[MOSAIC-news] May 6th M-CAST "Reading and Writing about Derivatives"
Nicholas Horton
nhorton at smith.edu
Wed May 4 12:01:27 CDT 2011
Be sure to join us for Friday, May 6th Project MOSAIC M-CAST at 2:00pm
EDT (1:00pm CDT, 11:00am PDT) entitled "Reading and Writing about
Derivatives".
May 6, 2011 Reading and Writing about Derivatives
Sommer Gentry, US Naval Academy
Phrases like "open-ended problems" or "word problems" are often about
modeling: translating from an English-language understanding of the
situation into a mathematical formulation. I'll describe some of the
exercises I use in my calculus courses to get students to interpret
newspaper reports in terms of the underlying mathematical concepts and vice
versa, translating mathematical concepts into English-language descriptions
that convey the mathematical ideas in a faithful way.
The website has an example of such an exercise, as well as instructor's
notes.
There are other M-CASTS organized by the MOSAIC Project
(www.mosaic-web.org) on a variety of interesting topics. We encourage you
to join in on the conversation and discussion for any or all of them.
May 13, 2011 Using active learning to teach math methods
More details can be found below.
Tuning in to an M-CAST: Instructions
M-CASTS are broadcast using the ReadyTalk computer conferencing system.
1. Direct your browser to the ReadyTalk web server
<http://www.readytalk.com/> and enter access code 2923887. This provides
the video component of the M-CAST.
2. For audio, telephone 866-740-1260 <tel:866-740-1260> and at the voice
prompt, enter the same access code: 2923887. You must dial in for the
audio.
The audio is two-way: a conference call that supports the seminar style of
the event.
May 13, 2011 Using active learning to teach math methods
Time: 1pm EDT (noon CDT, 10:00am PDT)
Gary Felder (Smith College)
Many physics and engineering curricula gather many math topics together in
one "math methods" course. Students in these courses are asked to rapidly
learn a wide variety of challenging math subjects with little motivation or
context and then to recall them when they are needed for a later course.
The results, as anyone who has taught these later courses knows, are not
always impressive. One tool I use to address this problem is "exercises"
that have the students work through a series of problems before they have
learned the material in a given unit. Some of these exercises are designed
to show the students why certain physical problems require particular math
techniques. For example I have them set up the differential equation for a
nucleus in a crystal and show that it can't be solved analytically, and
then I give them an approximate equation for the force on the nucleus, have
them show that it works as a good approximation to the true force for small
displacements, and have them solve the resulting simple harmonic oscillator
equation. This example motivates the unit on Taylor series, where I tell
them that they will learn how to derive such approximations. Other
exercises are designed to have them work out key math concepts on their
own, such as solving an ODE using separation of variables. My expectation,
which I plan to test in an upcoming NSF-funded research study, is that the
use of these exercises will increase student learning during the course and
retention in later courses.
What's an M-CAST?
M-Casts are 20-minute seminars broadcast over the Internet on the 2nd, 4th,
and 5th Friday of each month. They are part of Project MOSAIC
<http://www.causeweb.org/wiki/mosaic/index.php/Main_Page>, an NSF-sponsored
project to improve undergraduate STEM education by better integrating
Modeling, Statistics, Computation, and Calculus. M-Casts are designed to
provide a quick and easy way for educators to share ideas, get reactions
from others, and form collaborations.
M-Casts are recorded and posted on the Internet soon after the event.
This document is part of an interactive MOSAIC Wiki
<http://www.causeweb.org/wiki/mosaic/index.php/Main_Page>, which provides a
forum for sharing additional ideas and materials, for discussion, and for
reports of experiences using the ideas presented in the M-Cast. Access to
most of the Wiki requires a login account, available to educators by
request. Contact Danny Kaplan
<http://www.causeweb.org/wiki/mosaic/index.php/User:Kaplan> for an account
or more information.
If you have a MOSAIC login, click on the title of any M-CAST to access the
Wiki pages for materials, discussion, etc.
What's Project MOSAIC?
Project MOSAIC (www.mosaic-web.org) is a community of educators working to
develop a new way to introduce mathematics, statistics, computation and
modeling to students in colleges and universities.
Our goal: Provide a broader approach to quantitative studies that provides
better support for work in science and technology. The focus of the project
is to tie together better diverse aspects of quantitative work that students
in science, technology, and engineering will need in their professional
lives, but which are today usually taught in isolation, if at all.
* Modeling. The ability to create, manipulate and investigate useful and
informative mathematical representations of a real-world situations.
* Statistics. The analysis of variability that draws on our ability to
quantify uncertainty and to draw logical inferences from observations and
experiment.
* Computation. The capacity to think algorithmically, to manage data on
large scales, to visualize and interact with models, and to automate tasks
for efficiency, accuracy, and reproducibility.
* Calculus. The traditional mathematical entry point for college and
university students and a subject that still has the potential to provide
important insights to today's students.
The name MOSAIC reflects the first letters --- M, S, C, C --- of these
important components of a quantitative education. Project MOSAIC is
motivated by a vision of quantitative education as a mosaic where the basic
materials come together to form a complete and compelling picture.
Nicholas Horton
Department of Mathematics and Statistics, Smith College
Clark Science Center, Northampton, MA 01063-0001
http://www.math.smith.edu/~nhorton
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