Posts tagged Math 2.0

I am aggregating information on mathematical holidays, but now I want to think of another angle – mathematics IN holidays. Carol Cross from Teaching Your Middleschooler blog inspired this.

Carol is organizing an open online event today, April 21st 2011, at 7:30pm ET, about the science of energy, with a writer Kathleen Reilly. You can also add your name to win Kathleen’s book. Check it out!

Here is my favorite puzzle about the Earth. Imagine you put a string all around the Earth. Now imagine you want to enlarge your string so it can hang one meter from the surface. How much longer will your string need to be? Here are some data about the size of the Earth and here is the awesome Noon Day project for measuring it for yourself with kids and grown-ups from all over the world.

What is the answer if you use an orange instead of the Earth?

PBS Teachers has a collection of three series of group activities for Earth Day Mathematics. The recursive equation activities (population growth and decay) are rather fun.

The trash inventory activity consists of carefully tracking your trash for a day, a week or a month. We have done it with Girls on Track camp at NCSU, and it was a whole lot of fun. The shocking part comes when you start to multiply your trash by the number of days in a year or a decade, or by the number of people in your neighborhood. This is one of better examples of contextual mathematics activities I know.

In the last five years or so, calculating offset costs for this or that activity became popular. Here is an example of a lesson about it – how many trees do you need to plant to offset your car use. I would suggest finding and using online calculators, such as this one for carbon footprint, to see what online communities are engaged with them and in what ways – like Go Zero.

Here is a quote (pre-editing) from the Green Mathematics article I wrote this January for an encyclopedia of mathematics. I am really looking forward to the encyclopedia of 500+ articles on subjects from Accident Reconstruction to Zero. Meanwhile…
Different areas of mathematics allow different approaches to environmental problems. Algebraic reasoning, for example, assumes functional dependencies among variables and known operations. It is most appropriate in cases where algebraic relationships among variables are stable over time and can be established with empirical measurements. For example, producing one megajoule of energy by burning coal emits 92g of CO2. One can compute the carbon footprint of heating a house by coal algebraically, by measuring the energy consumption and multiplying it by 92g.

Calculus is the study of rates of change in variables, and limits of change. In green mathematics, calculus methods are most appropriate when algebraic relationships between variables and their changes over time are measurable. For example, rocket propulsion consumes fuel stored within the vehicle, making the vehicle lighter with time. The efficiency of rocket engines can be computed applying integrals over time to equation connecting changes in mass and the momentum resulting from the engine.

Differential equations is the study of unknown functions by known values and their rates of change, that is, derivatives – the situation frequent in ecology. Differential equations are extensively used in green mathematics to model interactions within systems, such as predator-prey dynamics, fluid dynamics in natural and human-made water and gas systems, radioactive decay, or economic growth.

Statistical methods deal with organization and interpretation of data that includes random elements. Descriptive statistics summarizes patterns in data collected from some group of objects or events, called population. It may include data calculations such as mean or frequency. Descriptive statistics is useful for comparing systems that include randomness, such as per capita consumption of energy in different countries, or recycling behaviors in neighborhoods of a city.

Inferential statistics predicts patterns in the whole population based on data observed in a sample of the population. It is extensively used in biology, ecology, and economics, because collecting data about everything or everybody in the population is rarely possible. One of the most powerful methods of inferential statistics is the analysis of correlations within data. For example, the levels of air pollution in cities correlate with the incidence of asthma among the population. Notably, even strong correlations between two variables do not necessarily mean particular cause-effect relationships. The first variable may depend on the second, or the second on the third, or both may depend on another factor. For example, in children under six problem-solving abilities strongly correlate with foot size. The reason is that both foot size and problem-solving abilities increase with age.

Data visualization is an interdisciplinary area spanning descriptive statistics, grid and graph use from algebra and calculus, specific representation methods from more narrow areas of mathematics such as tree diagrams from combinatorics, psychology of perception and learning, and design. Visual literacy combines the ability to understand and critically analyze visualizations produced by others, and to create quality visualizations for the purposes of analysis and sharing of messages. Because green mathematics frequently deals with controversial issues, individuals and groups promoting different agendas use and often abuse data visualization to make their point. Visual literacy is one of the “twenty-first century skills” whose importance is growing with heavier use of mathematics in ecology, and more emphasis on ecological approaches in all areas of life.