SLM521-Spring 2004
http://www2.mcdaniel.edu/slm/student/vaskisc/index.htm
Purpose of Web Site
The purpose of this web page
is to show high school students (11th and 12th grades)
some applications in the real world of secondary level mathematics. Many engineering and science careers use math
to create new devices and to operate those devices. For example, in the field of space
exploration, engineers when designing the Space Shuttle and the International
Space Station (ISS) used math models on computers. While these space vehicles are in operation,
math computer programs calculate their orbital paths (or positions in their
orbits) around Earth and generate commands to control their rotation or
orientation (the direction they are pointing) in space.
Many other fields use
mathematics as well. Some examples are
insurance companies (who use statistics and probability to determine risk
factors), medical technology (to create new devices to diagnose patients like
MRIs or Magnetic Resonance Imaging, ultrasound equipment, x-rays, and other
types of medical scanning equipment), and chemical companies who create new
formulas to improve our automobile gasoline, our medicines, and other products
such as plastics, building materials, paints, fertilizers, and insecticides.
This Web page looks first at
mathematics in space exploration and then at mathematics in computer image
generators (CIGs) and computer games.
The goal of this page is to inspire students to learn mathematics as a
tool for a future career and not be excluded from any job because they don’t
have the math background. When students
read about past mathematicians and scientists they may be inspired to make a
discovery of their own. Math has
improved our world in many areas and has allowed us to diagnose medical
problems early so that we can live longer and more interesting lives.
Activities
Web Link
Bibliography – The purpose of this bibliography, and associated drop-in
lessons below, is to broaden the student’s view of the history of mathematics,
its calculations and its real world applications. Many times students don’t know why they are
learning math and why it was created. If
students understand why the math was invented and how it is used today then
maybe the students will be inspired to create something new using these math
tools. There are four sections to this
applied mathematics bibliography. The
history of mathematics section points to web sites that describe the people and
situations where the math was invented.
The math computations section points to existing tools that teach the
student how to perform the calculations.
The math definitions section lists math dictionaries, encyclopedias,
libraries and software as a resource for the teacher or student when learning
about a new area in math. The real world
applications section lists web sites where math is being used in the real
world. The applications area is broken
into subcategories based upon the type of application.
http:/www2.mcdaniel.edu/slm/student/vaskisc/weblkbib.htm
Search Engine
Assignment – The Search Engine assignment reviews several search engines in
the areas of General Search engines, Meta-Search engines, News Search engines,
Education Search Engines, and Medical Search engines. It lists my favorite or best choices and
those that are not so easily used in the worst search engine category.
http://www2.mcdaniel.edu/slm/student/vaskisc/srengine.htm
Course Module
Assignment – Comparison Blog Shopping – This module’s lesson is to have the
student compare the dollars versus blog features for several web sites that
offer blogging. Blog windows are a place
to keep an online diary or journal and since it is a text Web window, not an
HTML file, it is easy to edit and maintain.
People use their blog windows to communicate with remote other blog
windows of family or friends. You can
set up several blog windows for other topics such as your own sports blog or
hobby blog window. This module has the
student reading about and comparing features that are similar across several
web sites that offer blogging and create a table to compare their cost versus
feature. Some extra features are also
compared for several sites. Then the
student picks their best value blogging web site and the worst, or most
expensive, site for a particular feature.
http://www2.mcdaniel.edu/slm/student/vaskisc/bloggmod.htm
Copyright
Assignment – For the copyright assignment I discussed the situation where a
teacher tells her hyper-active students to copy images and photos off the
Internet to their computers at school to keep them busy. I also discuss a man who purchased software
and copied it for his child’s school where they used it and won Nobel prizes as
a result of its use. The discussion is
about whether the students and their teacher or the man and his child’s school
are breaking copyright laws or invading author’s rights.
http://www2.mcdaniel.edu/slm/student/vaskisc/copyrite.htm
Articles Reviewed
Article 1
Review - Review of article “A Look at the Future” by David Pearce Snyder
describing use of the Internet in the future for teaching and research in the
classroom. The article describes the
many new Internet capabilities (file transfers or FTPs, Instant Messaging,
WI-FIs or wireless connections to the Internet) and new computer management
software to allow more efficient use of computer resources. Will the new capabilities be available to
everyone easily and will the advanced technology require costly training for
those who wish to use it?
http://www.asbj.com/2004/01/0104technologyfocus.html
Article 2
Review – Review of article “The new reality of the online education
community: Today, the Web represents a comprehensive, cross-functional
education resource, indispensable for successful school and district
strategies.” by Merna Smith & Paul Tumarkin of the Pearson Digital Learning
company. This article describes an
educational product called Concert Instruction & Assessment or Concert
IA. This product provides
curriculum-based lesson plans using the vast resources available on the
Internet and meets the state’s standards for the reinstated No Child Left Behind
Act. This product provides on-line lesson
plans, on-line student testing and grade reporting so that the teacher and
parents can monitor a student’s progress and prompt remedial help when
needed. Concert IA is also capable of
reporting overall student progress to the state for compliance with required
state and federal academic achievement goals.
