Of course you learn this in any subject. To master any discipline require a long, long process of thinking, working, reworking,... Discipline and focus lead over time to an increase in skill and understanding.
All too often in math courses, the content is broken down into bite size pieces. That is, the material is overly preprocessed for "easy" consumption. Students follow. Teachers get high marks. Life is good. But we know that's not good enough. Certainly this doesn't develop the kinds of work ethic, habits of mind, and problem-solving ability we value.
One issue that needs to be dealt with is the specific process students use in their daily practice. Do they just try something and either (a) get it or (b) give up after getting stuck? This is probably the case for far too many students. Poor process and practice leads to poor results, and diminished intellectual develop in the long run. To shift the nature of the practice is not an easy task, and what I propose is not *the* solution -- it's just a start to one.
How does it work?
In my classes, I require students to use a homework template. It's just a word document with the name of the course at the top and two little prompts. The first is the statement of the problem or task. The second is the solution/work/whatever the student has. Students are instructed to do scratch work on separate paper, and most importantly analyze their work and transfer it to a final version onto the template. One problem per page, unless the problems are really short. Students are given the option of including their scratch work to the problem.
This system forces the drafting process that is much more explicit in the humanities and is easy to pull off in math classes.
|A sample Template|
Does it work? Yes. The quality of student work improves considerably. Instead of getting scratch-work quality written work, students are now required to take their homework more seriously. Students also comment that they feel proud of their work, and why not? If you think of an original idea, and present it well, that's something you should be proud of. The homework has good content, it looks good, feel professional,... a job well done!
Does it solve all problems in the math process "pipeline"? No. Templates and requirements of drafting do not address all issues. Teaching is a complex system, and addressing students' process of doing homework is but one part of the picture (though a very big one). It is, however, a very welcome step in the right direction.