Every year we all experience this, right? We have big goals for the new year, we make promises and many of them fall by the wayside. I am going to be modest about my new year’s aspirations (at least in public!) and I am making a vow to myself to try something new for my Geometry kiddos this new calendar year. Awhile ago I got into a terrific twitter exchange with Henri Picciotto (@hpicciotto) and some other folks ( I wish I could remember everyone involved, I am pretty sure that Julie Reulbach (@jreuhlbach) was part of this) about HW. I mentioned that I will sometimes include problems in HW that touch on ideas we have not talked about yet in class. This brought up a conversation about leading vs lagging homework ideas and Henri is particularly articulate about these ideas over at his blog space (http://www.mathedpage.org) We tweeted about the idea of letting ideas percolate either before instruction or after instruction. I spoke about my feeling that it is important to have students struggle with an idea a bit to (maybe) help them appreciate a new idea/definition/formula when it does arrive. This, I think, is sort of like Dan Meyer’s series of if ______ is the headache, then ______ is the aspirin essays. One of the results of this terrific, spontaneous twitter chat was that I walked away with a commitment to instituting lagging HW assignments in my class. I wrote out a careful pacing calendar with the optimistic idea that I have a solid sense of how long these conversations will take and a hope that mother nature will not interfere by dumping snow on us at some point. Obviously, this calendar is not set in stone. What IS set in stone is my commitment to the pacing of the HW assignments. What I did was write out a pacing calendar that delays by three or more days any HW that directly relies on reading/instruction of a new section of my Geometry text. I do still feel a bit of a commitment to daily practice out of class – I know, this is another conversation completely – so I wrote a series of review HW assignments that reach back to old ideas/skills but I tried to do so in a way that is thoughtful and leads to preparedness for the new ideas we are discussing. I also wrote a series of entrance slips that I will start class with the day after we first discuss a section together. These will be collected and marked, but not graded. I am hoping that these will provide both me and my students a way of monitoring their developing understanding of new ideas. After three or more days they will final have a HW focused on a certain section of our text. Meanwhile, in class we will still be following a pace similar to what we followed last year in our first run through my Geometry text so I have some sense that this is a reasonable pace for our students. However, instead of going home and immediately practicing some new set of skills, they will be looking back either weeks (at the beginning of the chapter) or days (after a few days in) to ideas that have, hopefully, been percolating a bit in their brains. They will have had time to think about these ideas, they will have had an entrance slip check in on their facility with the ideas at hand, and they will have had further class time combinations of lecture and discussion to play with these ideas and build them up together. A few days afterward they will go home with focused practice and their assessments will also be lagging a bit to line up with the HW practice. I anticipate that there will be some concern expressed by my Geometry team and by my students because, you know, change is a bit of a challenge. This is especially true once you have established a rhythm and pace that you are comfortable with together. One of my three colleagues has expressed a desire to try this as well but the other two have not commented yet and I have no expectations that anyone else needs to follow me on this path. As department chair I kind of want to test the waters on this so that I can report back on the inevitable speed bumps as well as the successes that we encounter. If this works the way I think that it will, it will radically alter how I think about pacing and how my students think about HW. My biggest wish for this endeavor is that this practice will enhance retention and help my students think more about connections in the ideas we work with in class. I feel more confident about taking this leap in our Geometry course first for a couple of reasons. I feel more intimately familiar with the contours of this course since we are using a text that I wrote a couple of summers ago. I also feel that the Geometry course lies a bit outside of the vertical tower that much of our math curriculum builds. If we slow down a bit and there are not topics near the end of the course that we reach, it feels that there are fewer consequences in terms of what future courses and teachers will expect of these students. Also, these students are younger than those in my other two courses (a Discrete Math elective and AP Calculus BC) and I am optimistic that these younger students might be more flexible with the idea of changing their habits.
If you have not seen my Geometry book yet and want to take a look, you can download it from my Dropbox at this link. If you want to look at my Chapter Six pacing calendar, entrance slips, and HW assignments, you can find them all in this Dropbox folder
I am hoping that January will be a productive month for this blog space as I reflect and report on how this experiment unfolds.
Great idea, and clearly you’ve put a lot of work into this! I just checked out the first couple pages of the book and will look back it it when I have more time. Looks awesome!
Thanks for the kind words, Danielle. It was an awful lot of work but it was a bit of a labor of love the summer of 2014. I still view the book as a work in progress, hopefully in a couple of years I will be thrilled with it. Right now I am at least satisfied.
Interesting post! Thank you for sharing. I think this idea has some merit, for sure. I think it goes a long way toward creating life-long Learners and actual mathematical thinkers. I still hold on to the daily practice as reinforcement. I pepper in review assignments along the way. These are always terrible… Students can not independently perform tasks older than one week. Despite posted resources and videos to help them on a review assignment, they still can not complete correctly. If they by chance get it right, they haven’t learned it to store it in their long term memory. I think that this “spiral” of the assignment, or lag time as you call it, will help students process better. Will they keep it in their working memory or let it percolate in their long term memory?
I wonder if this will work for the “traditional” or average ability to high ability student? I think possibly. They too already have some organization skills to help here. What about the low-achieving and special Ed students? I feel like my special Ed kids would really struggle with where to go back to find how to solve. Maybe they just need re-trained.
Thanks for dropping by and taking the time to comment. I, too, have seen the problem (a persistent one!) of students not being able to independently review/recall ideas from the past and that is one of the motivations for trying this approach. Henri writes some eloquent ideas about it over at his page. I work at an independent school and we do not have special ed kids here. They would be an entirely different challenge for sure. We do certainly have some traditional, average ability students and I am interested in seeing how this process unfolds for them. I will certainly be blogging pretty actively about this adventure.