Tag Archives: learning

Moving toward more formative assessment

It’s been a while since I’ve had a chance to post! I’ve been doing some thinking about my classes in general, how SBG is going, changes I want to make in the coming semester.

A few people have asked me, now that I’ve got a semester of it under my belt, how do I like standards-based grading? The answer: I love it. I still believe what I did at the start – that SBG is a fabulous tool both for my students and for me. Students are aware of exactly where they stand on specific concepts. There’s no question of “but you didn’t say this would be on the test!”, because the Learning Targets are clearly identified for them. They seem to see more clearly that they are the ones in charge of their grades, because they are the ones in charge of their learning. I get to make sure kids demonstrate clearly that they understand the concepts, and I can hold them to a high standard without worrying about what happens if some people haven’t met it yet when we have the quiz. Parents are loving this system – I’ve had a number of them say that they might have enjoyed math in school had they had a teacher who graded like this.

All that said, I definitely have places to improve how my classes work, and I’ve been working on how I can better use this fabulous tool to promote student learning. My biggest concern is that I’m not giving my students enough feedback before they reach a quiz. I’ve been doing whole-class feedback, but not individualized, and that’s just not working. I don’t like waiting until the quiz to discover that the quiet half of the class all had the same misconception about a particular idea. I still want homework to be something that the students are in charge of (meaning it’s practice, not graded, and the students determine how much of it they need to do for their own personal learning).

I’m pretty sure I’m heading in the direction of a daily warm-up. My thoughts about how this will look: I’ll have half-sheets of paper ready for each class, and students walk in and pick one up, immediately getting started on it as they reach their seats. Each warm-up will look something like this (with the parts in bold being different each time):

When they finish, they turn it in, and then they look back over their homework so that once everyone’s done the warm-up we can review it. (This will have the added benefit of helping me structure my class time better. I have a tendency to let time be wasted, and I’m really not okay with that about my teaching.)

I’ll review their work each day. The homework completion goes in an ungraded category in my gradebook, so that I have a record of what they’re getting done (the warm-up sheets will also save class time in that they’ll just write it down and I’ll record it later, rather than asking each person at the start of class). I’ll write comments on their work so that they have individualized feedback, and this way I will have a better idea of whether there are some widespread misconceptions going on, so I can address them in my teaching. I want to use more formative assessment, and this is a step in that direction.

Things that worry me: I tend to get into a what-am-I-doing-next-period sort of place, especially given that this is my first year teaching any of these classes. This daily warm-up thing will require me to stay on top of things much better, given that I’ll need to write one for each class each day, but I’ll also need to read and respond to each student’s work each day. This scares me. I’m afraid I won’t be able to sustain it. But I can’t not try, because I really think this is something my students need.

I’m also worried about the self-check aspect of it, as I’m not entirely sure what I’m going to do with that besides making them think about where they are. I know that they need to be able to self-assess so that they’ll be able to identify their own areas of strength and weakness so that they can best use their study time. I guess the self-check part of the warm-up sheet is a way of starting a conversation? I don’t know. I don’t want it to be just something they fill out and then nothing happens.

Anyway, I’m out of blogging time for today. I have more ideas for the coming semester, but this is the biggest one, so it’s a start.

Advertisements

Wait, what?

I hate it when kids seem to really get something, it works great for them, they can do the problems…and then they ask me a question that shows me they missed the point of the whole thing.

My calc kids are taking a quiz over the precalc review stuff. One of the questions asks them to find a natural logarithm regression equation for a set of data. Should be no problem – they’ve been doing great with that.

But one of them just came up and said, “I found the equation, but when I look back at the x-values from the data we were given, it doesn’t have the right y-values.”

Now, I know it’s not the stats class, but still, I didn’t realize that they didn’t know what a regression equation is all about. I’m glad to realize it now, but I hate that I was just having them find regression equations without understanding what they were doing. Sigh.

So, what to do about it? I think I need to be more careful, more deliberate, about making sure they understand concepts that I think should be prior knowledge for them. I need to stop assuming that they know something because they can execute an algorithm; that doesn’t help them learn, and it will end up causing me frustration down the line when I want them to build on a concept they never had to start with.

Two Weeks In: SBG Thoughts

I’m liking this whole SBG thing. Here are a couple of reasons why I like how it’s working so far.

