As Dan Meyer put it, “math class needs a makeover.” It breaks my heart to hear students say things like, “I’m not good at math” or “I hate math!”
In my opinion, one of the first things that needs to change is the focus on correct answers and the need for speed. This leads students to believe that the only way to be good at math is to be right (quickly). The other practice that needs to be eliminated is the language we use as teachers such as “that’s right” or “you’re so smart.”
You’re So Smart
You’re so smart is one of the most damaging things you can say to a child. What is smart? What do we value and what are we showing them that we value? Being smart needs to mean learning as a means in itself. Or rather, the journey of learning. This is not fixed but ever-evolving as we seek out and synthesize new information.
As a parent, I have been guilty of this. I’ll blame it on ignorance, but the truth is I kept it up for years as a teacher and a mother. I knew the words tasted sour in my mouth, but they continued to come out and I continued to damage my child’s self-worth. Harsh? It’s true.
Here is an example:
My oldest son started the district gifted program as a first grader. I was so proud! From the time he was born, I had told him how smart he was. He had finally been classified by the school system in the same way. My job was done. From that day on, his life would be rainbows and butterflies.
The reality was that from that day on, he began to feel even more isolated. He went on to the full-time gifted program in sixth grade and I ended up pulling him out. His stress level was through the roof, he was failing ALL of his classes, our family time was dominated by reprimands of his failure to finish his homework (which was unending), and the school’s solution to the problem was to medicate him. We had failed him. We taught him that learning was about homework and work completion and not about creativity and problem solving. The other message we sent was one of conformity; You must fit in this box to be “smart” or successful.
He told me a few years later that he felt like the test had been wrong, that they made a mistake; He wasn’t gifted. He went on to say that he felt pressure to always have the answers (and have them fast) and when he didn’t his failure was paramount. Teachers expected more of him ALL THE TIME and living up to that expectation was stifling. I had taught him and the label had taught him that intelligence was fixed. We told him he was special, but not in a growth sort of way. He had already arrived at being “smart” and now he would have to maintain the title.
Luckily, my second child was eight years after my first and my message as a parent is now vastly different. I praise reflection and strategy and determination. I allowed him to be tested for the gifted program (telling myself that I could better understand his needs if I did, a lie to be sure). I realized that I had some lingering pridefulness attached to the label that I am still working out.
However, this time, when I presented it to him, I framed it very differently than I did with my first. I told him that there was a school with additional opportunities for learning that he might enjoy. I let him choose whether or not he wished to attend. He attended in second grade and decided to not attend this year.
My message to parents is now this: if you want to compliment your child academically, focus on effort and inquiry. Say things like:
“Wow, I can tell you really worked hard on that.”
“I love hearing about all the new things you are learning, I can tell how much you enjoy it.”
“What are you excited about learning next?”
You’re Right
More talk I’ve tried to eliminate along the way is saying “you’re right.” This simple phrase takes all of the learning away from the student and places the parent or teacher in the seat of a referee. Student work becomes not a creative endeavor, but a race to impress the parent or teacher. The focus is taken off of learning and put on performance (which is what is done when training circus animals).
If we really want students to become problem solvers, we need to ask the right questions and probe for understanding. Students need to own their solutions and the first way to do that is to change our language as teachers. Curriculum Associates has a great list of prompts teachers and parents can use to shift the focus to meta-cognition and justification. Many of the prompts illustrate how to help students own their own learning and be confident in their solutions, thus allowing them to engage in the standards for mathematical practice.
I have a couple of examples I would like to share about this topic. One comes from my own child who recently graduated high school (the one referenced above).
I can pinpoint the day he first viewed himself as a failure in math. It was third grade and his teacher was a wonderful lady who was energetic and nurturing. She had been teaching for almost thirty years and all the students loved her. She (like many still do) had students master multiplication facts using a battery of timed tests. I’m still not convinced she believed this was the best way to learn facts but like many others had been given the message that students needed to “know” their facts quickly and this was the way it was done. She had a cute little board that she used to keep track of their progress where they would build their ice cream sundae as they completed their facts.
