The Applesauce Story by Stacy Lovdahl:
Me: How do you guys feel about getting a failing grade?
Students: Bad. We feel stupid.
Me: What if I told you the failure was a part of life and is the way all people learn.
Students: (looks of confusion or maybe I'm crazy.)
Me: How many of you know how to use a spoon? (giggles/hands go up.) Have you always known how to use a spoon? Or, does your mom have a picture of you with applesauce all over your face?
Me: The first time you were given a spoon, you failed. And probably the second, and third.... But you didn't give up AND your mom didn't make you feel stupid because you didn't know how to use it immediately. She helped you and you accepted the help. She gave you chances to try and you took those chances and figured it out.
The Four Fours Problem
The four fours problem is a math puzzle. I allotted about 25 minutes today in each class to this activity. It was an experiment on my part; I wanted to see what the students would do. The objective is to use the number 4 four times to make every number between 1 and 20. For example:
In this problem you may use any math operation; the only rule is the number four (and only 4) must be used four times.
I explained the task to each class and did the first two examples shown above – then I turned the students loose. I asked that they use paper and pencil to jot down ideas. I encouraged them to check the order of operations with their calculators. What I watched unfold was actually quite amazing. I watched the applesauce story – or at least a version of it.
Here is what I saw and how I filtered what I saw:
The “honors” students get applesauce all over their faces. They squeeze it through their fingers, pour it out in the tray of their high chair and pat their hands in it. All of the time they laugh and giggle while a supportive parent smiles and encourages their effort.
These students were not afraid. They tried possibilities – often they were wrong. When they failed, they simply shrugged, backed up a step, and tried a new idea. They collaborated freely and built upon each other’s ideas. They celebrated success and insisted on sharing multiple ways to express the same number. It was significant that the students wanted to know the solution for every number – not just the ones they solved themselves. The students picked up new ideas from each other and quickly added new techniques to their problem solving toolbox.
The students seemed to view the problem conceptually. By that I mean they did most of their thinking with pencil and paper – they seemed to view numbers and operations visually as if they were puzzle pieces that simply needed to be matched together. Very few students used a calculator. They actually were frustrated in a couple of instances when I pointed out an error in their expression – they would have correct reasoning but an incorrect written expression. They didn’t want to see that as important. I thought that was great – they were more interested in problem solving than computational procedure. That’s critical thinking, folks.
Occasionally a student became a little too competitive and wanted to “prove” how smart they were, but it was not too difficult to bring them back with some gentle redirection. Mostly all I had to do with these students was sit back and enjoy the show.
A few students were less vocal. Some students didn’t process as quickly as others, but they were also not intimidated. I visited with a couple of those students and they said they enjoyed seeing the creative ways the other students thought. They said that was helping them learn to see numbers differently. As a group my “honors” students displayed a distinct growth mindset.
The next two “regular” classes displayed distinctively different behaviors. I imagined these students sitting in a high chair with their applesauce. I’m sure they smeared it on their faces, squeezed it through their fingers and patted their hands in it just like the other kids. But I see the parents reacting differently. I see them with frustration on their faces. I see them telling the child to stop making such a mess. I see them scolding the child for their “failures” and telling them to “get it right.”
These students embraced the game – and had fun – but they played it very differently. These students relied heavily on their calculators. They almost refused to use paper and pencil. Their problem solving strategy was to punch numbers into the calculator until the calculator displayed the “correct” answer. This caused an interesting thing to happen – students would discover “their” answer. They would declare, “I know five!” or “I’ve got 16!” as if that was “their” solution to contribute. In fact, they would call "dibs" on a particular solution and fight over who "called it" first. They worked alone instead of collaborating with others. Once a student found one or two solutions that were “theirs” they more or less quit the game. They showed little interest in solutions they did not find themselves. Students relied almost exclusively on addition/subtraction and multiplication/division. Many students wouldn’t try.
It was apparent to me that many of these students were afraid to be wrong – to fail. They protected their self image of intelligence by clinging to “their” solution; their “right answer.” Some protected themselves by pretending not to be interested or declaring the game was “dumb.” In three of my “regular” classes I was able to coax them forward. I was able to get some students to take a chance and talk through their thinking. I managed to get some students working together collaboratively. I was unable to persuade them to put down their calculator and use paper. I think the calculator is a bit of a safety valve – if they make a mistake, “it’s what the calculator says” as if the device is at fault. As a group these students demonstrated a mixture of growth and fixed mindsets – within each student. It seemed clear to me that they responded to growth language. It was VERY clear that if they noticed any body language, tone, inflection, or statement from me that they perceived as judgmental – they shut down and quit participating.
I have one class with a few students many would characterize as “low.” This class was particularly interesting. They used a strategy similar to the “regular” classes. Many students found “their” answer. One student found several solutions. What was interesting was the attitude of the class. They had a “let’s get this over with quickly” attitude. There was no joy. This was just “one more thing” to get done for the week. There was no curiosity. There was no collaboration. No one used pencil and paper – if I pushed they just wanted to quit. It was very clear that they perceived their ability to “finish” as a measure of their intelligence. There was a palatable atmosphere in the room that the students felt their worth was being measured. I’ll be honest – the joy was sucked out of the room. Most of these students clearly demonstrated a fixed mindset.
These students all took a district benchmark just a few days before this experiment. I think the results of that test are actually interesting and relevant. Interestingly, there was very little difference in the average grades across the different classes I described. The “honors” class has a couple of outliers on the high side that skew the average up. The “regular” classes have a few outliers on the low side that skew the average down. If you remove the outliers then there was little difference in the performance of the students as measured by a multiple choice test. Hmmmm. News flash! - there is an awful lot that a multiple choice test doesn’t measure.
It is very clear to me that all of my students are intelligent. What is also clear is that there is much variation in how my students perceive themselves and how they feel about how “smart” they are. Some students have gaps in their knowledge and skills. A few students demonstrate aptitudes that give them a competitive advantage. Most students however seem most affected by their own inner voice – their mindset and view of their own ability. That is both disturbing and encouraging at the same time.
I am disturbed at the negative way in which some students view themselves. It is disturbing because at one time they were all joyful children sitting in a high chair trying to eat their applesauce. It is the reaction and actions of others that have affected these students and created the mindset they are now demonstrating.
I am encouraged because the actions and reactions of teachers and others have the ability to change to way students see themselves. If we are careful not to judge students and if we carefully create a safe learning environment, students will begin to take risks and develop a growth mindset. It is clear that this process takes time and is prone to setbacks. There are many forces outside of our classrooms that work against us. Unfortunately there are many influences at home in the case of low socio-economic families that foster a fixed mindset.
It is worthwhile to learn about growth mindset. Growth language is definitely a positive influence in my classroom this year. If you are interested in learning more about growth mindset, visit Carol Dweck’s website found here. This recent article in TeachThought is brief but informative as well.