Monthly Archives: July 2010

Learning Targets and Brainstorming

Status on Learning Targets…

  • Calculus: done
  • Statistics: not all the way through the text, but I’ve gotten through everything we’ve done in the class I’m taking, and I can add to it later
  • Trigonometry & Analytic Geometry: done, unless I get through things and have time for an extra chapter, at which point I’ll add in those LTs
  • Geometry: just opened the book (I’ll spare you a link to an empty document ;))

If anyone feels like giving me feedback, please do so. This has been a bigger task than I anticipated!

Now for some brainstorming…I have an idea for how I want to structure my units. For each unit, I want to put one or more real problems (of the WCYDWT variety) up on the bulletin board. The idea is that I will choose these Big Problems (don’t I come up with creative names?) as things that can be found using what they will learn in the unit. We’ll keep looking at them as we go through the unit, evaluating how our new knowledge can help us reach new understandings about the Big Problems. (I totally need a better name than Big Problems.)

What I want my kids to recognize is that math can be useful. I think it will also push them in the right direction for completing each semester’s final assessment, assuming I stick with that idea.

So once I get my Learning Targets finished, I think I will tackle the first couple of units for each class and figure out…

  1. Big Problems
  2. Assessments
  3. Instruction
  4. Homework/practice sets

I think doing that will help me feel ready to start the year, though the more units I can prepare ahead of time, the better. Oh, and I also need to work on my Policies & Procedures sheet (to explain things like my crazy new grading idea).

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.

Habits of Mind

This post is coming after a Twitter discussion with @jybuell, who is reading about the 16 Habits of Mind as described by Arthur Costa and Bena Kallick in this book (let me know if I linked the wrong book, Jason). It’s actually a collection of four books that were originally published separately. My school has been using these books as part of our School Improvement Plan, and I’ve read all four, though it’s been a while.

Briefly, the idea is that regardless of content, we should be teaching our students how to think. We want them to develop a habit of persisting when they don’t get something right away, not a habit of giving up. We want them to develop a habit of thinking flexibly, not a habit of wanting to know The One Way That Things Must Be Done. We want them to develop a habit of communicating with clarity and precision, not a habit of talking about, you know, um, stuff. (Wikipedia has an entry that lists all 16 of the HOM, for anyone who wants to see the list.)

Let’s look at that last one I mentioned and see a specific example. I once had a student who, in the middle of a class discussion, was on the verge of making a very good point, but was struggling to articulate it. He stumbled over his words a bit and then abruptly turned to me and said, “Mrs. D, can you do that thing where you take what I said and make it sound smart?” I was amused, but at the same time, a little ashamed. Although I use rephrasing a student’s ideas as a way to make sure that (1) I’m listening carefully and (2) they know I’m listening, I shouldn’t be robbing them of the opportunity to make themselves “look smart.”

What can I do instead? I can ask questions to encourage clear, precise communication, returning the responsibility for the communication to the student. When they give me something clear and precise, I acknowledge it, using the language of the HOM. Students are great mimickers, and once I started doing that, they did the same to one another. With an environment established where one can’t get away with unclear ideas, students correct themselves. Some take longer to speak, pausing as they internally make sure that what they’re about to say is clear and precise. Others will continue to speak out quickly, but will immediately follow up with, “No wait! I meant [more precise wording].”

Just for the record, I don’t have this down – I tend to go in cycles where I let my own bad habits (taking over for others) resurface. But when I’m being consistent, I do see these sorts of results.

I keep the HOM posted on a bulletin board or somewhere else in the room; the visual reminder is good for both me and the students. I remind them that these are habits they can use in any class, not just mine. It helps that the other teachers at my school are also working with this same idea, but even without that, I can ask them what they’re reading in English class and how they have (to continue the same example) used clear and precise language when talking about that particular novel.

One of my favorite habits of mind is metacognition, or thinking about your thinking. Sometimes during or after a discussion or activity, I will say, “Okay guys, let’s do some metacognition. Which habits of mind did you need to use to complete this task? Which habits of mind did Suzie just demonstrate? Can we try responding with wonderment and awe in this situation?” The more frequently I am doing that, the better responses I get, because they’re more comfortable with thinking about their thinking. And that is pretty awesome to see. :)

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.

Final assessment idea

I’m required to give a final assessment at the end of each semester. For my 9th and 10th graders, the final is worth 15% of the semester grade (with each of the quarters in that semester counting for 42.5%), and for 11th and 12th graders, the final is 20% (each quarter 40%). Not all that SBG-friendly, since it’s not something I can reassess.

BUT…we can choose to have the students do some sort of “exhibition” in lieu of an exam. This, I think, I can work with, and still stay true to the SBG philosophy.

So today I thought of something I could have the students do. It’s not totally processed in my mind, so there are probably pitfalls and things that don’t make sense. But here’s where I am with it so far.

  1. Students choose something they’re interested in. Ideally this is some sort of issue that is important to them.
  2. Students find numbers related to their issue. They may have to look online, they may have to go somewhere and take their own measurements, they may have to call someone in the field to ask for numbers.
  3. Students perform calculations on the numbers. At this point it will tie in with the Learning Targets for their course that semester, and they will have to demonstrate and explain how they have used a certain number of concepts. (Certain number from each unit, maybe? Not sure.)
  4. Students interpret their work. What does their work do to help us understand the issue better? Does it help us develop possible solutions? What action can they take now that they have done this work?
  5. Students develop a way to present their work – maybe an oral presentation, maybe a backboard for a “Math Fair,” I’m not sure yet.

Although the product (which would be a presentation of all the work) would determine their grade on the “final,” it’s something they would be working on over the course of the semester. I imagine setting due dates for the different parts of the project, requiring students to plan out what data they will look for before they go and get it, etc.; I’m not planning to throw this out there and say “do it.” I also expect that I would offer individual student conferences (formal and informal) so that they could get feedback on their work, make sure they really are demonstrating mastery of LTs through it (there’s that opportunity for reassessment), etc.

What do you guys think of this as a final assessment?

Starting to make LTs

Today has not been particularly productive; Little Precious had a fever of 104.7 at 2:30 this morning, so I have spent the day (after my class) taking her to the doctor and subsequently hanging out with a sick and clingy toddler.

Yesterday, though, I got through 3 chapters in the calculus textbook and set up Learning Targets. It feels like I have too many of them, but I don’t know that I really want to combine them, because I do want students to learn each item on the list. I borrowed heavily from one of the sample syllabi (pdf alert) that the College Board has up for AP Calc AB to create the Learning Targets; the course outline is aligned with the text I’ll be teaching from, so I used that as a starting point and just adapted a bit.

So take a look and let me know your thoughts on the first part of my LT list. I am thinking I’ll end up using problems that address multiple LTs. And…there was something else I was going to say here, but a few interruptions from Little Precious have made me forget what it was. Oh well.