Michael Shields blog XML

You know, for kids

In an article published in the current issue of Communications of the ACM, George Fletcher and James Lu argue that the logical thinking underlying computer science is broadly useful in life and should be taught in K-12 schools even before programming. Just as children learn algebra, calculus, literature, and composition, they argue, children should also learn “computational thinking”.

How are kids in the US doing at algebra, calculus, literature, and composition, anyway? In 2007, 61 percent of eighth-graders were unable to meet the “Proficient” level of national standards:

Eighth-graders performing at the Proficient level should be able to conjecture, defend their ideas, and give supporting examples. They should understand the connections between fractions, percents, decimals, and other mathematical topics such as algebra and functions. Students at this level are expected to have a thorough understanding of Basic level arithmetic operations—an understanding sufficient for problem solving in practical situations.

About two of five kids are unable to handle that.

How about reading? Fewer than one-third reached the Proficient level.

Fletcher and Lu give an example of what these middle school students are missing in their curriculum:

[C]onsider the standard notion of the greatest common divisor (gcd) of two integers a and b, a useful tool that students encounter during the study of fractions. Euclid’s classic algorithm, applied to computing gcd(56,21), for example, proceeds as follows: (56,21) ⇒ (35,21) ⇒ (14,21) ⇒ (14,7) ⇒ (7,7). Here, “⇒” is an abstraction of the function λ a,b.if a<b,(a,b−a); else (a−b,b). We can compare the efficiency of Euclid’s algorithm to an exhaustive linear search. This comparison further provides a chance to discuss representation and decision. For linear search, a single number captures the complete state since each subsequent state is a unary function of the current state. For Euclid’s algorithm, a pair representation is necessary as each subsequent state is conditioned on both of the current values.

I agree that it would be nice if eighth graders were generally able to discuss this.

posted at: 2009-02-09 23:18 UTC | permanent link to this entry | comment