I contend that one of the big reasons why U.S. students lag behind their peers in many European and Asian countries in mathematics is because we are lax in helping children develop critical thinking skills.
Critical thinking skills that require students to apply content knowledge to real-world problems is of great importance. It’s very clear that if students can recall discrete content knowledge but cannot apply it, they’re going to be in trouble.
Here’s an example. By the time students have mastered rudimentary math, elementary-school pupils should understand that the numbers on either side of the equal sign are equivalents. Many students drilled in rote memorization don’t always grasp the concept of equivalency. I’ve frequently seen sixth graders who still believe that the equal sign means “the answer goes here”.
Equivalence/equality is undoubtedly one of the most important, connecting ideas in school mathematics. Developing this concept of equivalence calls for lots of experiences with materials as students are developing their conceptual understanding of numbers and operations. More important, it calls for teachers to help students connect their experiences with the mathematical idea(s) they are developing, in this case, equivalence or equality.
One of the experiences elementary teachers can use to help develop this understanding of equivalency is math games. The following is one of my favorites, and I use it with first through sixth graders.
Balancing Act
What you need:
2 players
deck of cards, face cards removed
cut a 3×5 card in thirds. On two of the thirds write a + sign. On the last third write an = sign.
Shuffle the cards and deal six cards to each player. Stack the rest of the cards facedown in a pile.
Each player chooses four cards from his/her hand. The object is to balance the equation by arranging the cards into two addition problems with equal sums. A player earns one point for balancing the equation.
Example: a player could place a 7 and a 1 on one side of the equation and a 3 and a 5 on the other (7+1 = 3+5)
A player can also place two cards of the same value on the equation to balance it (4+0 = 0+4).
At the end of a round, the cards played are placed at the bottom of the deck. The dealer shuffles the cards and gives six more to each player. Play continues in the same way.
The game ends when one player reaches ten points.
Variation: Children can play a similar game using subtraction or addition and subtraction. Change your “operation cards” so that children can create various balancing equations.
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