Do Statistics Lie?

This is a post from Samuel, a good friend of mine. The following describes how statistical data can be decieving.


"....A/P Chua Tin Chiu quoted some eye-catching headlines from newsapers,
...."You have 40% chance of living up to 100 years old if you are the first born"
Then he asked: Are you sure about the conclusion statements?..... he said, "The survey has been done in a village in china, where the study was done only to people who live up to 100. However, the number of first born will always be more than the number of 2nd born, who will always be more than the number of 3rd born etc (haha...for obvious reasons right? You need a first born before you can have a 2nd born) and so the number of first born who live up to 100 should also be more than the rest....

A/P Chua quoted more newspaper reports with regards to statistics in newspaper, and asked, "Why do you think percentages have been quoted in areas where direct figures might be more accurate, and vice versa? Isn't it the way the media (or the government) want to bring across a particular idea?

Another wonderful headline that students will love to quote if true,

"Study shows More tuition = poorer grades"

Well, the study was concluded based on a huge pool of students who wrote down their grades, as well as the number of hours they had for private tutoring. But the BIGGEST question is, "How will the students who have private tuition fare, if they do not have private tuition? Isn't it true that those who need private tuition are generally those who may not cope that well, and so extra help to be given?"

Curriculum focal points in the States

In today's Straits times (16 Sept), there is an article on page 36 entitled: "Maths teaching in US moving back to basics." Here the article points out that "new ways of teaching maths, introduced in the US almost two decades ago have not added up much." These new ways refer to the constructivist approach where "children learn what they want to learn when they're ready to learn it". Instead, the National Council of Teachers of Mathematics(NCTM) urge that the teaching of maths in kindergarten through eighth grade focus on a few core skills. These skills, which they term as the curriculum focal points, are classified under each level*:

• Pre-K (under 5 years old): Develop an understanding of whole numbers and how to count and compare them.

• Kindergarten(5-6 yrs old): Use numbers to solve quantitative problems, count numbers in a set, and create a set within a given number of objects.

• 2nd Grade(7-8 yrs old): Learn how to count in units and multiples of hundreds, tens, and ones; understand multi-digit numbers in terms of place-value, and how to compare and order numbers.

• 4th Grade(9-10 yrs old): Develop understanding of multiplication, including “quick recall” of multiplication and division facts; select correct methods to make mental estimations and calculations.

• 6th Grade(11-12 yrs old): Know the meanings of fractions, multiplication, and division; understand relationships between decimals and fractions, and how to multiply and divide them, using multistep problems.

• 8th Grade(13-14 yrs old): Use linear functions, linear equations, and their understanding of the slope of a line to solve problems; understand verbal and graphical representations of functions; describe how the slope of a line and the y-intercept appear in different verbal, graphical, and algebraic representations.

* Taken from NCTM website :http://www.nctm.org/news/ext_articles/2006_0912_edweek.htm
Read more about this math education reform via the above URL.

There is also an interesting article entitled the 10 myths of NCTM learning where university professors detail some problems that face math education in US. The URL is:
http://www.nychold.com/myths-050504.html

My final comment on the "10 myths": A very informative read and thought provoking. Any math teacher or anyone who is interested in mathematics reform should read it. The curriculum reform as stated above is actually in response to the "10 myth" article.

Learner.org

This is a very useful website for teachers. It contains tonnes of resources and videos on teaching high school mathematics. There are many interesting teaching methods for various subjects such as algebra and statistics. Many of these ideas are conveyed in videos. Although the videos are streamed, they have good resolution.

In sum, this site is well worth visiting.

Click here to access the site

Numb3rs

Numb3rs is a CBS production of how FBI solves crimes with the help of a mathematician. In each episode, a different concept is introduced to aid the detectives to identify killers, track down suspects and solve robberies. Accompanying the show is a website that provides mathematical activities for the related episodes.

The URL is

http://www.cbs.com/primetime/numb3rs/ti/activities.shtml

For more information about the show, go to

http://www.cbs.com/primetime/numb3rs/index.shtml

This show is a hit, and hopefully it gets shown in Singapore. Clips from the video can be used to teach math in class.

Polya's "How to Solve It"

This problem was taken from the above mentioned book, which is considered a classic on concepts mathematical problem-solving skills. It is a good example of how algebra can be applied to geometry, and how the heuristic "working backwards" (and many others) can be applied to solve the problem.

Given all quadilaterals with the same perimeter, which one would have the biggest area?

Thanks to CJ for the correction.

An Arithmetical fallacy

Here is an interesting clip avaliable at google that shows 25 divided by 5 equals 14.
What is the common misconception in the 3 different workings?

http://video.google.com/videoplay?docid=7106559846794044495&q=ma+and+pa+kettle