The other day I had one of those "Aha" moments. Seemingly from nowhere, a random, moderately intelligent thought popped into my head. Perhaps this rare moment of clarity was due to the work that I have been doing with Disciplinary Literacy and preparing for presenting a Socratic Seminar to college students at the local community college. The latter is a pretty scary and daunting task for a "math specialists." However all survived and the students even seemed to understand the take-away that I was hoping for.
The moment occurred when I was driving home. For some unknown reason I was thinking about my days as a student in middle school woods class. I wasn't a very handy youngster. Breaking things and losing them were more my specialty than building and fixing. However, I was always very curious about how things worked. I saved up all my pennies from allowance to buy a Fast Traxx remote control car and took it apart countless times.
I studied the gears and all of the internal parts to figure out just how everything worked. Like most people, unless I had the opportunity to get my hands on something and see and feel how it was put together I didn't understand it. Unfortunately my middle school woods teacher's teaching style didn't match my learning style. He was more of a "show you how to do it once and you better get it" kind of teacher. I don't think he had any ill will toward me or had cooked up a scheme to keep me from ever having the ability to build something on my own. However, I was very frustrated in the class and remember crying with my mom about how difficult it was and I "Just didn't get it." The class was split into two portions. Book-work, where we learned the names of the tools, safety, different styles of cuts, joints, etc, and measuring, and the project, which required building a clock.
I excelled at the book work portion, acing assignments, quizzes, and tests. I bombed the clock. Several times the pieces I built were rejected by the teacher's quality control team that consisted of himself. Rather than giving me a second opportunity to learn what I did wrong and rebuild the piece, he would select the proper piece from a surplus of clock pieces that were collected over the years from student projects that were never completed. Half of "my clock" is really due to the work of other students. I feel like there should be a list of credits on the back. "Thanks to Billy for the face-plate since mine sucked!"
The point is, I knew how to use the tools, understood the safety and could measure like an expert. The area where I lacked, was using the tools to create a product. I'm not blaming the teacher. I'm sure that he was doing the best for me that he knew how and probably thought I had no interest in ever building anything after his 1 semester class. In fact, I should probably thank him. Perhaps this event is partially responsible for my view on teaching. If a student doesn't understand something and be able to apply it when appropriate, I take it very personally. It becomes my mission to help these students understand and conquer!
In essence, I am no different than many students in math class. Many students can repeat the steps that are taught to them by a teacher. Isolate the x, keep flip and divide, use the quadratic formula, etc but are completely lost when asked to apply their math skills to solve a "real-life" problem (how long will it take to fill your pool?). I knew how to use the tools that were available but was unable to use them in an application (build a clock).
This is exactly what we have been doing in math classes for a long time. We have been teaching kids a set of procedures that are seemingly unrelated and are then surprised that even though they may score well on our assessments they fail miserably when asked to apply these skills in novel situations. This is the concern that Common Core addresses. Not only in math, but across all subjects. Common Core asks us to help students really understand the concepts that we are teaching them and give them opportunities to apply what they know. The inquiry portion of Common Core math lessons are great! These answer the question that students have been asking for decades...I'm sure I don't have to write it but I will. "When will I ever use this?"
I know this change in teaching is challenging and scary and tons and tons of work. But what a great opportunity. I have been talking with teachers recently and one of the things I emphasize is when students are in the inquiry phase we shouldn't care about the answer. In fact if we don't know the answer, or how to get the answer, or scariest of all, if there is an answer, it's ok. Life will continue. The students will be uncomfortable, frustrated, whinny, and even obstinate. But, they will be thinking and learning math as long as we foster the conversations and allow students to discover, experiment, fail, and try again.We need to put our focus on their thinking. Concentrate on what they are saying and how they are supporting their claims. This is the mathematical thinking that we have been missing. We need to focus on teaching students both the skills (procedures) and how they can use these skills to build a product (use their understanding of math to solve a problem). Just as in woods class it is important to be able to use the tools and build a product.