In today’s society we can find answers at our finger tips. With smartphone, tablets, laptops, WiFi, and other tools at our finger tips, we can quickly find out thing we need to know quickly. This has created a society and a group of students that are not comfortable with struggling, at least in the sense of finding information. Who remembers going to the library, using the card catalog to find a book to do research, then having to know the Dewey decimal system to find where the book was, then going into the stacks with a bunch of note cards and writing down the important information. Today’s students can accomplish this feat in seconds using technology, they have become spoiled!
They want the same type of quick resolution in math, but when they can’t google a math problem or use Photomath to do it for them, they get frustrated. Struggling to solve a math problem is a necessary evil in becoming a good mathematician! It is the struggle that makes us recall all the tools that we have to solve problems. One of my favorite things to do as a math teacher is to discuss with students the different ways of solving the same problem. These are some of the best discussions in a math classroom, I love asking students why they chose a specific technique or a specific order in doing a problem. It gets them verbalizing and thinking about mathematics in a different way.
When students are really stuck on a math problem I love to ask them to give me some type of informal analysis of what is going on in the problem. This can sometimes start us down the right path to the solution. We have to teach students that informal analysis like sketching, making conjectures, and estimating is necessary when we first observe a problem. Once we complete the informal analysis we can develop a plan how to transition from informal to formal, and create a need for certain computational skills and processes. This is just part of what I enjoy about the design thinking behind most Desmos Activities (click here for more).
I also think it is important for students to be wrong in mathematics. I don’t mean that they added wrong, or missed a negative sign, I mean did a problem completely wrong. We learn from our mistakes, and in mathematics I think this is a great learning tool. When we can have a dialogue and observe others solving a problem, especially one which we got wrong, we see a different perspective. As I progressed through high school, college, and even now as a teacher; I have learned the importance of doing something wrong, and trying to avoid that from happening again. NOBODY IS PERFECT!! It frustrates me when students are upset about getting a 97% on a test, but they don’t want to ask why they got something wrong. numerical percentage grade for me are a waste, and a hindrance. When students stop being afraid of being wrong and losing points, that’s when we can learn.
This week we are giving the PARCC test in my school. I am administering the test to my Algebra 1 students. People have mentioned that the PARCC is too hard, and not fair. Let me tell you what I have notice:
- My students worked really hard! Harder then I saw them work all year
- My students struggled, going back and forth between the questions
- My students had some great mathematical conversation when they were done the test
- My students used a ton of different skills to solve the problem
- My students weren’t afraid to be wrong and tried almost every problem
- My students enjoyed being challenged!!!
Adversity is not a bad thing, we learn from it. My students took a really challenging standardized test this week, and hopefully they learned from it. I hope they learned that everything in life is not easy. I hope they learned how smart they really are. I hope they learned never to give up. I hope they learn that struggling is a good thing!!