Reflections on Fifth Grade Division (That Sounds So Sad)

 I have experienced a few pendulum swings over the years.  When I first started teaching in Hawaii, we had homogenous classes for language arts and math. I had the remedial class and used a skills-based curriculum in which they could progress at their own pace. For the past 7 years, I have been a math and science specialist in classes that include several English Language Learners in heterogenous classrooms, with a wide range of abilities from being at grade level to several years behind grade level. Because our school keeps all the gifted and talented and many high achievers in one class, we rarely have students who are above grade level.

   When I first entered teaching, we taught math pretty much how we were taught. I call it, "just do it" math. You don't have to understand it, you just have to follow the steps like I tell you to, and you will get the right answer. About eight years ago, our school chose a method of teaching math in which the point was conceptual understanding. The program itself was called Investigations, and I became an avid proponent.

 My math education was a result of the "just do it" approach and I blame that approach on my math phobia, my Ds in Algebra in high school, and my general hatred of math. The trainer, Gail P., opened my mind, exercised my math muscles, guided me to understanding. I was sold. There were some problems with this curriculum, admittedly. It didn't align well to Hawaii standards. This didn't  mean our school was necessarily on the wrong track, but we didn't test well; standardized tests don't assess conceptual understanding well. It was also inefficient, and perhaps too free-flowing. We want kids to develop understanding, but we want them to be disciplined thinkers. It didn't emphasize fluency so much, and many kids just did not have their "facts" down. We ended up having to do a juggling act, to include all the different components and expectations into our program. 

And now comes Common Core. The PR on it claims to be about critical thinking and conceptual understanding. But when it comes down to it, it really goes back to the "just do it" math. This is what I am experiencing as we implement our new GoMath curriculum that is aligned with the CC. I believe there was a conflict among math educators about computational fluency versus conceptual understanding. It seems as if elements of both got into the CC, but what side is going to rule supreme? 

I just discovered that the CC standard does not specify the use of the traditional algorithm in division until 6th grade. This is somewhat good news, as my students, who have been developing conceptual understanding, are having a hard time making the leap to "just do it" math. I can go back to school on Monday, and tell them what I have found. This will relieve some stress, I hope. It's strange because the GoMath curriculum includes the traditional algorithm in division. The writers were probably on the side of computational fluency in the math wars.  

I have several students who have transferred from other schools or even other countries. When we were working on conceptual strategies (distributive property, inverse operations, partial quotients, using models), they struggled. Now that we have moved on to the traditional algorithm, they are so happy, because they have already been taught this and know it by rote. 

My other students, most of whom I have had since 4th grade and have been in our school since kindergarten, are reacting the opposite. They don't understand it because it doesn't make sense. They are right. It doesn't make sense. It only makes sense to mathematicians and maybe math teachers, because they understand how it works. When you try to explain to a 5th grader how it works, it is very abstract and leads to confusion. If you teach the "just do it" way, there is no expectation to understand how it works, so it was easier for students to learn it. 

But it contributed to the prevalence of rote thinking. So what? you may say. They'll get the right answer and that's all that matters. And therein lies the question. Is getting the "answer" the most important thing? You see how the math wars went?

 In the end, a math teacher has to take a stand one way or the other. This is my process for deciding my stand:  (1) Why is math important to the average person? Math helps you to understand the world. If you have a sense of numbers and what numbers mean, you have a better sense of your place in the world. (2) So what method is better for an average person to make sense of the world? Conceptual math, I believe. Anyone can compute any problem on a calculator. No one really NEEDS to learn how to add, subtract, multiply, or divide. But an educated person needs to have a sense of what the numbers mean in order to make sense of the world. Learning to do computation is a good mental exercise because it develops an understanding of what numbers mean. But computation at the expense of thinking leads to rote thinking, surface thinking. It does not pass the litmus test of helping you to understand the world. 

There may be some students who will not go into the deeper areas of conceptual understanding, who will only do the "just do it" way, and they will generally be fine, calculator in hand to subtract 123- 12. But my goals for my students are more than that. My goals for my students are for them to be so comfortable with their sense of numbers and how they work, that they will see a scam right away, they will see mistakes in computations,  they will be able to identify when something just doesn't make sense, they will be questioners and thinkers, they will feel confident in the world and in what they can do in it. 

So, if you wonder why I am so uncomfortable teaching kids to "just do it," that's why. 

 Keeping track of their division progress. It was a bad day for the beginners.