It is easier to teach students a formula than to have them discover the formula on their own. But no one said teaching was supposed to be easy.
Facilitating students through the discovery process takes time, patience and collaboration. Having parents, guardians, caregivers, tutors or afterschool educators on board with the importance of discovery is absolutely necessary. It is imperative that the teaching of the standard algorithm does not interrupt the discovery process prematurely. Deriving a formula and/or algorithm helps build number sense and critical conceptual understanding.
As usual, I have included three varying examples in the weekly blog. The first example is self-created and includes the two images at the beginning of the post. Teaching multiplication through the area model/arrays can be an excellent way to build conceptual understanding prior to the memorization of the standard multiplication algorithm. The second resource is a video taken directly from the Teaching Channel. Challenging Students to Discover Pythagoras shows one teacher’s journey through the teaching and learning of this daunting 8th grade standard. Our final example is an article from Business Insider. In There's a New Way of Doing Subtraction-And it's So Much Better Than How You Learned in School, Joe Weisenthal demonstrates how CCSS and number lines turn math into a road map. He argues that in this particular case, the discovery is simpler than the memorization.