I started teaching about eight years ago. My teacher program was very much a constructivist tilt. I am not an expert, but I think teacher programs tend to be more constructivist leaning than the schools and districts that employ the graduates of these programs.
I took all the lessons to heart, seeing the merits of students teaching each other and figuring things out on their own. I then took this perspective to my job. My district was also on the constructivist side of the spectrum, especially in terms of teaching math. Little side note here, teacher training in this country is a total mess. Intensive classes at a university with time in a classroom student teaching and then they plop you in your own classroom. Scary for a good reason.
What I came to realize quite quickly is that there is a place for the “just sharpen your pencil and bang out a bunch of problems” in math. I can’t speak to primary or high school level, but most of the concepts students learn in middle school require quite a bit of automaticity in math facts, which most of my students do not have.
I continue to struggle with this give and take of letting students take time to figure things out on their own and giving them 20 problems to practice and cement the concepts down. The struggle continues in part because I do not have a reliable source of practice problems, which forces me to spend a lot of time I don’t have making up practice problems.
Maybe in the past math was a “here is the skill now practice it” subject that the pendulum has swung to the other side, stressing the discovery of concepts. Unfortunately, I came along after the pendulum swung, so while they were stressing the “figure this one out” method, I had not received the indoctrination of the “better sharpen your pencils ‘cuz we got a lot of problems” method. I am now struggling to find the balance, and I find myself leaning more to the drill and kill side of things. I see students struggling with basic math facts (“7+3 is…um” student pulls out fingers and counts, “7+3 is eleven?”). The struggle puts up a barrier, insurmountable for some, to gain confidence in new concepts.
There are days, however, where I have swung to far back, with students spending too much time on becoming proficient on a skill they will ultimately forget how to use, or not now how to apply when the time comes.
I feel a discussion needs to be had about how to properly proportion the exploration part of math and the practice of math skills. This year I have relied a lot on Dan Meyer and his Perplexity problems (I highly recommend his work). I find that the perplexity problems can capture the students’ need to solve the problem. I have also found that the lower students quickly give up with either a defeatist attitude or with just not having any idea how to get started.
I started teaching eight years ago, but I feel no closer to having a handle on this craft. I believe it is partly due to my somewhat lackadaisical organization. It is also in part due to the tug of war between giving students time to practice a skill and giving them time to discover a concept.