Meaning and Algorithms

My third and fourth grade classes are exploring computation algorithms this week. Taking apart and putting together numbers is one of the skills needed to tackle higher level math concepts. I find it interesting when this topic is brought up as I sometimes hear students commenting that they already know how to add/subtract. Many of my students have been instructed to use the traditional algorithm to add large numbers.  After digging a bit deeper I started to see students falter with their explanation of the traditional method.  I asked them to explain their thinking. I found that their reasoning started to turn into comments about the process. Students explained the steps involved to find the product.  One student told me about the example below.

traditional-01
Traditional

The process, although important, doesn’t reflect mathematical understanding. Students didn’t mention place value at all.  Place value within the traditional method is evident, it’s just that the students weren’t able to explain it with confidence.  It reflects more of an understanding of the procedures required to find a solution. Most of the students that I see are used to adding/subtracting numbers on a number line. They can hop up and down the number line with ease.  Once they feel comfortable with that, parents or others start to show students the traditional algorithm. Students become familiar with the terms carry, borrow, cross-out, add a zero, and others without necessarily knowing the reasoning behind the process.

This past week I introduced the partial-sums algorithm. This is one of my favorites as students start to see the reasoning behind the process that they’ve been following for years.  Although at first it can seem clunky, students started to see how place value can be a key indicator in determining the sum. That’s an #eduwin in my book.

partialsums-01
Partial-sums

Later that hour students were given an assignment where they had to find the sum using the partial-sums method. Some students struggled a bit to move out of the traditional algorithm process and move to a different algorithm. Afterwards I gave student the option to use whatever method best meets their needs. It’ll be interesting to see the progression that students make as they decide on an algorithm. When asked about how and why the algorithm works I’m hoping they’re able to confidentially create their own proof.

We’re making progress!

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