Over my career, I’ve been trimming homework more and more – at least required homework. I allow unlimited redoing of homework assignments, my grading has focused on completion far more than perfection. I’m looking at making even more changes for next year – assigning even less, not grading it, and further emphasizing process over final answers. But I’d like to share a story of a student who found success through some dedicated work outside of class.
Ben came to my Trigonometry/Pre-Calculus class this year as a senior who has never felt like he was any good at math. He’d made his way through, but never completed his work on time, didn’t show his work, and when it came to math tests and quizzes, always seemed to fall apart. Even if he felt like he understood something in class, nothing made sense when the test came, so he figured he really didn’t understand things in the first place, and just wasn’t a math person.
Much of this year wasn’t too different. Ben’s assignments were frequently late, and he sometimes missed class for various reasons (often on test and quiz days, which may have been a coincidence). On those days when he did take a test or quiz, he did not perform well at all. I’ve had students like these over the years, and refuse to believe that they aren’t “math people”, although maybe they haven’t been “math class people”. But just because a student hasn’t been any good at math class doesn’t mean they aren’t good at math. It’s not to say that I’ve seen every student of mine turn into a complete success in my math classes, but there may be a variety of reasons for that – maybe I (despite my best efforts) just didn’t find a way to click with a student, maybe the student wasn’t ready to put in the necessary effort and I wasn’t able to help motivate them to do that, and maybe there has been a decade of math phobia and anxiety that is difficult to undo in just a year or two.
Quite frankly, I thought that perhaps that would be the case again with Ben, but for a variety of reasons (support from home, from his other teachers here, and some strategies that I suggested), little by little, he started to turn things around. It seemed to start with him showing his work, absolutely beautiful, creative, and organized work for his homework assignments. This helped him to follow his own thinking better, and helped me to give him better feedback, which he started to read and work to absorb. He redid assignments to correct his mistakes, and was able to describe them to me. But he still wasn’t really retaining what he was doing between the assignment and a test or quiz.
Recently, we went over his study strategies, which were somewhat typical among traditionally “good” students – read notes, practice lots of problems, and get math fatigue before each test, a total overload of information that he was having trouble organizing in his head. I suggested a new strategy. Instead of doing a whole bunch of problems, do 1-3 problems every night, but do them slowly and thoroughly. Get to know each problem, every detail of the problem, different approaches to that problem, things that seem to work and things that seem to lead to dead ends or circles. At the end of a week, he would have gotten to know about 10-20 problems very well, and started to see similarities and differences.
The end of the semester came, and Ben had one previous test he had to make up because he hadn’t passed it the first time, one previous test he just had not taken, and the final test of the semester. Over the course of less than a week, he took all three tests, and not only did he pass them all, he scored 87%, 91%, and 92%. What an amazing achievement, and one that really confirmed for me the benefits of reducing the number of problems, but focusing on each one, going deeply into the math more than going as wide as possible.
More than anything, I’m really proud of Ben, who I hope will realize that he has every ability to be successful in further math classes. He’s off to college next year, and even though I wish I had another year to work with him and help him continue to develop these great study habits, as well as his confidence, I have faith in his future. Ben may not always be a great math student (though he’s developed a lot of skills that should help), but he’s definitely a math person.