Beliefs, Biases and Compromises

Forgive me for the multiple posts about things other than just lesson planning for Algebra, but I think it's important to lay the groundwork first. In my last post I talked about some of the specifics of my situation, because every school and every classroom is different, and those differences are very important in the planning process. In this post I'm going to talk about what some of my core beliefs are about teaching Algebra (or perhaps some of my biases if you prefer), and then some of the compromises I will inevitably have to make between my beliefs and the reality of my classroom.

If you've read The Fischbowl much over the years, you pretty much know what a lot of my beliefs (and biases) are, but let me summarize some of the most important ones as they relate to planning for Algebra 1 for next year.

Beliefs

1. I believe that a lot of the courses we currently require - including Algebra - should not be required for every student.
   
2. I believe that the specific skills we teach in Algebra are not important for every student to learn, and that standardization is not optimal for learning.
   
3. I believe that the justification that it's okay if high school mathematics is sometimes useless and needlessly abstract because kids learn how to "problem solve" in math classes is well-intentioned, but wrong. (If our goal is to teach problem solving, I would suggest that there are more meaningful ways to have kids solve problems than abstract Algebra.)
   
4. I believe that much of what we assign for homework is benign at best, and downright harmful at worst. I also believe that if homework is given, it is for exploring and for practice, and therefore is always formative.
   
5. I believe that students actively construct their own understanding.
   
6. I believe that all assessment should be formative assessment, and that students should be given as many opportunities as possible to demonstrate their learning.
   
7. I believe that students should be able to use all of the tools and resources that are available to them, both in the learning process and in the assessing process.
   
8. I really like it when my students do things on time, and I think it helps their learning, but I also believe they shouldn't be penalized for "late" work.

 Compromises

1. Algebra is currently required for all students, and we do have a defined curriculum. Students who leave my Algebra 1 class will go on to someone else's Geometry, Algebra 2, etc. class, and I would be doing them a disservice if I set them up for failure later. Not really any compromise here, just capitulation, as I don't have any control over this.
   
2. See #1, students have to take Algebra and I have to teach it. Future teachers are going to expect that I have "covered" certain topics and that students know certain skills. My compromise here will be to emphasize the parts of Algebra 1 that I feel are most important and most useful for kids, and simple expose (or occasionally even skip) those that I don't. This is a tricky line, but one I will try to straddle. Part of what gives me comfort is that most students are not really learning many of these less important (in my opinion, of course) topics even if I spent as much time on them as other teachers might, so it's a false comparison to suggest I would be depriving them. My belief (hope?) is that if I provide them truly meaningful learning experiences, that will serve them better in the long run.
   
3. Again, kids have to take and I have to teach Algebra. I do value problem-solving, and certainly having students become better problem-solvers is something I would like to see happen. So while I don't think it's necessary to have kids take math to learn problem solving, since they are taking math, I will try to structure my lessons in such a way that they actually get to problem solve. This is tricky, since it's relatively easy to structure Algebra 1 where kids "solve problems" but don't actually "problem solve."
   
4. The reality is I only have them for four days a week, and roughly 130 class periods (some of them shortened) a year, yet I'm supposed to "cover" all of the standards in Algebra 1. That's impossible to do without having them do some work outside of class. (In fact, even with them doing work outside of class, it's impossible to do.) There is also the reality of expectations - from other teachers/administrators, from parents, and even from the students themselves - homework is an expectation for many (all?) of those folks. My compromise is that I will assign one problem for homework each night, it will (hopefully) be more interesting and more in-depth than perhaps a "typical" homework problem in Algebra 1, and I will ask them to explain their thinking thoroughly (more on this in a future post). Homework will be graded on "sincere completion", not correctness.
   
5. If students actively construct their own understanding, then I have to structure my class so that they are doing more of the thinking. This is hard for me because, like many teachers, I enjoy explaining, and kids enjoy being explained to too. It's often hard to structure lessons that let students actively construct their understanding that are also successful at the students achieving that understanding. But I'm going to try. My goal is a combination of Gary Stager's "Less us, more them" and Dan Meyer's "Be Less Helpful."
   
6. With the exception of the final exam each semester, students will be allowed to re-assess as many times as they want (need) to in order to demonstrate their understanding. There is no "penalty" to their grade for re-assessing. If they ultimately demonstrate that they know the standard, their grade should reflect that. The majority of their grade will be determined by these on-going, formative assessments.
   
7. With the possible exception of any "common assessments" I might be required to give, all assessments will be "open Internet". This is going to require me to come up with some really good assessments, so I'm going to need your help. At this point in time, my compromise is going to be that while I want them to be able to use all the resources they would be able to use in a non-school-test setting, and I'm going to allow all technological resources, I will still require them to complete their work individually. In other words, despite my beliefs, I'm not going to allow them to use each other on assessments. (That's my thinking right now, I'd love to be convinced otherwise, but just haven't figured out an effective way to do this.) As a side note, I also want to minimize the time taken for assessments in my class, in order to maximize the time spent learning. So think shorter (5-15 minutes) assessments, not longer (full class period). Conceivably some assessments might take place outside of class time (although I hesitate to ask of more time from my students).
   
8. The expectation is that students will do things on time, because that's what's best for their learning. But to the extent that "homework" contributes to their grade (which will be a small percentage), students will not be penalized for "late" work. My compromise here is that when the work becomes "very late", I will perhaps penalize them slightly.

All of this is just "general" philosophical thinking to set the stage for the actual lesson plans to come. It will undoubtedly change as I enter the actual lesson planning process, and likely change again when I'm actually interacting with students, but it at least gives you an idea of where I'm coming from when we start discussing actual lessons.

As always, questions and feedback are welcome (that's the whole point of this blog, remember?).