I always knew when it was a testing day, because my son would come home with a look of failure on his face. Math was no longer about creativity for him, it was about being fast and being right. He did not perform well under time constraints and though his idea of fun in the car was to practice multiplication problems and discuss his creative strategy for solving them, it had lost its luster once he was asked to do it quickly. He took Algebra 3 times and finally passed due to a teacher who really understood his learning style and a course that was self-paced. He hates math and instead of wanting to pursue a career in astronomy or chemistry like he previously had dreamed of, he decided that he was too bad at math to go into those fields. My heart broke when he first told me he just didn’t think he could cut it through the math courses; It broke.
Another example can be provided by a middle school student whom I tutored for about a year and a half. She was failing sixth grade math and had severe anxiety about it. The first time we met, I gave her an assessment on number sense. She quickly (very quickly) would give me an answer in a very fast, short response, then look at me in terror and say, “is that right?” I knew immediately that this girl did not struggle with math, she struggled with confidence due to the experiences she had been provided. We quickly came to an understanding, one my students know well. “I don’t care how fast you come to a solution as long as you can walk me through your strategy and prove it.” I have had the exact same experience with every student I tutored over the years. They are terrified of being wrong, and they have no way of proving they are right because that has never been the focus of instruction. I wonder if the focus had been on understanding if they would have ever “needed” a tutor.
Lessons Learned
What I have learned, thanks to many phenomenal authors and researchers and my experience teaching diverse learners, is that all students have individual strengths and passions and they all deserve diverse learning experiences in math and outside of math.
Perhaps we need to quit asking all students to “master every standard” in every subject and agree on a set of skills required to be contributing members of society and then let students find their passion and develop it. We need to remove the labels and focus on the individual. Students need to be exposed to new ideas and problems so that they can find their passions, but asking them to master every concept is no longer something that our world requires of them and perhaps never did.
I will end with this, it is my belief that the most powerful thing we can do for a child is teach them how to learn.
A Few of the Resources That Have Helped Shape My Beliefs:
Mathematical Mindsets
Mindset
Number Talks
Teaching Number in the Classroom
USMRC
Dan Meyer
Robert Kaplinksky
Jo Boaler
Graham Fletcher
Twitter – #Elemmathchat
There are many ways to organize your lessons, but I have included a picture of the way I laid out our lessons for math each day. For young learners (and old) it is important to provide them a snapshot of the materials needed for the lesson so that once they begin the video, they have all the necessary materials to complete it.
that geometry is one of the more concrete concepts for students to grasp in primary grades; quite literally. There are tons of ideas of how to construct shapes on the internet, in math books, etc. I love the activities with spaghetti and with Popsicle sticks and gumdrops, but those activities can be limiting when working with shapes with curved sides. These activities can be misleading when students decide to extend shapes and we have to be very careful that we not provide fixed and limiting language such as, “the gumdrops are the vertices” because that is not true in a shape like the one to the left.
Open-ended tasks like these are my favorite because they allow opportunities for students to explore misconceptions like the one here. This student doesn’t yet understand that a shape must be closed. This was an opportunity for me to quickly see that and perhaps more importantly for other students to notice and provide feedback. The picture on the right is the square after he corrected it (and his understanding of shapes).
vocabulary because they end up making shapes that they cannot name. This leads to all kinds of discussions on how to categorize shapes and the difference between two dimensional and three dimensional shapes. I provide students the written names of shapes once they name them and ask how to spell it or if they cannot name it and I am helping them name it for the first time. Here are some examples of two-dimensional shapes students created:
This student started out with a square and built onto it to make it a rectangle. She discovered how to 
combine shapes to make new ones.
This student is one of my very low performing student sin most subjects, but in math he excels because he is able to make sense of his own learning through play and discovery. 
stories. The learning goal was to use objects to represent an addition story and then tell the story and write the addition sentence that was represented. My main goal was really to get students familiar with stop motion in this context and to get the process of shooting the videos and writing the caption in #Seesaw to become easy.
Many of our struggling and reluctant learners lit up when they got to pick out animals for their videos! I didn’t have to convince them to complete the assignment…they wanted to! Which as you know by now, are the type of assignments I love to give!
My goal is to have Stop Motion Math be a station choice in our room and provide open ended prompts or learning targets to prompt their creations. Things I would like to do in the future include providing number sentences that need to be represented with a story, providing word problems to solve with a video, and expand into all other standards as a means to show mastery of a concept.
mscastillosmath 