"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.

I couldn't agree more. Homework needs to be changed to fit in a wide variety of problems instead of a large amount of the same problem. Although I do think that repetition on certain things is necessary in order to get to higher level thinking. For instance, I think in an algebra 1 class, solving for a variable a bunch of times is going to be very beneficial in the future because not as much time will be spent on solving for the variable. It will be second nature. Good job with connecting back to the book though, that's always a plus. I also want to add that I think its wrong to grade homework that is given the day the students learn something. The student most likely doesn't fully understand the topic anyway so how would a teacher grade a student on something they don't even know yet. Its wrong. But good job, I like the topic.

ReplyDeleteI struggle, as a teacher, finding ways to try to put students in a position where they can fail safely. Math is about doing, so I want students to get a chance to do, but if it's an exercise instead of a problem, is it even worth their time? The need for space to be wrong is so crucial (I'll echo Corey and say good book connection) - where should it come?

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Kelsey I really enjoyed reading your blog. I loved how you related it to the book and to life. I especially loved the first two paragraphs of your blog because I could really relate to what you said. I think you have a good point about homework and to how stress is involved. Again great job Kelsey. I enjoyed reading it.

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