There is a debate raging in math education today centered on an an old question. “Which is the more important when teaching mathematics – algorithm or conceptual understanding?” The question stems from different mathematical points of view. Countless studies for both methods of teaching exist, but the latest research being presented may be the “peace offering” to both sides of the debate.
The most recent research from the National Council of Teachers of Mathematics focusses not on which method of teaching mathematics is better, but in the assurance that good, logical, and concise teaching of mathematics is happening.Good teaching of math needs to be equally focused on two areas to create well rounded students who can take the mathematical principles learned to deeper levels. Teachers need to be developing a good conceptual understanding while facilitating efficient skills. It is the teacher’s role to organize, pace, and present information that both challenges the students’ understanding of concepts while sharpening their skills. When done well, it is the conceptual iron sharpening skill iron. When well equipped with conceptual understanding and skills, students can make connections between different mathematical ideas. Having a foundation in skills allows students to focus attention on applying these skills and facts in different ways and apply them to a multitude of different tasks. When conceptual understanding was the focus of a math lesson, the students were found to increase their skill level to equal or higher than the students who just had skill training. Students who are well rounded in their mathematical understanding are then able to figure out harder concepts on their own, applying the foundation that has already been laid for them.
How does one implement this balance? For starters, teachers would do well to understand the need for both methods of teaching. Next, teachers need to be willing to let their students struggle through math problems and discover their own understanding of procedures and concepts. When students struggle through the process that is being presented to them, they have no choice but to apply the skills and facts that they have learned. We need to be constantly reinforcing the foundations laid by previous teachers in both facts and conceptual understanding. One might start the lesson with throwing a ball around the room, the catcher answering a multitude of different age appropriate mental math questions. Those mental math questions or fact remembrance moments can set the ground work for the concept that is going to be expanded on within the lesson. Do not hesitate to throw a facts test in the mix, even with older students who have “mastered the facts.” Iron sharpening iron calls for constancy in review and practice. The goal of teaching is to be carefully stretching our students to ensure that learning is happening and a state of complacency is not seen. Schools where teachers are consistent and faithfully presenting challenging problems and situations to their students are more likely to develop increased understanding and application of concepts and skills.
Grouws, Douglas and Hiebert, James. National Council of Teachers of Mathematics. 2013. www.org/news/contens.aspx?id=8446