Monthly Archives: September 2014

A Flop

Had a pretty big lesson flop today. I was frustrated at the end of the particular class, but I’ve thought about some things I can do to improve. Fortunately, I’m on an A-B schedule, so I get to re-do the lesson on Monday with another class. (My A-day kids always get the flops.)

I’m almost too embarrassed to write about the lesson because so much was wrong with it. I am tweaking every part of it for Monday. I thought about scraping the main task altogether, but it’s a good task that was ruined by poor implementation.

First, I am not going to assume the students remember how to do something even though I know they studied it last year. Flying through one example and saying, “This is familiar, right?” isn’t going to cut it. It turns out what they learned last year was a “trick” anyway, so I definitely need to do a better job explaining explicitly what is happening conceptually.

Second, I am not going to throw a handout at them and expect them to get to work. I am going to do a better job explaining the task and modeling how they should get started. I just read the phrase “model curiosity” while surfing some blogs, and I think it perfectly describes what I need to do at the beginning of a task.

Third, I’ve got to follow through on my behavior expectations. I had too many non-participating, off-task students. Worst of all, I let them behave that way. I let them get out of their assigned seats. This is my problem. I don’t like telling people what to do. I just want them to do the right thing. But I have to remember that high schoolers are still kids, and they still need guidance. Basically, I’ve got to toughen up. I’ve got to enforce my expectations.

Fourth, I want to do a better job structuring group work. I think this will also help me with my classroom management issues. I think I need to bring the groups back for a whole-class check-in more often. If there are four parts to the task, then I think I should bring everyone back together to go over each one before we move on to the next. In contrast, today I just said “do it” and consequently lost a lot of people, who never came back when I tried to go over everything at the end. So, on Monday, as students make progress on part 1, I’m going to bring us back together and have groups share. Then I’m going to explain part 2 and let them go. Then I’m going to bring them back again for a whole-class discussion on part 2. Then I’m going to explain part 3, and so on.

The tricky bit will be bringing everyone back. They’ll want to keep talking to their friends, but I need them to pay attention to me or whoever is sharing. I really need something to get everyone’s attention back. Maybe a timer, but students might work more slowly or more quickly than I anticipate. Another new teacher, who is in the English department, shared with me her method for bring everyone back. She simply says, “I need everyone back up here in 3.. 2… 1.” That sounds magical to me.

I can probably pull it off. I can do anything, right? I think what will work for me and for my students is to explain to them at the beginning what it’s going to look like. I will explain that I will let them work on part 1 for a bit, but that when I say “I need everyone back up here in 3, 2, 1” they need to stop where they are, turn to the front, and listen because we are going to share ideas at that point.

Overall, I think I need to be a better communicator. Specifically, I need to be more explicit with my directions and my expectations. More explicit with some of my explanations of content would also be good. Again, these are kids, not adults. They are learners, not experienced mathematicians. They are relying on me to communicate well.

1 Comment

Filed under classroom management, group work, planning

Always, Sometimes, Never

I debated some Always, Sometimes, Never statements with my Geometry kids today. In groups, they had to choose the word that they thought went in the blank, as well as draw a picture to explain their choice.

Some example statements (taken straight out of our textbook):
Two planes ________ intersect in a line.
Lines ________ have endpoints.
Lines that are not parallel ________ intersect.
Two points _________ determine a line.

That last one created some interesting discussions, particularly in my last period. Many students wanted to put Sometimes in the blank. I didn’t look at the textbook’s answers, but I assume the authors wanted Always in the blank.

Why did so many students think Sometimes? Well, I think the statement was kind of confusing to them. What does it mean to “determine” a line? Does “a” line mean one line or does it many any line? I tried to resolve the matter by putting two random dots on the board and drawing a line through them. “Look, I can draw a line connecting any two points.” Not particularly convincing.

The students then told me to draw a line going through each of the points (parallel lines, for example). “See,” they told me, “there’s two lines, not a line.” I didn’t really know how to respond to that. I told them yes, I can draw different lines through each point, but only one line will connect them.

Well, I think I convinced them that any two points could be connected with a line, but we just left the Always, Sometimes, Never question unanswered. Which is okay. Of course, some kids insisted, “But what’s the answer?” and I replied, “Well, I think it’s Always, but I don’t think it’s totally clear.”

Perhaps the answer would have been less ambiguous if the original statement was Two points can _________ be connected with a line. But that statement seems way less powerful. So now I am intrigued by the word “determine”. I definitely think it’s important. It’s hard to explain to the kids what is meant by “determine” though.

One instructional difference I would have made during the activity was to require new people to be the writer and the speaker for each statement. In a couple groups, it was very obvious that two or three students were doing all the work while the others checked out, so some sort of rotation would have been smart.

