Thursday, December 5, 2013

Struggles and Frustration

Today was a hard day. 

First, I was hoping we could develop the definition of a tangent line in our shortened class period. It's a discussion I've done every year, and it can go very quickly. I give the girls these 6 pictures of tangent lines, carefully chosen so their previous definition of "touches a function at only one point" will not hold, and tell them that they are all pictures of tangent lines. Their job is to come up with a definition of what a tangent line is. 

Graph A
Graph B

Graph C
Graph D

Graph E
Graph F

 The first problem is that none of them had even taken the time to look at these pictures ahead of time, like I asked them to. They came in cold to the discussion. Of course, I didn't realize it until I started moving around the room, noticing that there was nothing written in their notebooks. No wonder it was like pulling teeth to get them to list anything. 

The second problem is that when a student offered up "It touches at only one spot, it doesn't go through..." and trailed off, I jumped in with, "What about graph C? Or E and F?" Centering myself in the conversation seems to be the fastest way to kill it. 

I tried asking a question and just waiting. And waiting. And waiting. Then, I'd cave, and ask another question (or a variation on the last one). I still got blank stares. Thank God for the three girls who were willing to eventually speak up.

On the bright side, one student asked if I could give them a definition of a secant line, so they could work from there. Here's what I gave them: "A line that cuts through two points on a curve and whose slope equals the average rate of change of the curve between those two points."

Eventually, I told them to think about these bullet points we'd developed and come up with a statement about what makes a tangent line different from just a secant line:

  • Touches the curve at at least one point
  • Touches but doesn't go through (what about E & F?)
  • Some tangent lines can also be secant lines (B, C and E, but not F)
  • Slope?
  • Terminology: point of tangency (See D)

I had to end the discussion a little early, because they have a take-home assessment on proving functions are continuous that is due tomorrow, and they asked for time to ask questions on it.

Enter frustration #2. On both sides.

They're somewhat upset that they don't have any examples just like these problems to refer to in their notes or practice problems. No, they don't. Instead, they have lots of examples and practices problems about different aspects of continuity that they can pull together to develop an understanding of the functions they have to prove are continuous. They get frustrated because I'm not pointing them to an exact template to follow. Instead, I'm suggesting that they think about what they know about what continuity and think about how it can be applied to these unusual functions. 

Who said take-home tests were supposed to be easy?

Here's what I want to say to them. I have the email written, but I'm not sure yet I'm going to send it.

Struggle is good. Embrace it. Work through it.
You have all the pieces you need. Now you have to put them together. Think about what you know about these functions. Think about what you know about continuity. Think about what you know about how properties and theorems work: conditions to be met, results you get when they are.
So the question of my day is, how do I teach them how to think and synthesize information? How do I get them to engage in the activities that will allow them to practice those skills instead of begging to be told "the answer" or "the method"?

Monday, May 13, 2013

"Temporary grades"

We just had conferences and mid-quarter report cards, and the Galileo Girls are now focused on their grades again. There's relief that reassessment scores for each topic replaces the old, but they're also recognizing the flexible nature of their grade.

In this class, I haven't been giving them weekly voluntary reassessment opportunities. I've been choosing what gets reassessed when. To balance this out a bit, I've provided a voluntary opportunity for reassessment: a 5-photo project on the course topic of their choice. (See below - I took AAPT's photo contest idea and ran with it.) They even have the choice if they're going to do it at all. One student came in see me about it after school and wrapped up her questions with, "And this is just temporary help for my grade, right?"


Yes, love, it is temporary, in the same way that every assessment you've taken thus far is temporary, and every one will be, until the last one on that topic. But the point is that you're going to show me how you've improved your understanding of the topic or your ability to explain your understanding.

It's about growth and feedback and then more growth.

I have to do a better job communicating this to them. I have to help them change their outlook on what grades mean (at least in my classroom) and what those comments on assignments that are returned to them are for.

The project:

Tuesday, April 23, 2013

My Year with Standards Based Grading (part 1)

I had big plans. I was ready and rarin' to go. I had a shiny new blog to talk about my shiny new grading system.

I made it to October. After that, blogging always got pushed off as other, more immediate, things came up. 

This is the last post I started:

"Several things are spinning in my head as I think about how this new grading system is working. I'm not thrilled with how I go about grading the quizzes, because of how long it takes. I struggle" 

I can't remember how I was going to finish that last sentence, but I think it sums up my year as it stands. I struggled. I chose to try a whole new grading system while I was still working on my masters degree, and I'm still not sure if it was a wise choice. Balancing my time between work, school and family is hard normally. Changing my classes into SBG classes was like adding a 4th ball before I'd really learned to juggle 3. On the other hand, I was unhappy with what I'd been doing. The philosophy of SBG clicked with me. I was happy and excited with my planned structure. There was an overall sense of change and growth in our upper school because we had created a think tank of faculty to determine how we needed to change our school and curriculum for the future so that we would be competitive and meeting our students' needs. It seemed like it was the right time to revamp my classes. I'm not sure that I could have waited 2 more years until I finished my degree to implement these changes. I wonder if I wouldn't have lost my drive and excitement in that time. 

Really, though, the question of "should" or "should not" is a moot point now. I did; it was hard, and now I'm making the time to reflect on it. 

I know I did one thing right. Whenever I thought of something I should write about, I scribbled a quick note on a slip of paper and set it aside on my desk. It's time to turn those prompts into real posts.