes have very direct health consequences, we should not forget the indirect benefits that accrue from a healthy planet. The principle that ‘we should hand on to the next generation an environment no less rich than the one we
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6 Population growth

Earlier it was stated that three factors check population growth. These are predation, disease and insufficient food supply. For much of our history, our ancestors’ numbers were indeed limited by wars, disease and famine. The world population remained relatively stable until around 300 years ago. Then at the beginning of the 19th century (100 years after population growth started its geometric increase), the demographer Thomas Malthus predicted that population growth would outstrip food pro
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4 4 Renewable energy sources

Fossil and nuclear fuels are often described as non-renewable because supplies are finite and will eventually run out. Renewable fuels are those energy sources that will not run out in the future.

Most renewable energy sources originate from the sun (solar energy), while tidal energy originates from the gravitational pull of the moon, and geothermal energy results from heat trapped below the surface of our planet.

Solar energy can be used directl
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Conclusion

In this Introduction we have explored the development of technology from the start of the Industrial Revolution to the present day. At the same time we have traced the increasing impact our industrial societies have had on our environment, and the role that science and technology has played in this. We have explored some major global environmental issues, in particular our dependence on the exploitation of fossil fuels, and have outlined some of the fundamental constraints on the abili
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6.4.4 Environmental limits

There are many different definitions of what sustainable development means; you were given one in Section 5.3, and how this should guide policy. The underpinning concepts are: equity for human development, and limits on the capacity of the environment. The idea of environmental limits on the ability of the Earth's biophysical systems to cope with and adapt to pressures from human activity, whether from demand for natural resources, the waste products of modern economies, or from habitat modif
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Acknowledgements

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The material acknowledged below is contained in: Ordering the International: History, Change and Transformation (eds William B
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