I’ll start by saying to everyone who doesn’t teach math, please don’t stop reading at the next sentence! I’m going to use some simple math examples to illustrate this article but I believe the thought processes apply to all areas. In order for us to teach the thinking skills that are necessary for solving math problems or understanding any concept in any area of study, we must first discover how we think and learn. Specifically, how do we gain real understanding, as opposed to memorizing a “trick” or set of steps long enough to pass a test with no ability to apply this knowledge to anything different or even recognize a similar situation a short time later? It’s all part of the way we think.

As a long-time high school math teacher, I often get frustrated reading posts on social media declaring that “they” should go back to teaching math the “old” way and that this “new” math is ridiculous. These declarations are often accompanied by a problem or picture of a worksheet to illustrate the point that “new” math is absurdly long and a waste of time compared to how the person posting learned the concept. First of all, I remember as a student growing up in the days long before social media, hearing adults talk about the “new math these kids are doing.” Math was not “new” then and it’s not “new” now! What is new is our understanding of how we learn and understand math. Usually the “illustrations” used (incorrectly) to make a social media point were never intended as a method for solving the problem but as a way to better teach and illustrate the thinking that we go through to solve a problem. Let me give a simple illlustration. Let’s say that you want to add 48 + 53. The method for doing this is to add 8 + 3 to get 11, writing down the second 1 and “carrying” the first one to be added to the 4 and 5. Now add 4 + 5 to get 9 and then add the 1 that we carried and the answer is 10 so the final answer to the problem is 101. Simple math, right? But, many people will look at this problem and think, “48 is two away from 50 and 53 is three over 50 and 50 + 50 is 100 and since there is one more over fify(3) than under(2), the answer must be 101.” This is a deeper understanding of how numbers work and that kind of thinking should be encouraged, not discouraged!

Our brains think by making connections. We make connections to the things we already know, to things we have read, to things we have observed and to things we have experienced. If we encourage our students to make connections even before we teach them methods, the methods will make more sense and are far more likely to “stick” as a part of the base of knowledge that can be built on. Asking and allowing students to make these connections on their own is sometimes labeled as a failure to “teach” them but it is in fact quite the opposite. It is actually enabling learning and retention at a much deeper level when direct instruction is applied. In the example in the previous paragraph, the idea that 50 + 50 = 100 was probably already a part of the student’s “base of knowledge” and it in turn was perhaps derived from the idea that 5 + 5 = 10 at an earlier stage of math development. This learning is based on making connections from prior learning and is far more likely to be retained long-term.

The next time you are trying to increase retention with your students, think about how we think and look for ways to connect current subject matter to things students already know or have experienced. Teach the thinking process as well as the material and you may find that because this better fits the way we think and learn that the level of knowledge retention increases as well!