I’m starting with assessment for several reasons. First, I’ve always liked the idea of “begin with the end in mind,” so focusing on what I’d like the outcomes to be and working backwards seems to make sense. Second, in this accountability-obsessed time, assessment is a pretty important topic that I not only need to get right for the accountability folks, but most importantly for my students. And finally, I think it makes sense to start with assessment because if you guys give me some ideas that make me radically rethink this, it would be better to do that up front instead of after working through all my other ideas.
So, what are my goals for this class? Well, there are a bunch, but let me try to narrow them down to the most essential ones.
Content Goal: Learn the Algebra skills.
Habits of Mind Goal: Become better problem solvers by getting better at asking good questions, thinking mathematically and reasoning mathematically.The first goal is obviously much easier to assess than the other three, so I’m mostly going to focus on that one in this post. But if you have ideas on some more formal ways to assess the Habits of Mind, Collaborative, and Metacognitive goals, I’d love to hear them. (I have some teaching techniques and activities in mind to try to foster those three goals, but am not real clear on a good way to assess how well we’ve done.)
Collaborative Goal: Become better at working together to achieve a common objective.
Metacognitive Goal: Learn more about themselves as a learner (via conversation and reflection) and use that to become better learners.
From my previous incarnation as a math teacher I remember being frustrated with my assessments. (Actually, I think I probably didn’t think too deeply about my assessments, but I was frustrated with how well my students did - that’s obviously a critical distinction and I hope to be a better teacher this time.) Students in Algebra often struggle because they accumulate both an understanding and a skill deficit – they only partially understand concepts and they only become partially proficient at skills and, eventually, they sink.
My previous assessment strategy didn’t do much to alleviate that, as their deficits were often masked by “just good enough” performance (as reflected in their overall grade) that made it appear as though they didn’t really need much intervention. So I’m hoping to implement a better system of formative assessment this time that will allow me – and my students – to stay on top of things better. I’m currently planning on having three categories in my gradebook (I’m not a huge fan of grades, but that’s a topic for another post): Preparation (10%), Formative Assessment (70%) and Summative Assessment (20% plus - more on the “plus” in a moment).
I’ve spent a lot of time struggling with this one. In general, I agree with the thinking that the practice and responsibility parts of being a good learner shouldn’t have much effect on their overall grade. “Being a good kid” is something I respect and want to promote, but it shouldn’t be reflected in their grade for Algebra. Since it says Algebra on the transcript, the grade should be a reflection of how well they know and can do Algebra.
On the other hand, I do want to encourage students to practice (because it will help them learn), and be responsible, and generally be a good kid. And I realize that their previous (and often their concurrent) experience often includes this piece as a big part of their grade. So my compromise is to include this as a small part of their grade. It will be comprised of a combination of homework, warm-ups, and other in-class activities. (Much more on homework in my next post but, for now, suffice it to say that it won’t be 1-31 odd.)
Formative Assessment (70%)
This is the heart and soul of my assessment strategy and the part that I’d really like some constructive feedback on. While previously I relied heavily on chapter tests, this time I want my formative assessment to be much more, well, formative. As such, I want it to be more frequent, more targeted, and have a built-in process to try to give students a better opportunity to master the skills in a timely manner so they don’t accumulate those deficits I mentioned before.
Algebra is very much skill-based (although there is certainly a bigger-picture mathematical thinking/pattern recognition piece as well). As I talked about in my previous post, my class will meet four days a week (MWRF) for 59 minutes at a time, so my plan is to give formative assessments roughly once a week (although that will vary a little bit with the calendar, the particular Algebra concepts, and other happenings at school). These will be short, targeted assessments of six questions, covering only three concepts, with each concept having one relatively easy and one relatively more difficult question. The assessment would then get entered into the gradebook by concept (so three grades for each assessment). This should help both me and my students identify what they understand and what they need to spend some additional time on.
After the students turn in their assessment, I’ll have students come up to the board and immediately work through the questions. This will then be captured (it looks like I’ll be in a room with a Smart Board) and posted to the class website (mostly likely run through a blog, but I’m still thinking about that). Students should therefore have a pretty good idea right away about how they did, but I’ll also grade these assessments and get them into our student information system no later than that afternoon. I’ll not only record their grade, but will also use the comment feature to indicate which problems they missed on each concept. When students login they’ll therefore be able to see which concepts they need to work on and they’ll be able to refer to the actual assessment – and worked out solutions – from the class website.
If a student doesn’t show proficiency on a concept by getting both questions right they will then have the opportunity to retry the assessment (a different version) once each day until the next assessment. They will only have to retake the portion of the assessment that they didn’t get correct the first time. In other words, if they get both problems on a particular concept correct the first time, they won’t have to retake that part.
They will have the opportunity to review on their own and/or get help from me, other math teachers, or peer tutors, and then typically have up to four retakes before the next assessment rolls around. The strategy is that this is providing students an incentive to become proficient on those skills in a very timely manner, before those deficits start impeding their learning on future skills. Their new score (assuming it’s higher) will go in the gradebook and the comments will then change to indicate any problems they missed on the concept on this assessment.
I’ve struggled with the idea of only allowing those retakes until the next assessment (about a week). Philosophically I would like to allow them to continue to try after that if they need to, but practically I don’t think I can make it work. First there’s the simple management aspect of it, but there’s also the concern that if I extend that indefinitely, that invites procrastination which defeats the purpose of eliminating the understanding and skill deficits in a timely manner.
Summative Assessment (20% plus)
We give final exams each semester at my school, with each final lasting for 85 minutes, and the final is typically about 20% of the overall grade. The Algebra team that I’m joining gives a common final assessment each semester, so I will be giving that as well. This is a summative assessment that gives students a chance to demonstrate what they know and are able to do, and hopefully gives them a chance to coalesce their knowledge and make it more permanent (that’s the theory, at least).
I will make my summative assessment worth 20% of their overall grade as well, unless their performance on the final exceeds their existing grade, in which case the final will be worth 100%. In other words, if they can demonstrate they know more Algebra on the final then what their previous grade indicated, then I’m going with what they can demonstrate. In the long run, I’m not that interested in how much Algebra they knew in October or March, I’m interested in how much Algebra they know when they (tearfully) leave my class.
So there you have it. I have made some compromises due to the fact that I’m teaching just one section of Algebra instead of being a full-time math teacher, but I think it’s a decent start on a good assessment strategy that is actually doable given my other job responsibilities. Keeping in mind that limitation (excuse?), I’d love some constructive feedback.