Using the grid, students color-in squares to represent numbers, and then count the end result.
For instance, to learn 2 + 6:
The student first colors two squares the same color, labeling them with a "2," and then six more in the same line using a different color, labeling these with a six, and finally, after counting up all the colored squares, labeling the entire set of colored squares with an "8." By this demonstration, it's clear that 2 + 6 = 8. [It's also clear that 6 + 2 = 8, 8 – 6 =2, and 8 – 2 = 6, thus completing a "fact family" cementing the addition/subtraction relationship of the numbers 2, 6, and 8].
After discovery of each math fact, students "collect" the facts by writing each one on a flash card for later games of "flip the card" to help with memorization (Triangle Cards can speed up the process considerably by emphasizing fact family relationships).
But memorization should only be attempted after discovery. Students must first discover the math fact experientially, preferably physically, in multiple ways, by repeatedly demonstrating the fact for themselves. Then they record the fact for purposes of memorization.
The order here is critical: discovery first, then recording, and finally memorization.
Consistent with the Scientific Method, it's best if students use more than one method, and repeat the experiment several times, to confirm results before recording them (e.g. first using a Centimeter Grid, then a Hundred Numbers Chart, and then counting pennies). This helps ensure the development of "number sense," a core mathematical capacity without which memorization is an empty exercise, at best. Memorization of math facts without corroborating discovery robs students of the intuitive "feel" for numbers they'll need to be successful in advanced courses later on.
Only if the student knows, experientially, by his own experimentation and record keeping, that 2 + 6 does in fact make 8, will he be able to make "sense" of that fact and integrate it with other ideas. This is a crucial distinction: the difference between mere belief and actual experience; between mastery and connectable knowledge on the one hand, and isolated, disassociated, meaningless memorization on the other.
Consistent with the Scientific Method, it's best if students use more than one method, and repeat the experiment several times, to confirm results before recording them (e.g. first using a Centimeter Grid, then a Hundred Numbers Chart, and then counting pennies). This helps ensure the development of "number sense," a core mathematical capacity without which memorization is an empty exercise, at best. Memorization of math facts without corroborating discovery robs students of the intuitive "feel" for numbers they'll need to be successful in advanced courses later on.
Only if the student knows, experientially, by his own experimentation and record keeping, that 2 + 6 does in fact make 8, will he be able to make "sense" of that fact and integrate it with other ideas. This is a crucial distinction: the difference between mere belief and actual experience; between mastery and connectable knowledge on the one hand, and isolated, disassociated, meaningless memorization on the other.
Download your own copy of a Centimeter Grid here.
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Copyright © 2006-present: Christopher R. Borland. All rights reserved.
