4.1. April 16, 2002

"Do not confuse the moon with the finger that points at it."--Zen proverb

Introduction to the Unit

As the class opens, "Coordinate Systems and Vectors" will be written on the whiteboard.

Randomly selected students will read numbered "announcements" to the class, pre-prepared on slips of paper, as follows:

• #1. We're starting a new unit today on coordinate systems and vectors (like it says on the whiteboard).
  
• #2. Ms. Lee has not finished grading the tests yet. She will try to have them back to us on Monday. She will tell us about test make-ups then, too.
  
• #3. We'll begin with a brainteaser, then a PREVIEW of the unit so we know what we're going to learn. We can consult each other or the textbook. Ms Lee will grade the PREVIEW on effort, not correctness (that would be silly).
  
• #4. After that, Ms. Lee will introduce the unit. Try not to snore too loudly. (Just kidding.)
  
• #5. A group activity will get our brains working in the right way. M. and L., please see Ms. Lee about this.
  
• #6. After group presentations and wrapping up, we will get the homework, which is due Monday. People who decide not to turn in the homework will have a quiz instead.
  

I instituted this system of announcements after seeing another STEP teacher, Treena Joi, use it in her middle school science classroom to good effect: students will generally listen more closely to another student than they would to me, it saves my voice, and it gives them practice in the useful skills of getting people's attention and speaking clearly.

The COORDINATE SYSTEMS PREVIEW (GIF scan) is an introduction to some of the skills covered in the unit. Students receive credit for making an attempt, and are encouraged to consult other students or the textbook. The purpose is so that I find out what they've already learned and also to catch a glimpse of potential troublespots; also, as students will be seeing similar problems on the end-of-unit test, it gives them a "road map" for what they will be learning to do. Ideally, they also gain experience in extracting useful material from less-than-ideal texts.

Students will be asked to hand in their PREVIEW when they are finished so I can give them credit for working on it and find out what they know. I will return it to them sometime during the next class.

The test and make-ups referenced in #2 are from the previous unit on probability, and are a standard policy that my cooperating teacher has had in place since the beginning of the year.

A Road Map: Coordinates and Vectors

I will give a brief lecture to let students know where they're going. I will write two key questions for the unit, "How does math describe the world?" and "What is a number?" on the whiteboard. Students will no doubt find coordinate systems, especially in their cartographical incarnation, a familiar answer to the former in this context, but it is unlikely that they have encountered vectors and an explicit discussion of what constitutes in "number." This way, students will have some idea of what lies ahead as they move to the group activity below.

Giving Directions

Students will be put into randomized groups (accomplished by counting them off) and be given the task of giving directions from one point to another in the classroom, shown by dots around the room. Each group will be given a different pair of points, and after everyone knows where their points are, the dots will be taken down. Students will be free to use whatever means necessary to get the directions across (diagrams, words, and so on), but everything must be on a physical sheet of paper, and they are not allowed to ask questions.

Each group will receive a GIVING DIRECTIONS handout (download in RTF format) with guidance and criteria for the activity. One important rule is NO ISLANDS, i.e. in a group all desks should be physically touching each other. The reason is that this way students have less excuse to tune out or exclude others from group discussions. This is also why I dislike having groups with more than 4 people (except for temporary two-group discussions), as one or more people inevitably are relegated to the periphery. Unfortunately, the vagaries of student attendance mean that occasionally we have groups of 5, as I truly don't know how to "catch up" a group composed solely of people who missed out on the previous day without neglecting the rest of the class. There also wouldn't be enough time for them to start from scratch.

While they work, I will circulate around the room to observe, answer questions that come up or intervene if necessary, and take notes on how individuals are contributing (or not). In my experience, having a designated "question person" takes care of the majority of questions before I need to step in, as having to tell the "question person" what the question is often results in some group member realizing s/he knows the answer. Other questions can be referred to the reader (who is responsible for making sure the group is aware of the directions), or even posed to another group member, whose response tends to prompt a group discussion wherein the issue is resolved without further need for teacher intervention.

Groups will be paired to trade directions. The first group will try to use the directions to find their way from the first to the second point; the second group will observe them and take notes but cannot offer any help. Then the two groups will switch roles.

Both groups will discuss similarities and differences between the directions they gave, the directions' effectiveness, and what made the task difficult or easy. The scribes for both groups will summarize this discussion to be turned in. The reporters will be expected to have notes to show me when I come and check on the groups.

Each group's reporter will report to the entire class on their results. They may enlist the help of whatever people they or the group deem necessary. Non-reporters will be asked to give brief written feedback to the reporters.

Two students who considered groupwork "unhelpful," M. and H., were given a choice between working in one of these groups or completing an OBSERVATION REPORT handout (downlad in RTF format) as "group-watchers." One took me up on the offer.

Wrapping Up

At the end of class, students will receive HOMEWORK PACKET #1 (GIF scans: page 1, page 2 and page 3) for the week, due on April 19, Friday. The purpose of the homework material is to acclimate students to different coordinate systems, including a simplified Battleship scenario and an example involving non-orthogonal bases; this will also happen during Thursday's class.

Students are obliged to put the room back in order (as groupwork entails much moving of desks) and, as a class, remind me (and themselves) of their homework assignments at the end of the class, before they may leave.

Copyright © 2002 Yoon Ha Lee <requiescat@cityofveils.com>
Last updated on 18 May 2002