Helping mathematics students develop information competency

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Helping mathematics students develop information
competency

• Section NExT, Spring 2003
• MAA Southern California Section

Bruce E. Shapiro bruce.e.shapiro_at_csun.edu http//w
ww.bruce-shapiro.com/presentations.html
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Information Competency

• How do we obtain a process information?
• Good communication skills are the key to
  advancement in any job
• Writing
• Speaking
• Electronic communication
• Navigating the world-wide-web

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What we expect ...

• Read the book
• before the material is discussed in class
• Attend class
• Take notes as necessary
• Reinforce what they have read
• Raise questions, clarify difficulties
• Review notes and text after class
• Do homework, i.e., work problems

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What really happens ...

• Come to class (sometimes)
• Look at the homework
• Look for examples that are similar to the
  assigned problems
• Mimic the examples
• when that fails, look for examples in notes
• when that fails, ask for a worked example
• when that fails, give up
• Read the book ... not!

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Ereading Assignment

• Variation on weekly reading interpretation
  assignments
• Due Weekly Sunday Night at Midnight
• 48 hour grace (so really due Tuesday Midnight)
• Absolutely no exceptions beyond grace period
• Summarize
• What they learned in class last week
• What they learned from the text last week
• Identify at least one thing they did not
  understand in the text, the lecture or the
  homework

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Ereading Assignment

• No paper allowed
• Originally by email, now use cgimail (web form)
• Grading
• 1/0 turn in/not turned in
• Overall 10 of semester grade
• Math classes used in
• Math 103 - Business Calculus (1)
• Math 150A/150B/250 - Calculus I/II/III (1/1/2)\
• Math 351 - Differential Equations (2)

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Name Email
Assignment 7 Due October
20, 2002 ---------- ---------- What I Learned
in Class -------- ---------- 1. Directinoal
Derivative D f . grad f 2. D T rate of
change of temperature as we move in
direction. 3. A function increases most rapidly
in the direction of grad f. 4. Maximum rate of
change is grad f Minimum rate of change is
-grad f 5. Chain Rule du/dt Du/Dx dx/dt
Du/Dy dy/dt --gt u depends on x and y x and y
depends on t 6. Implicit Differentiation
dy/dx - Df/Dx / Df/Dy ---------- ----------
What I Learned by Reading the Book --------
---------- 1. Tangent Plane need a normal and
a point in the plane gradFltxo,yo,zogt DOT
ltx-xo, y-yo, z-zogt 0 2. f has global max and
global min values if it is continuous. 3.
Critical Points boundary, stationary or
singular points 4. Second Parital Test useful
to find local max, local min, and saddle
point. ---------- ---------- What Confused Me
-------- ---------- Lagrange's method is still a
mystery. ---------- ---------- Additional
Comments -------- ---------- nothing to declare.
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Name Email
Assignment 1 Due September
8, 2002 ---------- ---------- What I Learned in
Class -------- ---------- Well, aside from the
fact that I've learned not to take math 280 and
math 250 concurrently, I learned about vectors. I
learned to add 'em, subtract 'em, multiply 'em
(dot and cross). I also learned that I really
like the mint "Milano" cookies by Pepperidge
Farm. I wonder if people in Milan really eat
them? ---------- ---------- What I Learned by
Reading the Book -------- ---------- Key points
so far Vectors in three dimensions. Again,
multiplication--dot product, cross product.
Equation of a plane and sphere. Determinants
(interesting). Direction angles and
cosines. ---------- ---------- What Confused Me
-------- ---------- Problem 34 in section 14.2
was a little tough. With vectors, it seems as if
we generally think of them as emmanating out of
the origin. With this problem, however, it was a
little different--vector between two points.
---------- ---------- Additional Comments
-------- ---------- None at this time.
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Name Email
Assignment 5 Due October
6, 2002 ---------- ---------- What I Learned in
Class -------- ---------- I learned about limits
and continuity. ---------- ---------- What I
Learned by Reading the Book -------- ----------
The key points were limits and continuity and
differentiability. ---------- ---------- What
Confused Me -------- ---------- I didn't
understand problem number 12 on 15.3. ----------
---------- Additional Comments --------
---------- I have no other comments.
Name Email
Assignment 6 Due October
13, 2002 ---------- ---------- What I Learned in
Class -------- ---------- more on partial
differentiation ---------- ---------- What I
Learned by Reading the Book -------- ----------
directional derivatives and the chain rule With
partial differentiation ---------- ----------
What Confused Me -------- ---------- 15.5 number
20 ---------- ---------- Additional Comments
-------- ---------- I have no other comments.
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Ereading Summary

