Tag: teaching addition and subtraction

Posted in Elementary School Math

How should students understand the subtraction operation?

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Studies show that students whose understanding of subtraction is only to take away will have difficulty learning other mathematical concepts.

There are three ways by which subtraction can be understood: (1) Taking Away, (2) Difference, and (3) Inverse relation to addition operation. Pupils’ first experience with subtraction involves taking away. The dash sign means minus and minus is taken to mean ‘take away’.

Subtraction as ‘taking away’

Here are formats of subtraction tasks that involve taking away:

  1. Marco has 12 twelve marbles. He gave 5 to his friend Precy. How many does he have left? (This problem is represented by the equation, 12 – 5 = ____.)

    subtraction as taking away
  2. Marco has 12 marbles. He gave some to his friend, Precy. If he had 7 marbles left, how many did he give to Precy? (This problem is represented by the equation, 12 – ____ = 7.)
  3. Marco gave his friend 5 marbles. If has 7 marbles left, how many did he have at the start? (This problem is represented by the equation,  ____ – 5 = 7.)

Problem situation number 3  require subtraction representation but is actually an addition problem because the solution involve adding 5 and 7 instead of doing subtraction.

For most students this is all they understand about subtraction — to take away. This is probably because the use of subtraction in many daily life situations use this meaning. To compound this situation, many of the subtraction tasks in textbooks are also of this type. Very few, if there is any, will include problems that supports the development of the other meaning of subtraction.  And when for a long time all one know about subtraction is to take away, it would be very hard to accept other meanings. Studies show that students whose conception of subtraction is only to take away will have difficulty learning other mathematical concepts.

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Posted in Algebra, Curriculum Reform, Elementary School Math, What is mathematics

“New Math” curriculum

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math curriculumIn the video below, Tom Lehrer ‘explains’ and ‘criticizes’ the New Math curriculum in a funny way. I think the New Math curriculum was not that bad really. It helped the teachers to structure their math knowledge in a “mathematical” way. This is a good thing. The trouble was they taught mathematics in the mathematical way. Enjoy the video.

What is the New Math Curriculum?

New Mathematics or New Math was a brief, dramatic change in the way mathematics was taught in American grade schools, and to a lesser extent in European countries, during the 1960s. The name is commonly given to a set of teaching practices introduced in the U.S. shortly after the Sputnik crisis in order to boost science education and mathematical skill in the population so that the intellectual threat of Soviet engineers, reputedly highly skilled mathematicians, could be met.

New Math emphasized mathematical structure through abstract concepts like set theory and number bases other than 10. Beginning in the early 1960s the new educational doctrine was installed, not only in the USA, but all over the developed world.

Criticisms of the New Math Curriculum

Parents and teachers who opposed the New Math in the U.S. complained that the new curriculum was too far outside of students’ ordinary experience and was not worth taking time away from more traditional topics, such as arithmetic. The material also put new demands on teachers, many of whom were required to teach material they did not fully understand. Parents were concerned that they did not understand what their children were learning and could not help them with their studies. In the end it was concluded that the experiment was not working, and New Math fell out of favor before the end of the decade, though it continued to be taught for years thereafter in some school districts.

In the Algebra preface of his book “Precalculus Mathematics in a Nutshell,” Professor George F. Simmons wrote that the New Math produced students who had “heard of the commutative law, but did not know the multiplication table.”

— excerpts taken from Wikipedia