
RE: [mathlearn] Teaching addition and subtraction of fractions
Posted:
Oct 28, 2004 2:37 PM


At 06:41 AM 10/27/2004 0500, John Clement wrote:
>The results of the TIMMS study show that students in Japan and >other oriental countries are pressed to come up with their own algorithms >and they discuss the ideas.
There is no indication, from TIMSS or otherwise, that gives credence to the idea that student invented algorithms for arithmetic, including fraction arithmetic, are widespread in Japan and other oriental counties. I have much of the Japanese curricula and all of the Singapore (the country that came in ahead of Korea that came in ahead of Japan) and standard algorithms are standard practice.
As evidence, I'm looking at Singapore Primary Mathematics 4A (first semester, 4th grade). For example, Chapter 2 is "Multiplication and Division of Whole Numbers". Section 1 is "Multiplication by a 1digi number, Division by a 1digit number". Example (a) is the word problem: Sean has 1135 US stamps. He has 3 times as many foreign stamps as US stamps. How many stamps does he have altogether? That leads to 1135x4 written vertically with the "carries" written exactly as sensible people expect in four successive, absolutely clear, steps.
Example (b) feeds off of (a), "If Sean puts the stamps equally into 5 packets, how many stamps are there in each packet?
The presented algorithm for dividing the 4540 by 5 is also absolutely standard in absolutely clear steps of *the* division algorithm.
Multiplication by a 2digit number is the second section, again standard.
Chapter 3 is "Fractions" and the first section is "adding fractions". It starts with examples of "like" fractions and progresses to 1/2 + 1/4, nicely modeled with a pie diagram and then 2/3 + 1/6 using the famous Singapore unit bar diagram. By the next page, students are writing addition problems with equivalent fractions where one denominator is a divisor of the other followed by a dozen problems where students are expected to use that idea without any pies or bars. The next section is subtraction. Section 3 is "Mixed Numbers" and Section 4 is "Improper Fractions". Then lots of word problem applications.
Book 5A revisits these ideas quickly and then moves on to multiple digit division and addition and subtraction of fractions where neither denominator divides the other. It also introduces multiplication of fractions, first as fractions of a whole number and then "Product of Fractions". Then dividing fractions, but in 5A only by a whole number. Again, this is followed by lots of problems involving ratios and the like.
The curriculum is excellent and easily available to US children except for ed industry religion which appears to be an insurmountable hurdle.
Wayne.
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