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Topic: [math-learn] Teaching addition and subtraction of fractions
Replies: 47   Last Post: Oct 31, 2004 3:57 PM

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 Wayne Bishop Posts: 5,465 Registered: 12/6/04
RE: [math-learn] Teaching addition and subtraction of fractions
Posted: Oct 28, 2004 2:37 PM

At 06:41 AM 10/27/2004 -0500, John Clement wrote:

&gt;The results of the TIMMS study show that students in Japan and
&gt;other oriental countries are pressed to come up with their own algorithms
&gt;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 1-digi
number, Division by a 1-digit 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 2-digit 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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Date Subject Author
10/26/04 Rexboggs5@aol.com
10/26/04 Karl M. Bunday
10/26/04 Chris
10/26/04 Wayne Bishop
10/27/04 Paul A. Tanner III
10/27/04 John Clement
10/27/04 Ralph A. Raimi
10/27/04 John Clement
10/28/04 CJ Masenas
10/28/04 Ralph A. Raimi
10/28/04 John Clement
10/29/04 CJ Masenas
10/30/04 Wayne Bishop
10/29/04 Ralph A. Raimi
10/31/04 Paul A. Tanner III
10/28/04 Paul A. Tanner III
10/28/04 John Clement
10/28/04 Paul A. Tanner III
10/28/04 Wayne Bishop
10/27/04 Ron Ferguson
10/27/04 Paul A. Tanner III
10/28/04 John Clement
10/28/04 Paul A. Tanner III
10/27/04 Chris
10/27/04 Wayne Bishop
10/27/04 Ron Ferguson
10/27/04 Larry Sowder
10/28/04 Wayne Bishop
10/28/04 Paul A. Tanner III
10/28/04 Ron Ferguson
10/29/04 Paul A. Tanner III
10/29/04 Ron Ferguson
10/29/04 Paul A. Tanner III
10/29/04 Ralph A. Raimi
10/29/04 Paul A. Tanner III
10/29/04 Ralph A. Raimi
10/29/04 Ron Ferguson
10/29/04 Ralph A. Raimi
10/29/04 Paul A. Tanner III
10/27/04 Ralph A. Raimi
10/27/04 Chris
10/27/04 LnMcmullin@aol.com
10/27/04 Rexboggs5@aol.com
10/27/04 Rexboggs5@aol.com
10/27/04 Brian Kriz
10/27/04 Rexboggs5@aol.com
10/28/04 Paul A. Tanner III
10/28/04 Paul A. Tanner III