It also provides Internet links for professional teacher training. Concert IA meets four key elements to a good
learning management system: instruction, assessment, communication, and teacher
professional training and does so in a seamless manner.
http://infotoday.com/MMSchools/sep03/MMSWP0903.pdf
Other Article Citations
Other Article
Citations – List of other article citations.
Elective Activities
Elective 1 – Send Instant
Message (AIM) completed on 2/7/04. See
submission log.
Elective 2 – Distribution
List assignment completed on 2/15/04.
See submission log.
Elective 3 -
Hoaxes Review – The hoaxes web sites provide insight on how to identify
hoaxes and where they can be reported.
Some hoax buster web sites deal with specific topics such as the medical
community (diseases, health threats such as anthrax or small pox, seasonal flu
viruses), governmental concerns (terrorism, computer viruses, chain letters),
and urban legends that have been passed around for decades.
http://www2.mcdaniel.edu/slm/student/vaskisc/e3hoaxes.htm
Elective 4 –
Search Tips – This assignment lists several Web searching tips while using
search engines. It gives a brief
tutorial on each tip and explains why you should use it.
http://www2.mcdaniel.edu/slm/student/vaskisc/e4srtips.htm
Elective 5 –
Silicon Snake – Clifford Stole complains about the Internet and others
react to his book. I share my views on
his concerns and discuss the wise use of the Internet.
Elective 6 –
Online Shopping - Online shopping
can be easy to do but there are security reasons for protecting your personal
information when purchasing online. This
chart discusses the shopping techniques of Browsing, Comparison Shopping,
Auctions, Wish Lists and Gift Giving.
http://www2.mcdaniel.edu/slm/student/vaskisc/e6shoppg.htm
Elective 7 –
Evaluating Websites – A checklist of characteristics of Web page content
and validity was created and then used to evaluate two different Web pages for
their level of quality.
http://www2.mcdaniel.edu/slm/student/vaskisc/e7evalws.htm
Elective 8 –
Teacher Sites – Two Teacher’s Web sites are reviewed and critiqued.
http://www2.mcdaniel.edu/slm/student/vaskisc/e8tchrst.htm
Elective 9 –
Worksheets for Instructions – Linked list of Math Linear Algebra and
Matrices worksheets.
http://www2.mcdaniel.edu/slm/student/vaskisc/e9worksh.htm
Elective 10 –
Field Trips – The Virtual Tour takes you through NASA’s Mission Control
sites. It shows you the Space Shuttle
and Space Station to see what astronauts do there.
http://www2.mcdaniel.edu/slm/student/vaskisc/e10field.htm
http://www2.mcdaniel.edu/slm/student/vaskisc/e11games.htm
http://www2.mcdaniel.edu/slm/student/vaskisc/e12sound.htm
http://www2.mcdaniel.edu/slm/student/vaskisc/e13filtr.htm
http://www2.mcdaniel.edu/slm/student/vaskisc/e14plagm.htm
Web Dropins
The first drop-in site explains
how math models, or coordinate systems, are used to describe three dimensional
space and the objects within them. The
second drop-in site explains how to mathematically rotate those objects in
space so that they point in a new direction in order to complete their
mission. The third drop in site
discusses orbital mechanics in terms of the mathematics involved and uses a web
site that shows the Space Shuttle and International Space Station (ISS) in
their orbital path around the Earth in real time. The student is asked to figure out their
location on the Earth’s surface in one of the coordinate systems and to find
the time when they are most likely to see the Space Station next. The fourth drop-in site deals with the
controversial issue of whether to continue funding the Space Program or
not. The students are asked to review
several sites that cover the benefits (pros) that have come out of the Space
Program and what problems there have been (the cons). It asks them to debate whether the Space Program
should continue as planned at the current level of government, international,
and commercial funding or not. The fifth
drop-in site covers how math is used to create the computerized terrain and
models in Computer Image Generators (CIGs) and in computer games.