• Students are about as likely to do their homework
  as they are to come to class
• Is there a weak correlation between compliance
  and grade?
• Turning in homework leads to good grades, OR
• Good students turn in their homework

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Term paper

• Classes
• Upper Level Differential Equations (3 times)
• Upper Level Numerical Analysis
• Structured writing assignment
• Topic is chosen by student
• Must be something that is not covered in class
  that semester
• Proposal (abstract plus 5 references, 1-2 pages)
• Paper (page limited)
• Presentation (Limited to 5 minutes)

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What does this have to do with technology?

• Doing a term paper is not the same thing it was
  10 years ago. A literature search has changed
• Online electronic book catalogs
• Online journal search engines Medline,
  MathSciNet, WebOfScience, etc.
• Most journals are online
• Tremendous amount of on-line material
• Students dont know how to wade through all this
  material
• A literature search is not a Google search.
• Learn how to order/obtain material that is not
  physically in the library
• Learn how to use Library facilities

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Typical topics chosen

• Differential equations
• Fourier Analysis
• Transforms
• Various PDES wave, Laplace/Poisson, Maxwell,
  Schrödinger
• Population Biology
• Stock Options
• Electrical Circuits
• Chaos, Fractals
• High School teaching programs
• Special equations, e.g., Bessel

• Numerical Analysis
• Image processing
• Graphics
• Solving systems of nonlinear equations
• Chaos, fractals
• Monte-Carlo simulations
• Encryption
• Systems of ODEs
• Various work-related topics

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Early Homework Assignment

• Go to the library, pick any journal you like, and
  find the instructions for authors. From these
  instructions, give an example of precisely how
  you would format each of the following in your
  manuscript
• a) A reference to a specific text.
• b) A reference to a journal article.
• c) A reference to a web site.
• d) A reference to a chapter in a book where every
  chapter is written by a different author.
• Indicate both how you would refer to the
  reference in the text of your manuscript and how
  you would refer to it in the references section
  of your paper.

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Why write?

• Hone writing skills
• Learn to do discipline specific research
• Learn to learn on their own.
• A finished project is a great confidence builder.
• Learn to follow directions grant application,
  company pub, journal article.
• Students are given specific format instructions
  Fonts, page numbering, margins, bibliographic
  styles
• Learn to typeset equations
• Use Equation editor, compatible with most major
  word processors (Not allowed to use Latex)
• Microsoft Word (Universal US Govt Std.)

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Why Talk?

• Students will need to be able to communicate
  their ideas to others in virtually any future
  employment
• Students are allowed to use any AV equipment they
  desire most choose overhead, some do powerpoint,
  posters, chalk (difficult in 5 minutes).
• First time before a live audience
• They learn not only by doing but also by
  observing their colleagues
• Students do simple written critiques
• Many students are in math education!

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Student Evaluations
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Final exam question

• Write an essay discussing the most valuable
  lesson(s) you learned doing the project. Discuss
  the significance of this (these) lesson(s) in
  terms of your personal educational and/or career
  objectives. If you had it to do over again, how
  would you do the project differently? Having seen
  everyone elses presentations, would you do the
  presentation differently? If so, how, and if
  not, why not? There is no right or wrong
  answer to this question. Can you come up with a
  list of pointers for someone who is making a
  presentation?

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Common Answers

• I learned that I could learn about something in
  math on my own.
• Giving a talk is harder than I thought.
• I learned how to express my ideas on paper - I
  didnt know I could do that in math!
• I finally learned how to find stuff in the
  library.

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And from a graduating senior

• this is the first time I ever had to actually go
  into the stacks in the library and find a book.