1. I feel like I can expect clarity from my students.
When grading in the past, I often found myself interpreting students’ answers. “Well,” I would say to myself when reading a response that could have been clearer, “he’s saying this, but I’m pretty sure he means this, so I’ll give him credit, or only take off one point.” That was something I didn’t like about myself as a teacher…but at the same time, if the question was worth 5 points, marking it completely wrong would hurt their grade. What if they really did get it, and they just didn’t make that clear? Not good for me to take points away, necessarily. But on the other side, what if I decided they got it, but they really didn’t? I hated those times when a kid would say, “Really? I got some points on this question? How’d THAT happen? I just put down a random guess!”

Now, though, I don’t have to worry about the points. A geometry student wrote down that the pattern for a sequence of numbers was “divide the number and its quotient by two, then two again.” I was pretty sure he understood that the pattern was to divide a term by two in order to get the next term, but that wasn’t quite what he communicated. So I gave him a score of 3 on that Learning Target (there were other aspects of the problem wherein he demonstrated better understanding, but he wasn’t all the way there). He came back for a reassessment and showed me that he did understand it clearly. He wasn’t stuck with a bad grade, and I wasn’t stuck having to guess whether he got it or not. Taking the focus away from the points lets me demand excellence in their communication skills, and so far, they’re rising to the occasion.

2. I can see clear relationships between students’ homework effort and their understanding.
I am keeping track of homework completion as a gradebook category that I’ve set to 0%, and I just mark each assignment as 0 (less than 25% done), 1 (25-75% done), or 2 (more than 75% done). With the scores on quizzes separated into Learning Targets, it is so clear that there’s a connection between doing the homework and understanding the material. I love how this system lets me see that the kids who scored low on Concept X are the same kids who got 0’s or 1’s on the homework for Concept X. Much clearer than a score on Test #3.

3. Students are taking charge of their grades.
They aren’t asking for extra credit or how they can bring their grade up. They’re coming to me and saying, “I want to have a reassessment for Learning Target 2, the one about domain and range.” Some of my high achievers are shocked to realize that they got a 75% on something (if they scored 3 on my 4-point scale), but I just say, “You know what to do if you’re not satisfied with that,” and they say, “Right. Reassess. Can I come in at lunch on Tuesday?”

—–

So, yeah, I think the SBG kool-aid tastes better and better. Some things I need to work on:

A. Broader Learning Targets.
I knew when I was writing them that I was probably focusing too narrowly, but now that I’m walking it out I’m seeing how I can make LTs that are more broadly defined. This may be something I just make notes to myself about and then change next year, since I already made up all the LTs for the year. I have decided at assessment time to skip a Learning Target here and there, but I think the overall restructuring is something I’ll just do next year.

B. More frequent assessments.
I have never been good at remembering to give frequent quizzes. I’ll plan them, and then forget to announce them, and then it ends up being too close to the test over the whole unit, so…yeah. With SBG, though, I really want to give more frequent but shorter assessments. The biggest thing really is remembering to announce it to the students. I don’t know why that’s always been such a challenge for me. Right now it isn’t helped by the fact that I’m still figuring out how to pace things with math.

Those aren’t the only things I need to work on, but they’re the most glaring in my mind right now.

Listening to the Inner Teacher

I’m probably not the only one with an Inner Teacher – that part of me that wants to go into Teacher Mode even when I’m not in the classroom. Sometimes my Inner Teacher just wants to tell store cashiers to spit out their gum. But sometimes she wants to make sure people learn.

My Inner Teacher won out today in my statistics class. There’s this guy who has been coming in to class with a look of defeat; he asks questions, but he keeps struggling to understand. The past couple of days I’ve heard him asking the instructor about the tutoring resources that are available on campus, asking if there are any videos that she can suggest to help explain the concepts, etc.

I had been struggling with the desire to offer him help versus the desire to avoid doing something weird/rude/othernegativeadjective. As much as he was asking the instructor for help, he wasn’t asking me, so I didn’t know how he would take it if I offered. But today after class, I caved to my Inner Teacher and asked the guy if he wants help from me. He seemed appreciative of the offer, and I’ll be working with him after class on Monday. I hope I can help him understand.

Lessons from Statistics

(Refresher background info: I am taking a statistics class at the local community college, since I will be teaching statistics in the coming school year.)

I’m finding the content in my statistics class to be interesting and logically intuitive, and I’m really looking forward to teaching it. The class itself…well, I kind of feel like a spy in there, gaining insights for teaching as I play the role of student. So here are some things that I have learned (or have had reinforced)…

  1. Don’t take over. Allow students to build the connections for themselves.
  2. If someone asks for clarification on how to do something, make sure you understand which part they’re struggling with. If they can’t articulate it for themselves, listen as they continue to ask questions while you go through the process again.
  3. If someone asks a question about application, extension, etc., do not dismiss it as “not what this class covers.” Encourage thinking! It’s even okay to say, “Let me think about it / look at some resources / etc. and get back to you,” or, “I would love to discuss that with you, but can we talk about it after class so we don’t lose our train of thought here?”
  4. Be willing to admit when you could change a question, example, etc., to make it better for the students. Value feedback.
  5. If you tire of hearing from a particular student (or of answering questions in general), don’t let it show. Not all students are concerned enough about their learning to make sure they keep asking questions anyway. Care about student learning.

