Redefining Failure & Remodeling Homework

"The biggest mistake you can make is being afraid to make one." I pulled this quote from a book called Mathematical Mindsets, a book that is designed to help teachers understand how they can assist students in finding their potential [in math]. One of the things that this book talks about is the importance of making mistakes for all students. We live in a society where we look down on mistakes; we want to do everything perfectly the first time, and if we mess up, we are automatically embarrassed. In regards to school, I think this is definitely most prevalent in math classes. When a student volunteers their answer in class and is wrong, it is more common for a teacher to simply tell them they are wrong and dismiss them without explanation or praise for trying. Teachers check homework for correctness and deduct points for wrong answers, but generally don't tell the students what they did wrong, not wanting to repeat lessons, hoping that their students will eventually figure it out on their own. Doing these things definitely doesn't encourage mistakes, and because of this, students remain nervous and afraid to volunteer responses in class.

One of the biggest outcomes of teaching in this way is that of stress. Obviously there are many things in life that cause stress, but I think in regards to school, our expectations of straight-A, mistake-free students is a huge factor as to why we as a society are so stressed now. Like I said above, we are a high-achieving society, drawn to be the best of the best in all that we encounter. While it isn't necessarily a bad thing to have the desire to do well, it is unhealthy to instill the mindset of not wanting to make mistakes on students immediately upon starting school. Mistakes should be something that students are encouraged to do, in every aspect of their lives, to ensure learning and the ability to do better the next time. Striving to do our best will only come from first making those mistakes, followed by making the connections to discover what went wrong. In my mind, the stress formed at school never goes away; it continues to grow as we continue on into college, then into the real world and the work force. The stress of not wanting to make mistakes in school carries into the rest of our lives, throwing us into an already fast-paced society, that is now one where you're required to be free of mistakes as well. There's always the fear of disappointing someone with your mistakes, of embarrassing yourself in front of other people, and on top of that, the stress of time. All because of the stress that is piled upon us as students.

So what does all of this have to do specifically with homework? Well, I think another idea we have stuck in our heads is that repetitive homework problems is the best way to make sure our students don't fail, especially in a math class. Generally, students in math classes get assigned an insane amount of problems to do from their textbook for homework, every single night. There has been a lot of debate about whether or not this is an effective way to give homework, or whether homework is even necessary at all. In my opinion, the process of learning requires variation more than repetition. In one of my previous posts, I mentioned the idea of memorizing vs remembering. By using repetitive structures such as homework problems assigned from a textbook, we are encouraging the idea of memorizing. This method of teaching leaves nothing for the students to grasp onto, it simply implements the stress of needing to pound information into your head before you can finally forget everything after the end of year. Remembering is encouraged by incorporating more assignments or activities that fall along the lines of 'out of the box' thinking. It's important to try new things, to allow our students to experiment with their hands before being given the full tools to solve a problem. In using this approach, students find a more comfortable, less stressful environment, and can leave with a memory rather than a fact. I can't help but think that if we, as teachers, started including activities that encouraged experimentation, there would be less stress on students to feel the need to be right, and therefore, less of an emphasis on incorrect work. In this way, I think we can slowly start to encourage and show students that failing or being incorrect is definitely not a bad thing, but in turn, it actually helps guide the way to understanding.

To close I want to go back to Mathematical Mindsets. Carol Dweck, a psychologist and fellow writer says, "Every time a student makes a mistake in math, they grow a synapse." So am I saying that students should just decide to not try? That they should just purposely fail at everything they do in an attempt to grow? Of course not. Believing in yourself is still incredibly important in the development of each student's mindset. In my opinion, the key to tying failure and believing in yourself together, is finding that balance. It's not specifically one or the other that helps the brain grow, but the idea that when you believe in yourself, you can fail as many times as you need to, because you also know that at some point, you'll succeed. Jo Boaler, author of Mathematical Mindsets, claimed that the people in our world who are the most successful, have made the most mistakes on their way to achieving where they are know. Instilling this knowledge in our students and showing them that the value of correct work is much less important than the value of mistakes is a great place to start. I can only imagine how much more our teachers and our students could change the world if we work together to achieve this new mindset.

