18.02 Calculus

2/6 1st

Here are some suggestions for your recitation on Wednesday.

Please hand out the "flash cards" that you will have gotten from Galina in 2-285, and ask students to bring them to every lecture (and to recitation too if you plan to use them).

Remind students to sign up for Piazza.

--- Do at least one geometry proof using vectors. I would write the proof on the board in full detail, using full sentences, since many of the students have seen only the two-column proofs in 9th grade geometry - they desperately need a good model. For instance, if you do 1A-11, I would write something more substantial than the solution in the supplementary notes, something like the following:

"Let A, B, C, and D be the vertices of the parallelogram in order.

   [Here I would stress the need to define the variables one is using.]

Set up a coordinate system with the origin at A.

   [Here I would explain that in geometry problems like this
    one is free to choose the origin in a convenient place.]

Let X be the midpoint of AD, and let Y be the midpoint of BC. Then the position vectors \BB, \CC, etc. corresponding to these points satisfy

  \CC = \BB + \DD      (by the parallelogram law)
  \XX = (1/2) \CC
  \YY = (1/2)(\BB + \DD)

so

  \XX = \YY.

Thus X = Y, which means that the diagonals AD and BC bisect each other."

---

Review the intuitive meaning of the scalar component of a vector, comp_b a (and also how to compute it, but usually it is the meaning that is harder for students to grasp).

--- As a review, perhaps ask students if they can express <2,1,-2> (or something like this) as a positive scalar times a unit vector.

--- Perhaps also review the right-hand rule and the notion of right-handed coordinate system (the first half-page of Section 12.2). This might be more successful in recitation than in lecture, since you at close range can make sure that they use their hand correctly! Also mention the usual way of drawing the x-, y-, and z-axes (x towards the class, y to the right within the blackboard, z up within the blackboard).

Here are more general suggestions from Haynes Miller, which you may take or leave.

> What to do on the First Day of Recitation > > > The first day of class is very important in setting the atmosphere > and expectations in the classroom. You may be nervous, and the students > may be nervous too. Here are some suggestions to get things moving in > the right direction. > > Introduce yourself. Write your name, office address and telephone number, > email address, and office hours on the blackboard. Announce your position, > what you want the students to call you, where you are from, > what your major or research is in, other personal information that you > think will help students relate to you as they try to learn mathematics > with your guidance. If you are not a native English speaker, acknowledge > this fact and thank them for their patience. You could propose a trade - you > help them with the math, they help you with the English. > > There is a supply of 5 x 8 index cards in the Math Headquarters. Pick up > enough for your recitation. Hand them out and instruct the students to fold > them the longway and write their names, in large letters, on front and back > like a delegate's sign. Remember, the students don't know each other any more > than you know them, at this point. They want to know the names of the > students in front of them. > > When a student speaks for the first time, ask the student to say his > or her name, and where he or she is from. This will help everyone to > fix the person and the name in their minds. > > Often you will be seeing students before the first lecture. > In this case, have with you copies of the syllabus, and, if possible, > the first homework assignment. Study this material with them and answer > questions about the structure of the course. In many basic courses we > use "flash cards." These originate as sheets of bright yellow paper > with numbers 1--4 and 5--8 printed on them. You may be asked by the > lecturer to distribute these to your students. If you were not given > them at the class orientation meeting on Reg Day, you can pick them > up at the UMO. Show the students how to cut or tear the sheets into > four parts and manufacture a small booklet using a stapler. Try to bring > a stapler to the recitation for the purpose. > > The course lecturer will have given instructions about what to > work with on the first day. > > > > Haynes Miller > Academic Officer, Mathematics > August, 2010