After an inexcusably long delay, the Better Assessments blog is now up and running. Head on over to have a look at Stephanie Reilly’s Algebra 2 quiz on exponents and adding polynomials.
Add your voice to the conversation by asking questions and providing feedback in the comments, and consider submitting your own assessments while you’re at it! Details (including alternative ways to play) are over at the blog.
I recently joined a conversation on Twitter about pathways through the Common Core State Standards and potentially-shifting opportunities for advanced students. It seems I’m not alone in wondering how a transition to the CCSSM will play out in our actual classrooms and departments.
I teach in a very small math department (two members for the entire 7-12 program), so I am particularly curious to know how debates are unfolding and plans are taking shape in other school districts (like yours!).
For districts both large and small, I imagine it would be helpful to know the questions others are grappling with, as well as the solutions they’re proposing to the many challenges that will arise as we make this transition. If you’re interested in adding your voice to the conversation, drop a line in the comments describing as many of the following as you please:
Since I’m not interested in highlighting our approach as anything worthy of emulation, I’ll share my school’s plans, questions, and so forth, in the comments.
Thanks in advance to all who chime in!
Finals week often has awkward down time for students. With that in mind, I made a game for my middle school students to play next week.
I’d love some feedback on the directions, the scoring system, and the game itself.
And if you play with your students, let me know how it goes!
The decision to award more points for even values was arbitrary (I could just as easily have chosen odds) but also intentional (I want to motivate students to observe patterns/behavior and use their observations to target certain values or types of numbers).
More points for higher numbers was un-arbitrarily intentional (I want to motivate students to tinker with larger numbers).
I want students to hunt in a clearly defined, finite space, hence the 1-100 boundaries. Good idea? Bad idea? I’m not sure yet. I’ll let you know how things go next week.
Howdy, Internet. Thursday I asked this:
Suppose a school is transitioning to CCSS with an integrated sequence in 9-12. How do you remediate for students who fail, say, Gr 9 course?—
Michael Fenton (@mjfenton) April 25, 2013
I immediately received a link to a helpful article from @reimerpaul. Shortly after that @wahedahbug and a few others expressed interest in having a larger conversation about how best to remediate for students who aren’t really ready to move on to the next course in the CCSSM sequence.
(For the record, at my school we’re going integrated in high school, but I think best practices/wise policies regarding remediation can easily apply in either pathway.)
I really want to know three things from as many people as are willing to share:
If you’re interested in reading responses, and even contributing your own, head to the Google Doc!
For background, go here and here.
Once you’re ready to play, do this:
I’m a little conflicted about whether there should be a deadline for submissions, so I’ll let you self impose one if you find that helpful. The idea is to submit something relatively soon so we can move on to the next steps (an ongoing discussion centered around the submitted assessments).
More details about the structure and expectations for the discussion will come soon. For now, get those assessments ready!
P.S. Details regarding the other major component of this project—gathering assessment-related resources and posts here—will also come soon.
P.P.S. If you have suggestions for how to improve the form (#4 above) or the submission process, drop a line in the comments or send a note to @mjfenton.
If my WordPress stats reveal anything, it’s that the blogosphere likes me best when I’m in reflecto-panic-crisis mode. Well, thanks to a post from John Scammell over at Zero-Knowledge Proofs, I’m back at it. The subject this time: Homework.
I’ve spent a lot of this school year weighing the usefulness (or lack thereof) of my various classroom practices. I lecture too much, my students spend far more time doing more “exercises” than “problems,” my assessments need some serious work… The list goes on. In recent months I’ve thought occasionally about the effectiveness of my homework policy. John’s post has me thinking about it again, and this time I don’t believe I’ll be able to rest until I’ve sorted out what my approach should look like and how I’ll get there.
