One of the first things I noticed when teaching students math using a Singapore approach was that students had to do math in so many different ways. I learned to do math in ONE way. I followed the rules, and the answer always worked out for me. I had a great working memory and had no problem memorizing the steps.
Now we are seeing students learn multiple ways to model a problem. Some of these ways seem crazy to me! So many long steps and processes. Why are we doing it this way?
It took awhile for me to see the difference and to see why it mattered. Students can't just be expected to follow a series of procedures. Sure, they might remember the steps now, but what happens six months from now? A year from now? Will they remember or will it be a brand new skill? (All my memorizing did not help me remember how to do calculus or remember anything from trigonometry.)
Think of a short cut you might know through a park. The only reason you know it's a short cut is because you have been the long way. You have seen how you can cut through a section of the park to get there faster, but you never would have known if you haven't explored the park.
When students have time to dive in and explore concepts the long way, they begin to understand the short cut. They understand why it works. The beauty of learning this way is that if the short cut method is forgotten, the understanding and reasoning is still there. Students have a strong foundation that can be used to reason through the problem and find the short cut again.
I think one of the best examples of this is when students learn to rename or regroup. (Renaming is what happens to each place value when writing it and describing it. Regrouping is the physical action of changing the base ten form.) Whether adding, subtracting, multiplying or dividing, students rename numbers and need to understand why only digits up to 9 can be in each place value. This teaches flexibility of numbers and is a HUGE difference maker when students are performing operations mentally.
So, you know I have a game right?! I'm all about games this month! If you login to the Member's Area of my site, you will find some awesome resources for teaching renaming using spinners. Regardless of what operation your student is working, the ability to think of numbers in different ways will help your student make sense of what's happening and lay that strong foundation.
Does your student do this? Here's an easy way to check. Ask some of these questions:
Describe 428. What's another way to describe it?
Can 428 be represented as 3 hundreds 12 tens and 8 ones?
How would you divide 12 hundreds by 2?
What happens when 3 thousands are multiplied by 4?
Now, check out this FREE resource and see if your student can give you some examples!
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