We spend the toddler years endlessly teaching children to memorize numbers, counting them in order. The numbers are repeated over and over, songs are sung, toys are counted and the exercise is celebrated and rewarded. Most children come to school able to count, many to a hundred and beyond.
What we really need to encourage is an understanding of what those numbers actually mean. There needs to be a connection between number and meaning. In our efforts to push children into math, we have lost the understanding of how and why numbers actually work the way they do.
For instance why do we borrow, regroup, or any of a number of words we use in math texts to describe what happens when we are in the one’s column, for instance and the number on the bottom is larger than the number on the top? Why does that process work? I sat with a group of adult learners in a graduate course as the professor had us work through various place value games. There were many “aha” moments as adults who had been proficient in math for most of their lives, saw it in a whole new light, finally grasped the why’s, not just the how’s of what they were doing. It was a powerful moment to see people come to terms with something as basic as subtraction. Instead of memorizing a series of rules, this group of people had constructed valuable meaning that they in turn could pass on to their students about why math works, not just how to make numbers behave.
So, the tip for today is to spend some time with place value when working with students. There is a wonderful game called “Race to One Hundred.” Students use linking cubes, or I have even used Lego’s, and dice to play the game. Each pair, or individual, creates a place value chart, with columns for ones, tens, and hundreds. The dice are rolled and that number of cubes is linked together and placed on to the board in the appropriate column. When the ones column reaches 10, the students take the complete set of 10 cubes and move it into the tens column leaving and remaining cubes in the ones column. When the children have created an additional ten it is added to the tens column, until they are able to move ten, tens into the hundreds column. Some people choose to start with one die to avoid the need to move items out of the one's column immediatly. That is an option.
When students have played this game over a few sessions, try having them race back from one hundred. This is more challenging, but it builds the skills required to handle regrouping faced in subtraction. They will need to move a ten into the ones column when the number required to be removed is more than the number in the ones column. This will also occur when tens are removed from the the hundreds column when the tens column is short.
Eventually, this process can move to paper and support math on paper. Students can set up the math problems on the place value board using the blocks. The math is done with the blocks and recorded on the paper. The goal is to have students understand what they are doing, not just memorize the rules for doing it. I have them use the notebook paper sideways as described in the previous tip. After they have the ability to work through the problems with the manipulatives, we work on how to work without them. However, the strong basis is built.