Problems for Problems

The #slowmathchat discussion on Twitter got me thinking about what I assign for homework, why I assign it, how it has changed over my career and where do I think it is going?  I started as most teachers do at the beginning of their career.  After correcting the previous day's assignment, which consisted of me at the overhead (dating myself) demonstrating what was expected on each problem, I would then give a brief lesson on the day's new topic. After the lesson I would write the day's assignment on the board at the mid-point of the class period.  Whatever did not get finished in class, was to be completed as homework.

I relied on my sense of humor, engaging personality and excitement for learning to keep my students interested each day.  While I still use those aspects to my advantage, they are not the cornerstones to engagement in my class. Lessons have evolved to inquiry-based activities and investigations. Learning comes from student talk and not teacher talk, and thus I needed to change the homework assignments. They became hand-selected purposeful problems to practice previously learned concepts and not to finish the day's learning.

Usually on Monday and Tuesday we investigate new concept(s) in class and I assign specific practice from the concept(s) we investigated on Thursday and Friday.  Wednesday I start to assign problems we investigated on Monday and Tuesday.  The homework assignments typically are "naked math" and we work on "real life" in class.  Naked math are straight up math problems, no words.  This continues with each set of problems scaffolded in difficulty to the class's progress with a concept.  Once the skills have been mastered, I will assign "real life" problems for homework.

Depending on the concept(s), the typical assignment is 4-8 problems.  I find that 10-15 minutes of hand-selected purposeful practice improves skills, improves confidence, reduces frustration in students and provides access for all learners.