There may be more to come…three more weeks of the class.

Thesis work

Assuming that Little Precious* does not spike a fever tonight (which is entirely possible with her), I should be going back to my thesis work tomorrow following my statistics class. What is my thesis on? So glad you asked! :)

I am looking at four French mathematicians from the seventeenth century (Rene Descartes, Girard Desargues, Blaise Pascal, and Pierre de Fermat). I am examining their mathematical writings with an eye for the pedagogical techniques they used to describe their ideas, and seeing what (if anything) those mathematical writings reveal about their beliefs about pedagogy.

What’s that? Your eyes glazed over? Sorry about that. I think it’s interesting, and I won’t make you read it. ;)

Anyway, I am just at the point where my prospectus has been approved by my committee and I’m coding the texts for instances of particular pedagogical techniques. I have a set of questions with which I plan to analyze my data once it’s collected. I’m hoping I turn up something interesting. If not, well, I’ll be able to say that there’s nothing interesting in that direction. ;)

The goal is to finish the thesis by the time my school year starts back (mid-August), defend early-Septemberish, and then receive my Master of Science in Mathematics Education in December. The summer has included some unexpected things that the goal didn’t take into account, but I’m not counting it as lost yet.

*Her name is not actually Little Precious, just for the record. This is a pseudonym for my 17-month-old daughter. I just wanted to disclaim in case anyone thought I had named my child Little Precious.

Reading too much into the question

More thoughts on my statistics class from today. We were going over some review questions, and I said that one of them didn’t have enough information for us to determine an answer. The instructor responded,

You’re reading way too much into the question.

Well, no, I really wasn’t. It was a poor question. I’m really not sure why she didn’t just acknowledge that it’s a poor question – it’s not even a pride thing, because these questions are from the textbook publisher, not from her. And even when I am the one who wrote questions, I’ve told kids who challenged them, “You know what? You’re right. I could be asking this question more precisely.” And I make a note to improve the question for the next time I come to that material.

So the first part of my point here is, it’s okay to recognize that a question/assignment/whatever is not the best and could be improved. I think my students like knowing that I will receive their critiques (delivered respectfully, of course) and consider their feedback. I know that I didn’t like feeling like I wasn’t being listened to, being told to just write down the “right answer” and move on.

But the second thing I wanted to say in this post is a question I thought of as a result of this experience. Is there a point at which it’s okay to tell a student “you’re reading too much into the question”? Obviously we want to stop kids from saying,

“Well, Johnny won’t have ANY apples left after he gives 3 to Suzie, because right at that moment Suzie gets turned into a ZOMBIE, and she doesn’t care about the apples anymore but just wants to eat Johnny’s BRAAAAAAINS, so Johnny figures life is more important than apples and he drops the apples so he can run away. Will he survive Zombie Suzie’s attack? Just wait until I turn in my next homework!”

Because that would just be silly.

But. There’s a lot of good thinking that students can do in between “just give the answer you know I’m looking for” and the zombie scenario. I’ve read several bloggers talking about WCYDWT (What Can You Do With This), which is all about posing new problems, digging deeper into what’s right in front of you instead of just relying on the (possibly/probably poorly written) questions in the textbook.

There probably are good occasions for telling a kid he’s reading too much into a problem. But I think we might jump there a little more quickly than we ought to sometimes.

Going back in time?

I’m taking a class that started today. I’ve never taken statistics before, but I’ll be teaching it (one section that will probably have both AP and General kids) in the fall. So I thought that taking it would probably be a good plan.

I’m still processing the reasons why, but it felt somewhat surreal to be in a 2000-level course again. I’m looking forward to learning statistics, definitely; I have thought for a while that I would like to take a course like this. But actually sitting in the class just feels strange. It’s very different than the classes I’ve been in over the last 3 years as a master’s student, and it actually feels much more like I’m back in high school (except the part where the homework is all online).

I’ll have to continue mulling this over. It feels like there are things I can learn through this about becoming a better teacher, but I’m not completely sure what those things are yet. Maybe it will become clearer to me as the next few weeks go by.