In my first year of teaching, my homework sins were many. (1) I tried to grade it all myself. For about two weeks, anyway. Then I tried to grade 5 problems per assignment, all myself. Still terrible, and now for twice as many reasons. Eventually I “outsourced” homework grading to the students themselves and a TA. Better in some ways, worse in others, but still broken, because… (2) I would allow the start-of-class homework discussion to last 15 to 20 minutes (out of a 45 to 50 minute period). Horrible. Shamefully horrible. There was then never enough time to address new material, which meant I could expect widespread struggles on the next homework assignment, which meant another long homework discussion to start class the following day, and on and on. For me, it was wash, rinse, repeat at least 150 times per semester. (3) “Preparing students for the homework” became the driving force of all my instruction. Which was weird, because I was the one who selected the homework, but then once I did that I felt like I was no longer in control. The assigned homework was in control. When we weren’t prepared for the sometimes well-selected, sometimes poorly-selected assignment, I felt like the day was lost. I would occasionally send kids home to suffer through the assignment anyway (lots of frustration and tension and guilt mixed in with that approach). Other times I would postpone the assignment (which was always received with loud applause from students) and consider myself a failure—at least for the day—because the lesson didn’t “work” and we were “falling behind.”
It would take thousands of words to describe all of my imperfections as a teacher. But I could probably use almost as many to describe the ways I’ve grown over the past nine years. I may not be particularly good at this teaching gig, but I’m better than I used to be.
I feel like I’ve successfully addressed the major issues outline in (1) and (2) above by streamlining our in class “homework check” routine. Of the many things I’ve tried over the years, I’ve been reasonable happy with two approaches: Hard copies of solutions (one paper per pair of students) or slides of solutions, with either method placed right at the start of class. There have been advantages and disadvantages to each approach, with each growing larger or smaller depending on the particular group of students, but the common result has been a start-of-class homework routine that usually takes between 2 and 4 minutes and provides every student with feedback on every attempted problem as “immediately” as I can manage given my available tools and my limited skill set.
Issue (3) is an ongoing struggle, and something I hope to consider further. Maybe it’s related to what I discuss below, maybe not.
For all the improvements I’ve realized, there are still some glaring weaknesses in my current approach to homework. In my honors classes, almost all of my students complete the assignment each night, but some of them spend a ridiculous amount of time on it. Is this the most effective way for them to learn? Is this the healthiest way to spend their evening? Is there a way to transform what I do in the classroom so that they end up learning and practicing at least as much as they do now, but without my stealing so much of their non-school time with school-related things? (If you think the answers are not “No, no, and yes,” you are hereby required to explain in the comments.)
Should I do away with homework all together? Posts like John Scammell’s make me think I should. But then most of my classes don’t have the dismal homework completion rates that John and many other thoughtful teachers point to as one advantage of the no-homework approach. Will I use Dan Meyer’s 2007 approach? Or his 2008 approach? (Anyone know the latest thoughts out of Camp Meyer?) And while we’re linking to blog posts about assigning or not assigning homework, are there other posts I should read?
In all likelihood, my course responsibilities for next year will include AP Calculus AB, Honors Precalculus with Trigonometry, Honors Algebra 2, and Honors Algebra 1. In these classes, the homework completion rate is through the roof, plus or minus 3%, and (as I’ve shared above) I think many of the students benefit from the practice. It would be tempting to say that my homework policy is “good enough” for these classes. The students will do the work, they’ll remember to bring it to class, they’ll grade it efficiently, I’ll assume they’re getting the feedback they need to draw conclusions about their strengths and weaknesses, and that together we’ll be able to decide how to proceed from there.
One of the classes I don’t expect to teach next year is regular Algebra 1. This year’s section of Algebra 1 has been my most challenging ever. Among other things, my homework completion rate has been discouraging and not at all like the majority of my classes. I would guess that less than 50% complete the assignment each night, and for those who do only about 20% (or less) benefit from the practice. For a class like this, my current homework approach isn’t working. They need (and deserve) something better, something more thoughtful, something less frustrating, something more effective, something like what John Scammell describes in the post I mentioned above.
Does the fact that they aren’t served well by my current homework system mean that my other more compliant classes would also be better served with a different system? Or does the high completion rate mean I should leave things the way they are for these classes?
Should I have one approach to assigning homework for all of my classes, irrespective of the habits of an individual class? Or should I tailor my policies to the tendencies of my students, and define effectiveness in relation to the particular set of students?
Clearly I need some help sorting all of this out. Thanks in advance for anything you can offer in the comments.
“A Day In…” posts are averaging 1997 words per post. Holy wow! Time for a shorter one.