I want to start the next class by playing Sarah Rubin’s Draw It game because some of the drawings I saw today were definitely off the mark, but that’s okay. Visualizing lines and planes and space can be tricky. I love seeing their eyes widen when they begin to “see” it.

Leave a comment

Filed under conversations, Geometry, group work

Factor Craze

I didn’t have the greatest teaching day today, so I thought I’d try to remind myself that I CAN do this teaching thing by describing an activity from a few days ago that was successful.

Factor Craze, which I think I found via Fawn Nguyen, is one of NCTM’s monthly “Problems to Ponder”, and it asks:
Which numbers have exactly three factors?
Which numbers have exactly four factors?
Which numbers have exactly five factors?

This problem was a great introduction to factoring with my FST (2nd half of an extended Algebra 2) kids. They saw factoring last year, but this year I wanted them to really understand how they were coming up with the equivalent expression instead of following a list of steps from the teacher. So I used Factor Craze to spark some conversations about factors.

I have my students seated in groups, but I had them think on their own for a minute before working with their group. I actually started with the question Which numbers have exactly two factors?, which may seem rather elementary for high school juniors and seniors, but as I suspected, many had very little knowledge or experience with the concept of prime numbers.

Most groups started by writing down examples of numbers that had the required number of factors, but I prompted them with, “What’s a way to describe ALL numbers that have exactly ___ factors?”. All groups eventually came up with prime for exactly two.

When they got to exactly three, most groups found out that 4 and 9 worked. I asked them if there was anything special about numbers 4 and 9. “Oh, oh! They’re perfect squares! Perfect squares have exactly three factors!”

So I respond with, “Do all perfect squares? What about 16 and 25?”

“16 doesn’t work. Oh. But 25 does!”

So I say, “Nice. So some perfect squares but not all perfect squares. What type of perfect squares work?”

And so on. Most groups figured out that squares of prime numbers have exactly three factors. Only one group in each class was able to delve into exactly four factors before we ran out of time.

I really liked how this problem posed a challenge for every student. For some, just remembering what prime numbers are like was a challenge. For others, it was recognizing a theme for exactly four factors. Either way, all students were developing an understanding of factors.

We later moved on to greatest common factors and factoring expressions, and I think laying the ground work with Factor Craze made a difference.

Leave a comment

Filed under FST / Algebra 2, group work, productive struggle

High and Lows (Mostly Highs!) of the First Two Weeks

I survived my first two weeks as a high school math teacher! So many things have been running through my mind, but right now I’m going to make a list of things that are going well and things that need improvement. I just want to get it all out. I hope to blog more regularly from now on!

Things that are going well

  • I love my school. It’s so, so, so good. My colleagues are incredibly supportive and amazingly talented. Our students care about their school and each other. I am very fortunate to be part of such a strong community.
  • There are some very effective school-wide policies in place that administrators, teachers, and students are all on the same page about. I feel like this really promotes school pride and diminishes behavior problems.
  • My Geometry and FST students are awesome kids. I am so impressed by them.
  • Creating a classroom that values mistake making. This is a work in progress, but I’ve got a decent start.
  • Establishing a classroom community where the kids feel comfortable talking to each other. Seniors are good with this (too good, actually), and I’m still working on Geometry kids.
  • I have established some classroom routines! Phew. Thank you Andrew Stadel for Estimation180. It’s been a great way to start class every day. Similarly, ending class with an exit ticket lets students know that we work until the bell, as well as provides me with some great feedback.
  • Using whiteboards (both big and small) has been an effective way to get students to share their thinking and to just get some students to write something down.
  • I’ve done some deep activities, problems, tasks, or whatever you wanna call ’em that have produced good results.
  • I am learning every day.
  • I am finding time to exercise and cook dinner. (Sleep is another matter. Looks like I might pick up drinking coffee again…)

Thank you to all the inspiring teachers who share their wonderful ideas and activities so that I can use them. I stand on the shoulders of giants.

Things to improve

  • Classroom management. Can you tell I’m a first year teacher?
  • Similar to the first point, I struggle with engaging every student when I’m talking to the whole class. Group work is my strength: students discussing with each other with me floating around from group to group asking questions and guiding them along. In contrast, I feel like I’m not strong enough at whole-class lecturing and encouraging note-taking. I think I just need to be more strict about it. No talking when I’m talking. Pick up a pencil and write something down.
  • Kids who are absent. And the kids who are just now switching into my class. How can I get them up to speed?
  • Checking homework and going over answers. What a big ol’ unproductive time sink.
  • Better hand-writing. I save my Smart Notebook documents and upload them to my class website for students to use as a reference. Neater hand-writing would be easier for kids to read and follow.

Have a lovely weekend, everyone! Here’s to a great year!

Leave a comment

Filed under culture, productive struggle