Those annoying standardized tests. Like most teachers, I get some pressure to get kids to do well on standardized tests. Nothing too crazy, but from what I’ve seen, the vast majority of standardized test prep leads to very little genuine math learning, and lots of anxiety and disillusionment.
This year, there’s a new test in town, and in Massachusetts, that test is PARCC. We reorganized our scope and sequence to accommodate this — we will be finished almost all of the Algebra I standards by the end of March, when our kids take the first PARCC test. I’m not proud of that. We’ve rushed through a lot of worthwhile mathematics, and I don’t think it has helped my students. But that’s a conversation for a separate post.
Maybe those questions aren’t intimidating to you, but they are to me. It’s pretty tough to categorize them by standard, as they synthesize multiple concepts, or seem to be written based on the vague Seeing Structure in Expressions and Creating Equations strands. While PARCC still has some multiple choice questions, many more involve filling in a blank or using a drop-down menu — very different from a traditional multiple choice test. When questions are asked to align with a specific standard, like this one, they are often asked in unconventional ways:
Basically, PARCC asks a bunch of hard mathematical questions that fall under the Algebra I standards, but seem to be written to look as little as possible like what most teachers are actually asking students in their classrooms. Maybe someone out there is clairvoyant and can predict every question they’re going to ask. Another possible response is to take these questions and have students practice solving them. But that sounds pretty boring and not very useful for my students actually learning mathematics.
I don’t want to make an endorsement for PARCC. I’m not sure I’m crazy about the new test, and I’m definitely not crazy about the amount of time I’m losing to give it, or high stakes testing in general. But I think there’s real potential here to rethink what it means to prepare students for tests.
Before PARCC, we had a pretty good idea of what was going to be on the test. So teachers had a choice. Teaching deep, meaningful mathematics in a way that fosters understanding, or have students practice the specific skills and question types that would be on the test over and over again.
Now there’s no cheap way to get higher scores on the new test. Instead of trying to find some new magic test prep bullet, I’m going to do something different:
My plan: One day a week, kids will solve a few open-ended, difficult problems, that span our course and the mathematics that comes before it, justifying their reasoning and critiquing the reasoning of others. Might look something like this:
Kids come in, usual warm-up. We start with a scaffolded task that we start as a class, then release kids to finish on their own. Kids have some independent work time to produce the best work they can. When time is up, kids take whatever they have and share it with a classmate. I would love to develop a generic rubric for students to analyze each others’ reasoning. Students give each other feedback, and have a chance to improve their answers and justifications. After this round of feedback and revision, I’ll grab a few exemplar papers to examine as a class — looking first to make sure their reasoning is clear, then analyzing why their approach worked and what they did to communicate it clearly.
Round two, students get a second task to try all on their own. Go in cold, and do the best you can.
I’m excited about this for a few reasons. First, it’s a great place to use awesome lessons I haven’t found time for earlier in the year. I’m thinking in particular of Mathalicious lessons and Three Act Tasks — no worries if they don’t fit our current unit, let’s just do some meaningful math.
Second, it sends an important message — math is just math, doesn’t matter if it fits in this unit, or last unit, or last year. It’s math, and if you can’t do it, let’s help you and figure out how to make it so you can.
Third, I’m finally making good on my interest in Michael Pershan’s awesome writing on revision as feedback in math class. Getting students to seriously engage with their own thinking after the fac is a component of problem solving that is too often lacking from my class.
Finally, if I do this once a week, I can avoid doing any of the boring crammy, multiple choice test prep in the week before PARCC. I’m still putting my time in, just spreading it out beforehand — so hopefully it leads to some real learning.
I’ve got a lot to figure out about this. How to message what exemplar work looks like, what to use for a rubric, if/how to grade it, what scaffolds students are going to need so everyone can access the tasks. Plenty of work left to do. But I’m pretty excited about this idea.