The typical rationale for assigning mathematics homework is for students to independently practice what was taught in class. After all, practice makes permanent. While the opportunity to practice must be present for students to gain procedural fluency, we should rethink mathematics homework as an opportunity to change mindsets, too, around mathematics and perseverance with problem solving. Don’t get me wrong, skill development with repetition is important. Just ask any basketball player about practicing their on-court drills or a musician practicing their scales as part of their craft. Yet, it isn’t the drills or scales that are the end goal for the athlete or musician; instead, the goal is to use those skills to compete against another team on the court or perform music with an ensemble. So why do computation and rote skills become the goal for learning mathematics? Instead of sending students home to complete 10-20 practice items that have no intrinsic value whatsoever, what if we sent home only 4-5 items with a couple that specifically focus on applications, problem solving, building arguments, and perseverance (i.e. the Standards for Mathematical Practice & Colorado 21st Century Skills and Readiness Competencies in Mathematics).
In other words, assignments should have a mix of problems and exercises. What’s the difference? From the High School Publishers’ Criteria for the Common Core State Standards for Mathematics, “the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Problems are problems because students haven’t yet learned how to solve them; students are learning from solving them.” If students are truly asked to grapple with problems, then we shouldn’t expect right answers coming to class the next day (in contrast to exercises, where correct answers should be expected). This means documentation of an initial strategy may be sufficient for homework, knowing more progress will be completed in class through a small-group or whole-group discussion.
What are the potential benefits are rethinking mathematics homework in this way?
- Students may actually complete the assignment if it is shorter in length.
- Assigning a few purposeful exercises can reduce the chance that students may repeatedly practice incorrectly without timely feedback. The assumption is that timely feedback would come in class through daily formative assessment and opportunities to practice.
- Reducing the assignment set focuses the homework review routine in class the next day to meet specific learning goals. Adequate attention can be given the to skills along with appropriate discussion of the exercises. This is much more purposeful than teachers asking, “which ones would you like to see?” The teacher gives up all control and the opportunity to build connections is lost when homework review is left up to going over randomly-requested problems from the assignment set.
- Having a couple of contextual application problems that incorporate the Standards for Mathematical Practice help students investigate non-fiction texts in math class, which is a focus of the English Language Arts standards and all other content areas. Breaking down a problem to identify what it is asking is more cognitively complex than performing the computation(s) to solve the problem. Close reading and citing evidence have a place in mathematics, too!
Instead of treating mathematics homework as a right of passage that generations of mathematics students have endured, let’s focus on quality assignments that reflect rigor, as defined within the Colorado Academic Standards (conceptual understanding, procedural skill & fluency, and applications with equal intensity). Less can be more, and we may find shifts in mindsets and attitudes toward mathematics in the process.