Equal or Equivalent?

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CZ Romani girl solving math problem in special school

Does 2 + 2 = 4?

Are the group of numbers on the left side of the “equal sign” really “equal to” the number on the right side? By presenting this problem to students and using the word “equal,” we are telling them that those two little parallel lines mean there is only one possible answer, and by doing so, we may be missing an important opportunity to introduce algebraic thinking at an early age.

Research has shown that teaching elementary age children to think algebraically is a precursor for success as they move toward advanced levels of mathematics. By introducing the idea that the “equal sign” represents a relationship between two mathematical expressions, students begin the important process of relational thinking.

Let’s look at the following example:

7 + 3 = 2 + 8

If we say that 7 plus 3 equals 2 + 8, we are essentially limiting the ability of primary grade students to comprehend this unique relationship. Seven plus three does not ONLY equal two plus eight; it also can equal nine plus 1, and one plus one plus eight, etc. By using instead the words “equivalent to,” parents and teachers can emphasize this relationship and begin a math dialogue with their children to encourage a better understanding of mathematical expressions.

Understanding this concept can also help the student who struggles with memorizing addition facts. Using mental math, students can explore the concept of “friendly numbers,” those numbers like 10 and 20, which are easy to compute mentally. Asking a 1st grader to tell you the sum of 19 plus 28 may create a sense of panic in those who rely strictly on memorization. But when young children begin the process of decomposing numbers and understanding that there are numerous ways to create any given number, their computational fluency increases dramatically. Some students may decide to increase the number 19 to 20, by reducing the 28 to 27. So the problem 19 + 28 becomes equivalent to 20 + 27! Others may change the 28 to 30, thus creating the equivalent expression, 17 + 30.

At Posnack, we have encouraged all elementary level teachers to adopt the phrase, “equivalent to” in their math classes as a means of emphasizing this relationship and starting the journey to algebraic reasoning at a young age. Watching the Kindergarten and 1st grade classes in the morning is an amazing display of mathematical wonder. Students use the number of days they have been in school to develop word problems, number bonds, and mathematical expressions. And while many may still have a little difficulty pronouncing the word “equivalent,” they have no problem at all explaining how it works using two- and three-digit numbers. Watching the excitement in the classrooms as the students discover more than one “right” answer, is a thrill that is “equivalent” to none!

 

 

3 responses »

  1. Great and very correct. I am also glad to hear that mental math is taking a proper place in the math education of LS.

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