Math Uncategorized

Concept or Fluency for the Win?

March 15, 2017

This year my students have been having a blast learning their multiplication facts. They compete against themselves on mad minute tests, graph their progress, and celebrate moving from one set of facts to the next. They work through a binder full of challenging multiplication puzzles and games. They’re having fun NOW, but before they could do that, we worked for weeks on developing conceptual understanding of multiplication. This class has me wondering: when it comes to basic math facts, which is more important: conceptual understanding or fluency?

Concept for the Win

One thing I know for sure this year: my students have a solid understanding of multiplication. They can solve multiplication word problems, draw pictures to show their understanding, use different problem-solving strategies, and have great discussions with their peers about multiplication concepts. I am proud of them for the work they have done, and I love listening to them explain their thinking. I am especially happy that they seem to like math when they’re working on multiplication! Since I know their understanding on state testing will be measured through word problems and not basic algorithms, I am a happy teacher. This is why concept wins over fluency.

Fluency for the Win

But we are teachers, not testers. As much as we want them to do well on that state test, our students need to memorize their multiplication facts, and the only way to do that is with practice. Outside the classroom, their math skills will not be put to the test through complex word problems. They can’t draw a picture to solve every real-world mathematical dilemma. Their employers will not wait for them to decompose bigger numbers in order to make it easier to solve problems. This goes for basic addition and subtraction as well. When I see students using their fingers to count and solve 7 + 8, I cry a little inside. Real world application: this is why fluency wins over concept.

And The Winner Is…

Conceptual understanding and basic fact fluency are equally important! Even taking standardized testing out of the equation, students need to have an understanding of multiplication. It’s important for them to know that 5 x 7 represents five groups of seven items. I also believe that, once they understand the concept, it makes them even more motivated to memorize the fact tables. They can connect the facts to prior learning and real-world application. Fluency and understanding have to lean on each other to create the strongest knowledge base for our students.

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