Category: Elementary School Math

Posted in Elementary School Math

Teaching the meaning of equal sign

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Here’s how I sequence my lesson to develop pupil’s understanding of the meaning of the equal sign. Actually the lesson uses the context of the meaning of equal sign to introduce the students to the meaning of variable intuitively. The students enjoyed this lesson and they said they loved the way I made them think. Scaffolding was done through questions that engages pupils in reasoning and making decisions. Note that the emphasis of the lesson is not on computations but on thinking and problem solving. This is also an example of teaching algebraic thinking in the grades.

I first wrote the equal sign on the board then said What does the equal sign mean? You may use an example to explain your answer. One boy said it means you add or do the operation and provided this example 2 + 10 = 12. I asked the class who agrees with him and 25 out of 35 showed hand.

What about in 15 + ____ = 21 + ____? One girl said “It means balance” and explained that 15 plus a number balances with 21 plus another number. When I asked the class who agrees with her 30 out of 35 raised their hand. Everyone’s eyes was on me, waiting for me to say which meaning of equal sign is correct. I just gave them a wink to heighten their curiosity.

Now that I got them all thinking, I asked: Do you think you can put just any two numbers in the blanks? With this question I successfully divided the class into two camps: those who say yes and those who say no and everyone is challenged to prove themselves right or prove the other wrong.

Click here for the slide version of this post.

Posted in Curriculum Reform, Elementary School Math

English edition Japanese Grades 1- 6 Math textbooks 50% off until September

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Last year I had the chance to do a few days work for a Japanese Mathematics textbook series translated in English. I just received an e-mail from one of the editors that the publisher is selling the books at 50% off. It will only cost about US$75 for the set of 11 books until September 2011. After September the set will cost about $US150. 00, the latest edition. I don’t have a copy yet of the books so I cannot show here a page  but my colleague and I did some editing for Grades 5 and 6 and we think that the Japanese really have a very different approach in teaching mathematics be it in textbooks and in teaching. There’s a very strong emphasis on developing mathematical thinking (I saw several lesson study demonstration teaching while there. Our Institute also had a 5-year math and science teaching project with Japanese educators). The solutions shown and the structure of the books model how students in that grade level think and would approach the problems. The books are a product of years of doing lesson  study in mathematics. I love the section “Let’s think about how to…”

The schools where you teach may already have a prescribed textbook but you will have a great resource in designing your instruction with this set. Your school might even decide to use the textbooks.

For ordering, please send your order to Mr. Serizawa: Continue reading “English edition Japanese Grades 1- 6 Math textbooks 50% off until September” →

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.

Continue reading “How should students understand the subtraction operation?” →

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