Last year I taught with curriculum that was based off of the idea that practice could lead to understanding. The philosophy was that following an algorithm for how to solve a problem repeatedly would somehow reveal to a student why the algorithm worked. One thing I know is that this does not work! It is not fair for us to expect students to gain understanding when all we show them is a process.
However, not all practice is bad. Students who have developed understanding often need practice in order to develop the skills to use the mathematics independently. This should occur alongside opportunities to strengthen understanding.
My struggle is finding the appropriate balance of practice for students. I find that often I actually stray on the side of too little (just basing this off of what I see on assessments after I feel like I have helped students develop a strong understanding). Here are some problems I have had with getting students the right amount of practice:
- If it is an out-of-class assignment, many students do not complete/start it
- If it is in-class, not all students need the same amount of practice, so major differentiating needs to occur. I struggle with differentiating appropriately as at different times different students are at different levels.
- If it is in-class, independent practice leads to more push back from some students, causing me to have to address many behavior issues all day long. Perhaps this is because I do not differentiate enough or because I have not stated my expectations clearly enough. Many reasons for this, but whatever the cause, it is a challenge for me.
- It is valuable to practice recall of the mathematics, so all learning cannot occur at one time. Students who are on top of the learning one day in class may come back the next day and feel totally clueless. The idea of working through recalling learning is super important for students. I feel it is harder to address this when all practice is done in class.
Thinking through all of this, I have decided that a good next step is to work on differentiating for in-class time to practice independently. I will have to state my plan clearly to students ahead of time, so that they understand I am not doing this to select favorites, but to help all students learn. Hopefully this can be helpful in finding an appropriate balance. I will let you know how it goes.