3rd Period, Wednesday, April 3, 2013
Honors Algebra 1
Bells rang. Sets were found. Homework was checked. Estimations were made, reasons were given, the answer was shown.
And then, the lesson began. (Full disclosure: I wrote the lesson a year after reading this, and was even more influence by a jigsaw-puzzle-building activity—solo, solo, then tag-team—I heard about from some friends who work here.)
Me: “Does anyone have a magic phone with a stopwatch?”
Student R: “I do.”
Me: “Awesome. Get ready. (Pause.) Ready?”
Student R: “Yep.”
Me: (Walking to the front of the room with my bucket of binder clips…) “The rules are as follows: I am allowed to use my left hand only, one clip at a time. Got it?”
Everyone: “Uh… What are you talking about?”
Me: “Ready?”
Everyone: “Okay, we still have no idea what you’re talking about. But sure, whatever.” (This is a paraphrase.)
Me: (While dumping the binder clips on the floor…) “Student R, give me a countdown.”
Student R: “3… 2… 1… Go!”
My task then becomes clear to the students, as I proceed to pick up and toss the binder clips into the bucket as fast as my left hand will let me (one clip at a time, mind you). I’m right-handed, so this takes a while. 100 seconds to be exact. (Two years in a row, 100 seconds exactly.)
It gets a little awkward after about 30 seconds (70 seconds to go!!!) so I banter with the students for about 20 seconds, invite them to hum the Jeopardy theme music for another 30 seconds, and ask them to cheer me on for the last 20 seconds. Some oblige, some do not. (Hey, that’s not unlike the rest of my experience in teaching!)
At that point we record my time. I then dump the clips on the group a second time. I ask for a volunteer. (“Thanks, Student J!”) This brave volunteer then picks up the clips as fast as he can using two hands, one clip at a time (per hand). His time is 59 seconds. (60 seconds last year.)
Then the fun part, essentially stolen from the world of Three Act Math Tasks: Students make an estimate for how long they think it will take the Fenton-and-Student-J-Tag-Team to pick up the clips (same individual rules apply).
Guesses are made, clips are dumped, the stopwatch is readied, and the clip cleanup commences.
We’re an amazing team, so we finish the task in 40 seconds.
From that point the lesson is rather predictable, so I won’t bore you with the details (though we did have some great conversations in this “predictable” portion because of the seeds planted in the introduction).
The lesson was fun to teach, and the kids were definitely engaged.
I love the extra buy in from students that I get simply by asking them to guess before we measure, calculate, etc..
All the guesses were reasonable! No one offered the absurd (yet tempting, for the totally lost) answer of 100 + 59 = 159 seconds. Why? Because the setting/context/problem type was set before the students in such a tangible way. “Of course the tag team will finish faster!”
The lesson doesn’t do a good job of building on the reasoning students were engaged in during the introduction once we transition to a search for more efficient solutions. By no means do I dive headfirst into a “watch and mimic” approach. But the students who had no idea how to approach the problem in the first place (i.e., the students who could do no more than make an educated guess) are still unable to do more than make an educated guess.
There is a decent amount of semi-downtime for students in the first 10 minutes of class. The advantage here is that we create the data as a class. The disadvantage is that only a few of us are actually involved in generating the data. I don’t have a fix for this yet, but I would like to involve more students or decrease the downtime (or both).
Immediately after teaching the lesson I began brainstorming improvements for next year. This is my attempt. My goal was to create something that would help students develop two efficient approaches that emphasize/promote understanding in the midst of finding the solution, but that didn’t require me to be a central part of the conversation while it unfolded.
I was happy with the handout and excited to use it sooner rather than later, so instead of waiting until next year I presented it to my students the day after the first lesson. I was pleased with the results, as students learned efficient methods without abandoning their reasoning. (Sadly, this abandonment-of-reason-for-the-sake-of-efficiency happens too often for many of my students, especially when we transition from estimates and arithmetic approaches to algebraic ones.) And while they didn’t develop the methods entirely on their own (to expect that of them at this point in the year would require that I’ve expected similar things all year long, which sadly I have not), there was a lot of great conversation followed by some favorable assessment results a few days later.
Need some inspiration before you head to the comments? Consider responding to one or more of these:
