I have a confession to make. I always thought I was good at math, because I could compute quickly. I was the kid who would win Around the World and would get 100 % on timed fact quizzes. Algebra and computation made sense to me. I thought that I could solve problems by just plugging numbers in.
That's what I liked about math. It had rules, and if you followed those rules, you would get the answer right. All was right in my world if you just followed the rules. (Wouldn't it be nice if life functioned that way?!)
The downside to this was my mental math strategies. I NEEDED the paper and pencil, because I had to plug numbers in. If you asked me to estimate, I would shake my head and ask why. I could just give you the exact answer. Who cares about an estimate?
I also started to meet people who could calculate numbers in their head by manipulating the numbers. When solving 97 + 25, they would solve it as 100 + 25 and then subtract 3. This made me extremely uncomfortable, because I felt like that was breaking the rules. You cannot break the rules in math...I thought. And I began to see that I had a fixed mindset about math and lacked flexibility in thinking.
I realized that I was relying only on algorithms and less about using strategies to solve mathematics. As a teacher, author and consultant, I have been blessed to meet some awesome educators who have helped me to retrain my brain. I have realized that algorithms have their place, but the true emphasis should really be on strategies.
An algorithm is what many of us remember from school. Follow these steps, and you will get the answer. A lot of times, lessons begin at this step. However, the algorithm should really only be used when students fully understand what's happening, because it's really a short cut. Most of us don't understand a short cut until we understand why the short cut works.
Follow a series of steps
Require students to have good computation skills
Usually are the most efficient way to solve a problem for some students
Typically only have one way to use the algorithm
Are more commonly seen
A strategy is different. Strategies encourage students to make connections between what they already know. When given a really good task, students can use whatever prior knowledge they have to break into the problem and solve. Whether students are using hands-on manipulatives or visual models, they may find that a strategy is just what they need to get to the answer. Then, students may even find there's more than one way to get to the same answer.
Allow various levels of students to access the same problem
Encourage the use of manipulatives and visual models
Help students to see the way math concepts are connected
Show higher order thinking and help students to justify their thinking
Both algorithms and strategies have their place in the math classroom. It's important that lessons are shaped around the goal and intent. Is this a lesson where students are using strategies or is this one where they need to focus on the algorithm? (If you are still considering this, I have a blog post coming up that will help! You can also access some sample videos from my video library here that demonstrate a strategy lesson.)
As a grown up, I've had to start rethinking about my belief about math. I've put down my paper and pencil (sometimes) and have started thinking about how I could solve with a strategy. It's interesting to watch students do this when they haven't been programmed to always use an algorithm. Guess what? It doesn't stress them out nearly as much as it does me.
What are some of your favorite math strategies? Leave me a comment!