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There are a myriad of thoughts on this topic. I’ll list a few teachers and reasearchers thoughts on practice and homework below then follow up with my thoughts.
As Shawn mentioned above, John Hattie does suggest homework for highschoolers.
Dr. Peter Liljedal suggested after the open task, having the students do 46 problems independently to practice the new skill, though I’m not aware of his stance on homework.
Dr. Jo Boaler suggests that homework should typically be a reflection on the math lesson (reflections greatly serve to reinforce learning) and/or maybe an inquiry project (i.e. having the student look around their house and see if they can connect things in their life to the math less) to quote Dr. Boaler from her book “Mathematical Mindsets” :
“Homework should be given only if the homework task is worthwhile and draws upon the opportunity for reflection or active investigation around the home. If homework was used in this way, and we removed the pages of mindless practice that are sent home daily, we would enable millions of students to use their time more productively, reduce stress, and take a giant step in promoting more equitable schools.”
Dr. Boaler also points out that assigning homework is a matter of equity, as some students have home lives that make it very difficult to get homework done, and so by assigning homework you are effectively providing opportunities for some students but not all, for this reason she is against assigning homework, but suggests the above if you aren’t ready or unable to not give homework.
Dan Meyer, the creator of 3act math, was also against giving homework. To paraphrase his logic, he said that his students practice a given formula or idea 2030 times before they leave his class, so he saw no need, though when his school switched to block scheduling so he saw the students every other day, he resorted to assigning one problem for homework just to keep the concept fresh in students minds.
In his book Necessary Conditions (which is kind of a handbook for putting together an inquiry based classroom) Geoff Krall suggests that homework or no homework can work either way, the key is to “make homework work for your student, not the other way around.”
From the reading I’ve done, it’s clear to be that there isn’t a clear cut answer to the question of homework, as all sides I think have solid arguments. It seems clear to me though, that if you do assign homework, keep it short, like what Shawn said he does. If you don’t assign homework, make sure the students are getting plenty of opportunities to work with and wrestle with the concepts.
I’ve been thinking a lot about this question because I’m going to start teaching in the fall. I’m currently leaning towards a simple reflection and an open math question or inquiry task. Something like “what are some areas you find ratios around the house?” or “Create a problem that uses a ratio, and then solve it.”
The principle of an inquiry based classroom is that students should be able to explore, create and try their ideas. Assigning loads of drill type problems is counter to that philosophy, as it suggests reinforces the idea that math is more about finding answers than the journey to those answers. On the other hand students need to master these ideas, both to move deeper in their exploration of math and to satisfy the standards. My thinking is currently that class should provide enough opportunity to practice the ideas that homework becomes about enrichment and playing with an idea more, and less about mastering the idea, as is the traditional purpose of homework.
I’m not 100% satisfied with my stance right now, but I think I’m just going to have to try it out and refine from there.
I’d love to hear what everyone else’s opinions are.
Sorry for the long response, as I said, this is something I’ve been thinking a lot about lately.