What Causes Students’ Success and Failure?

One year in my teaching experience stood out in shaping my professional priorities. 

I was teaching math in a charter school. Entering sixth-graders at that school were given a math placement test and then grouped by achievement level into separate classes. That year I got to teach both groups of outliers: the class with the students who did best on the placement test and the lowest scorers’ class.

It was such an interesting experience! Never before had I taught at the same time two groups of the same age that were so different academically! 

Observing and analyzing the differences in these groups’ behavior changed how I saw the causes of success and failure.

Let me tell you about these differences. 

How students asked questions

The striking difference I observed first was in their questions.

My high achievers asked twice - no, ten times - as many questions as my low scorers. Both shy and outgoing kids asked them: the shy ones whispered; the others yelled their questions out. Not all these questions were deep. I remember one of the questions particularly well. While solving the following problem, 

“A group of fifteen chickens and bunnies have forty legs altogether. How many chickens are in this group?”

one rather shy girl asked how many legs a chicken has. 

It was clear that these kids felt entitled to understand what they heard or read, and they were willing to work, even fight, even overcome shyness to achieve understanding.  They asked all kinds of questions: What does this word mean? Is this the same as multiplication? Do they want all answers or just any answer? The only “question” that I do not remember hearing from these students is the only one I heard in the other class: "I don’t get it." My advanced students "did their homework" before asking a question: they parsed the problem, located the parts that were understandable, singled out the source of their confusion, and only then asked their question. 

How much time an assignment took 

Quite a few times I had to administer the same tests (like MCAS and ACM8) to my two classes. At first, I was shocked when my strong students took almost twice as much time as my weak ones on the MCAS; the difference was even greater on the AMC8. But it is easy to understand if you see it as the difference between the time it took the low scorers to give up and the time it took the high scorers to be satisfied with their work. My low scorers sometimes could not even make themselves read a busy page, expecting that they would not understand it anyway; the high scoring class attempted every single problem, even when it was clearly above their heads. For them, not being able to solve a problem was something ridiculous, something out of place. If a problem seemed impossible to solve, one just had to think more, maybe try a different approach. They were willing to work as long as they had to - they were sure that they would succeed if they tried hard enough. 

Ways students learned

I found it so exciting to teach my high scorers one way to think about a concept and then help them see a different way! It is very rewarding for a teacher to hear "wow!" and to see shining eyes when students understand something new. All my high achievers enjoyed seeing something unexpected in what they already knew.  My failing students, on the other hand, expressed annoyance and puzzlement: "So what we learned before is useless?" It is as if for the successful students learning was a natural and enjoyable state of mind, while for the failing students it was a hard and frightening process that was supposed to be rewarded by some downtime.

The greatest challenge

For the students in my lowest scorers’ class, the greatest challenge was to get started on a problem: read it and try to understand it. Not that they were all bad readers (after all, they were already six-graders), and some problems did not even contain too much text. They were simply so sure that they had  no chance of understanding the problem that they thought it  made no sense for them to even try. Why waste time if you know you'll fail anyway? Their habitual “I don’t get it” was a cry for help: “Save me from this torture!” 

The most difficult thing for the students in my highest scorers’ class was letting go. It’s not that they were all perfectionists. A few boys were really sloppy. One girl was a dreamer. Some did not always do their homework. Regardless, it was hard for all of them to accept a simple fact: sometimes one understands a problem (knowing all the concepts involved) but cannot solve it - because the problem is so challenging. It felt like students in this class were convinced that if they had enough time they would solve any problem in the world. 

What makes learners so different?  

This is what I think:

Past experiences give weak and strong students very different expectations of themselves as problem solvers. Strong students have a history of being successful, of trying and achieving, of overcoming difficulties - and so they expect themselves to solve a problem, and are willing to invest more and more time and effort to succeed. Weak students have experienced the disappointment and shame of failure so many times that this is what they now expect, and they want to avoid experiencing it again by not even trying. So, strong and weak students act according to their expectations, turning their lives into self-fulfilling prophecies.

I think that in teaching children mathematics it is most important to provide them with experience of trying and succeeding, then trying even longer and harder - and succeeding again. 

Providing all students with a repeating experience of successful problem solving is now my priority as a teacher.