Note: I am definitely not trying to generalize and say all teachers are guilty of making their students feel this way. I am saying that this might not always be noticeable and that it might not be a bad idea to think about how current teaching methods are affecting students. I am simply calling out a problem that I have seen and experienced in an effort to help change the stereotypes about failure.

So, as always, I am a math teacher in the making, a fellow math nerd, and these are just some of my thoughts. Thanks for reading.

Observations from the Outside

Of all the different 'in-school' experiences I've had since deciding I was going to pursue a teaching career, I had never gone to a school for student/teacher observing up until a couple of weeks ago. As a requirement for a class right now, I needed to find a teacher who was willing to let me come observe his/her classroom for several days throughout this semester. As someone who is from the general area, I decided it would be easy to go back to my high school and observe a teacher there. I ended up asking a math teacher who I had never had while I attended high school, although I took the class that he is teaching. Mr. K is a math teacher at Grandville High School and teaches Pre-Calculus. Because I had never had the experience of having him as a teacher, I thought this would be a good route to go, as it would give me a new perspective that I had never observed before. My younger brother also happens to be in one of Mr. K’s classes right now and really likes the way he teaches; another reason I thought he (Mr. K) would be a good choice. 

One of the first things I noticed about Mr. K, was that he was a very genuinely nice person. Although we had never met, he was more than willing to help me out, and I didn’t feel uncomfortable at all while sitting through the class. Throughout the class time, you could tell that he wanted his students to have more of a personal connection to him than just that of “I am the teacher, you are the student”. He wanted them to enjoy his class, not dread it. This was also evident in the way the students acted with him. They were plenty comfortable with asking (and answering) questions, but they were also plenty comfortable with joking around with him and him joking back. I think the relationship that a teacher has with his/her students is one of the most important things for a teacher to establish. In some cases, students see their teachers more often than they see their parents, and because of this, it is important for there to be a positive connection, or at least the opportunity for a positive connection, between teacher and student, and I thought that was great to see in Mr. K’s classroom.

Mr. K’s general schedule for the day included time for questions about the homework, time for his lecture, time for questions about the lecture, time for example homework/practice problems, and time to work on the homework in class. I thought this was a great way to organize the time, in an effort to ensure that all his students understood what went on in the previous class period, as well as what is going on in the current one. During this class period, Mr. K just so happened to be teaching “Polynomial Long Division”, which we reviewed not too long before in our 229 class. It was interesting to be able to compare things we talked about in class to what Mr. K was implementing into his classroom. One of the things he did to begin this lesson was do a warm-up problem with synthetic division. I found this especially interesting, because this was not something I ever learned. The first time I ever saw synthetic division played out was in our class, this year. So it was interesting to see not only how he used concepts we talked about in our class, but also to see what has changed slightly since I had attended this high school. When Mr. K actually started the process of explaining polynomial long division, he followed the generic process that I have always been taught as seen below (we also did this in class). In any case, I thought he did a great job of explaining the method and process of how he obtained an answer. After explaining the first one, he took questions and then moved on to another example, explaining again very thoroughly. He repeated this until there were no more questions.

Another thing I noticed during this observation was that Mr. K didn't plan his lecture to last the entire class period. I think sometimes as teachers, we feel the need to fill the entire hour with the lecture, scrambling to assign the homework one minute before the bell rings, and therefore not allowing students to ask questions about the homework before they bring it home. Each of these classes at Grandville are only an hour long, and somehow Mr. K still had plenty of time to review questions from the previous night's homework, as well as to allow his students to work on their homework problems in class. Seeing this was, in my opinion, a really impressive way to see how Mr. K organizes his class time to ensure that his students were going home confidently, rather than confused.

Overall, after just one hour of observing so far, I am very impressed with the way that Mr. K approaches his classroom, and I am excited to see what I learn from him throughout the rest of this observation time. As someone who has always been on the inside, experiencing these things while they're happening, it was great to now have the opportunity to observe on the outside, looking in.

With that, I am a math teacher in the making, a fellow math nerd, and these are just some of my thoughts. Thanks for reading.