[MOSAIC-news] Project MOSAIC M-cast: Calculus operators in the mosaic package (Friday, November 4th)
Nicholas Horton
nhorton at smith.edu
Mon Oct 24 06:40:44 CDT 2011
Be sure to join us on Friday, November 4th for a Project MOSAIC M-cast at
2:00pm EDT (1:00pm CDT, 11:00am PDT) entitled "Calculus Operators in the
mosaic Package" by Daniel Kaplan of Macalester College.
Abstract: Last year we introduced R operators for differentiation and
integration. These have been extended to provide support for an easier
notation, multiple variables, and symbolic differentiation (to support
high-order differentiation). An important issue is notation: how to make
the link between the traditional algebraic notation students learn in high
school and the notation used in computational work. We'll discuss the
trade-offs between two approaches --- the close-to-traditional notation
used, e.g., in Mathematica, and the R-function notation used in our first
round of R calculus operators. The mosaic package uses a new, intermediate
notation, e.g. sin(2*pi*x)*exp(k*t) ~ x & t. We'll report on the student
experience with the system, which we will have been using at Macalester for
three months.
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 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.
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, an
NSF-sponsored initiative 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.
There are other M-casts organized by the MOSAIC Project
(http://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:
November 18, 2011 Developing a Concept Inventory for Modeling
Rebekah Isaak and Andrew Zieffler, University of Minnesota
Time: 1:30pm Eastern (12:30 Central, 10:30 Pacific)
Abstract: To teach modeling, you need to know what modeling is. To assess
how well students are learning modeling, you need to be able to break down
the overall framework into components around which assessment items can be
designed. The main purpose of our M-cast is present the framework that we
have been designing along with a process for developing assessment items.
We're hoping to solicit feedback from the audience about the
comprehensiveness of this framework, the ways that we've split it between
statistical and mathematical concepts, and the process for developing the
concept inventory instrument, starting with open-ended questions to identify
student misconceptions and eventually translating this to a multiple choice
format. In the end, we hope to have an instrument that can guide the
instructor in covering modeling in a comprehensive way.
December 2, 2011 Coupled oscillators: Joggers, fireflies, and finger
coordination
Tanya Leise (Amherst College)
Time: noon Eastern (11:00am Central, 9:00am Pacific)
Abstract: I'll describe a simple oscillator model that can describe the
position of a jogger going around a circular track, a firefly blinking on
and off, or the motion of a finger waving back and forth. We can add a
second oscillator to model two joggers, two fireflies, or two fingers trying
to coordinate their motion. I'll demonstrate how to use some basic analysis
involving derivatives to analyze the various scenarios, emphasizing the role
of derivative as rate of change.
December 16, 2011 Roundup of resampling methods: simple technology for
introductory statistics
Nicholas Horton (Smith College)
Time: 2:00pm Eastern (1:00pm Central, 11:00am Pacific)
Abstract: Resampling based inference (bootstrapping and permutation testing)
plays an increasingly important role in introductory statistics courses.
But instructors and students have been hampered by the lack of easy to use
interfaces to these approaches. In this M-cast, I will discuss the
advantages and disadvantages of several implementations, then facilitate a
discussion about the joys and challenges of teaching these concepts.
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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