Did You Say Mathematics?

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The topic was how do you make math fun? Because of time zone differences, I ended up writing a fairly detailed first post on the panel. I thought it would be of interest to readers of this blog as well. You can see the entire panel discussion here. Or rather, it can be fun.

Less is more

It can also be frustrating, illuminating, elegant, baffling, challenging, and addictive. Even if these existed occasionally, making them more ubiquitous actually changes how people experience the subject. When people are young say, 2 — 8 , mathematics tends to be a source of joy.

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Kids seem to be drawn to ideas about number, shape, pattern, and structure in a similar way they are drawn to language. They learn through experimentation, play, and repetition, and the exposure to mathematical ideas is fundamentally empowering. I think we need to create frameworks that imitate how young kids are drawn into mathematical thinking. Mine looks like this:.

One very important thing to note is that play supports all of this. For mathematics, play is the engine of learning. Playing games is great.

Is mathematics an effective way to describe the world?

Just living with questions and providing a space for questions to live is very powerful. September 26, Melissa 8 comments. Travis T. Maths Maths Math or Maths Math vs. Enjoy this article? Articles Featured Facts Language. Dr Curt Nicol D. September 28, am.

Math or Maths?

Adam October 7, pm. Rauf Tee October 27, am. He who knows that he knows not, is a sage. Tony Luxton October 27, am. Gerald Baton October 31, am. Erin December 19, pm. And abstractions are made not only from concrete objects or processes; they can also be made from other abstractions, such as kinds of numbers the even numbers, for instance.

Such abstraction enables mathematicians to concentrate on some features of things and relieves them of the need to keep other features continually in mind. As far as mathematics is concerned, it does not matter whether a triangle represents the surface area of a sail or the convergence of two lines of sight on a star; mathematicians can work with either concept in the same way. After abstractions have been made and symbolic representations of them have been selected, those symbols can be combined and recombined in various ways according to precisely defined rules.

Sometimes that is done with a fixed goal in mind; at other times it is done in the context of experiment or play to see what happens. Sometimes an appropriate manipulation can be identified easily from the intuitive meaning of the constituent words and symbols; at other times a useful series of manipulations has to be worked out by trial and error. Typically, strings of symbols are combined into statements that express ideas or propositions.

The rules of ordinary algebra can then be used to discover that if the length of the sides of a square is doubled, the square's area becomes four times as great. More generally, this knowledge makes it possible to find out what happens to the area of a square no matter how the length of its sides is changed, and conversely, how any change in the area affects the sides.

Mathematics as thought

Although they began in the concrete experience of counting and measuring, they have come through many layers of abstraction and now depend much more on internal logic than on mechanical demonstration. The test for the validity of new ideas is whether they are consistent and whether they relate logically to the other rules.

Mathematical processes can lead to a kind of model of a thing, from which insights can be gained about the thing itself. Any mathematical relationships arrived at by manipulating abstract statements may or may not convey something truthful about the thing being modeled. However, if 2 cups of sugar are added to 3 cups of hot tea and the same operation is used, 5 is an incorrect answer, for such an addition actually results in only slightly more than 4 cups of very sweet tea.

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To be able to use and interpret mathematics well, therefore, it is necessary to be concerned with more than the mathematical validity of abstract operations and to also take into account how well they correspond to the properties of the things represented. Sometimes common sense is enough to enable one to decide whether the results of the mathematics are appropriate. For example, to estimate the height 20 years from now of a girl who is 5' 5" tall and growing at the rate of an inch per year, common sense suggests rejecting the simple "rate times time" answer of 7' 1" as highly unlikely, and turning instead to some other mathematical model, such as curves that approach limiting values.

Often a single round of mathematical reasoning does not produce satisfactory conclusions, and changes are tried in how the representation is made or in the operations themselves.

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Indeed, jumps are commonly made back and forth between steps, and there are no rules that determine how to proceed. The process typically proceeds in fits and starts, with many wrong turns and dead ends. This process continues until the results are good enough. But what degree of accuracy is good enough? The answer depends on how the result will be used, on the consequences of error, and on the likely cost of modeling and computing a more accurate answer.

For example, an error of 1 percent in calculating the amount of sugar in a cake recipe could be unimportant, whereas a similar degree of error in computing the trajectory for a space probe could be disastrous.

Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?
Did You Say Mathematics? Did You Say Mathematics?

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