I believe that I work hard to teach developmentally. I consider what my students need in order to understand/create the next concepts from scratch and to integrate those concepts into their existing worldview, and I constantly reflect on how their age affects their motivation and their understanding of the learning process. I constantly revise, in my mind, what successful learning looks like, in order to better help my students.
But recently, I have been thinking that I have it all wrong. I am working way too hard, and ironically enough, my students are working way too little. Let me explain.
My latest belief is that what makes a student successful in math is a combination of sophisticated skills, raw intuition/understanding, and confidence in their own ability to attempt new problems. The more I think about this, the more sense it all makes to me. We often over-praise children for their "potential" or "understanding" in mathematics, and those same children walk away from that praise believing that being good at math means having an innate ability to reason. The more I think about it and observe children and think about it some more, the more I disagree with that belief and think it's bogus that we praise kids for their "potential" without making an immediate, stern emphasis on their lack of effort.
Here is a simple analogy I draw for myself: A musician or an athlete would never prepare for a gig / game by ONLY thinking in their heads that they need to "dribble the ball past their opponents and then shoot it into the basket." In order to do it successfully and consistently, they need to put in hours of practice to bridge the gap between theory and technical expertise. So, why do our children think that they can get better at math simply by thinking about it abstractly and passively looking at examples??
In Grades 3 through 6, we more or less teach kids the same skills and concepts over and over again, with a bit more depth each time. The kids who are intuitive and/or clever (and yes, they do exist) cannot help but be "good at math" by the end of Grades 5 or 6, because they've already seen every skill at least twice. Does it mean that they've "mastered" those skills? I think not, based on the fact that some of my most intuitive/clever incoming 7th-graders still could not recall basic fractional skills until we had reviewed them, even after years of learning the concepts. But, at this point, whether kids commit to practicing the concepts repeatedly does not immediately determine their test performance.
In Grade 7, the game starts to change a bit. The problems become multi-stepped, and new (algebra) skills come down the pipeline that require repeated practice in order to reach a point of effortless, automatic application. I am certainly not saying that understanding is not important in Grade 7 -- in fact, we do a lot of conceptual development in class before introducing any algebra methods -- but I find many of my intuitive students struggling with procedural issues in algebra, even though they understand in their heads what they need to do. They simply have not developed the work ethic to practice and practice again until their procedural issues are ironed out and they can consistently solve something without effort. In Grade 7, more than anything I emphasize work habit, because I find it so dangerous that those "intuitive" kids get passed on from teacher to teacher believing that AS SOON AS they would start working, everything would be dandy.
Because truly, I don't believe that. I have two amazingly intuitive 11th-graders, who lack the basic arithmetic and algebra skills to complete problems. If you throw them into a completely new type of problem, they can make headway better than their classmates. But then, put them in front of a common/simple skills application, they would have no idea what to do and invent crazy algebra rules. I can only imagine that those two kids have been praised by teachers all along for their intuition, without an equal emphasis on how much damage they are doing themselves by leaving such major gaps in their basic skills. At the same time, I've seen other kids go from struggling to mastering skills, and then tougher concepts. Those kids persevered until they mastered the basic skills, and now they can save their mental energy for the trickier/problem-solving parts of the task.
So, practically, what does that mean in my classroom? Besides praising effort, what else have I started doing in support of this belief that dedicated practice is important?
Well, one of the things I have been thinking about is that, despite my efforts to make learning exploratory and constructivist, my students are still far too dependent on me. They expect me to set the pace of my classroom, and when they are absent, for example, their learning suffers tremendously because they do minimal work at home. And this simply cannot be the case for the Grade 11's and Grade 12's.
I have made a homework schedule for my IB students in grades 11 and 12. I have never been a believer in mandatory studying outside of class, until now, because part of me hopes that the kids will see the importance of pacing themselves and setting their own goals. I can see, however, that my Grade 11's and Grade 12's are too comfortable; they come to class, do what assignments I have designed for the day, feel great about their understanding of the concepts, and then most of them walk away without practicing more on their own or struggling through practice problems in the textbook. It's simply not working, because I am working way harder than them for this class, and that cannot be the case when it is their learning we are talking about. So, in my new homework schedule, I assigned a Chapter Review from the textbook every week or two weeks, for a topic they should be familiar with. If there are questions they cannot answer, I urged them to look through the chapter at home to resolve their questions, and only bring to class the most complicated questions that remain unanswered.
And you know what? It has been wonderful. It has completely changed the dynamic of my classroom. Instead of feeling like I am on the hook for giving kids work and setting the pace for my class and making sure they get sufficient practice during class, our roles have somewhat flipped. Kids are in more control, and they are asking me questions that they want to know the answers to. It has changed the feel of the relationship between me and the students, for the better.
I am also experimenting the same with my younger students, except I am going to give them a quantity of problems (ie. 15) to bring me each week from the textbook, and they get to decide which problems they wish to practice. In doing so, the kids get to decide if they need more practice with current material (ie. weaker students) or if they want to use the "mandatory" practice as an opportunity to spiral review.
In short, as I think more about what makes a successful student, I want to think about ways of extricating myself out of that picture. I truly think that this will empower my students to feel like their learning is in their hands and to build their confidence outside of class, without changing the way I currently structure lessons inside the classroom. I think this is how I am going to help my students move towards becoming life-long learners.