To perform the exercises in
drop-ins 1, 2, 3, and 5 you will need to print out the graph paper
(mouse click) and print out several copies (it takes several minutes to load to
the web window) or obtain your own graph paper.
When the graph paper comes up you can scale each individual square’s
width by moving the window’s right edge to the left or right. When the squares in the grid look nice, print
one copy to check the appearance and, if okay, then print multiple copies for
the class.
Dropin#1 –
How is math used to define the real world?
This drop-in introduces three dimensional (3D) coordinate systems for
defining the objects and their locations in space. This drop-in is for 11th and 12th
grade students who have had basic trigonometry.
http://www2.mcdaniel.edu/slm/student/vaskisc/dropin1.htm
Dropin#2 –
How is math used to move and rotate objects in the real world? This drop-in discusses math calculations to
rotate an object in 3D space. The
exercises are for 11th and 12th grade students who have
had basic trigonometry. The first math
rotation calculations are done in the exercise for the student to see how it is
done and the final rotations are left for the student to perform. Answers are provided along the way. The general concepts of rotating objects
around coordinate axes could be demonstrated to middle school students and
older students with a simple three axis orthogonal coordinate system model as
the teacher or student reads the drop-in’s top level page. There are web sites throughout the lesson to
illustrate the concepts but the student does not need to calculate anything
from them. The exercises perform three
simple axis rotations and are self-contained on the lesson’s web pages. The web
sites at the bottom of the top drop-in page could be viewed and enjoyed by anyone
who has an interest in space applications.
The questions at the bottom of the drop-in’s top page make the student
think about how math is used to rotate objects and what some robotics
applications might be in the real world.
http://www2.mcdaniel.edu/slm/student/vaskisc/dropin2.htm
Dropin#3 –
How is math used in space applications?
This drop-in site discusses how a Star Tracker moves to point toward a
new star by performing some simple math calculations. The student learns how to calculate some of
these math functions such as using the previous operations of vector
translation from drop-in 1 and object rotation from drop-in 2. Also, the linear algebra functions of taking
the Dot product of two vectors and the Cross product of two vectors aids in
finding the final Star Tracker pointing direction to look at a new star. The real world examples of this operation are
discussed for Star Tracking, the Hubble telescope, and orbital mechanics for
the Space Shuttle and the International Space Station. Middle school aged students would enjoy
visiting the web sites listed and listen to the discussion in general. Older students in 11th and 12th
grade, who have had basic trigonometry, are needed to perform the math
calculations.
http://www2.mcdaniel.edu/slm/student/vaskisc/dropin3.htm
Dropin#4 –
First discover Mars and the robots used to explore the Martian landscape. This lesson discusses how math (drop-ins 1
and 2) is used in robotic movement as well as discussing robotic vision and
data collection. Each student will look
at one or more web sites listed to form an opinion on a selected perspective
topic and question. The class will form
an opinion about whether to continue the Space Program as currently planned by
President Bush. Students will look at
Web sites for NASA’s budget in 2004 and planned for 2005. They will look at what has been said against
Bush’s Space Program plan and allowing the Military into space. They will finish by debating the pros
(benefits of new technology and discoveries) and cons (cost and losses) that
have come from the Space Program and vote on how to continue the Space
Program. This Dropin #4 is for any 11th
and 12th grade high school student who has had some basic
trigonometry and can understand 3D coordinate systems (both Cartesian and
Polar).
http://www2.mcdaniel.edu/slm/student/vaskisc/dropin4.htm
Dropin#5 –
Math models are used in Computer Image Generators (CIGs) to create terrain and
object models that are placed on the terrain.
Math models are used to move and rotate the CIG object models and their
appendages. How the object models and
land are displayed from a selected viewpoint is discussed. The student is asked to create their own CIG
object model on graph paper or on the computer in a drawing tool and label with
origins, dimensions, and type of coordinate system used for movement and
rotation. This Dropin #5 is for any 11th
and 12th grade high school student who has had some basic
trigonometry and can understand 3D coordinate systems (both Cartesian and
Polar).
http://www2.mcdaniel.edu/slm/student/vaskisc/dropin5.htm
Web Quest
WebQuest
– The Web Quest is titled “Robots in Space, Today and Tomorrow … - To boldly go
where no Robot has gone before…”. The
Web Quest lists resources that describe how robots are being used today for
space applications and points toward President Bush’s plans for them in future
space exploration as well as the Military’s plans for a Robotic Army. The student will explore the Mars rovers web
site on the NASA home page to read about and see (video clips) how the rovers
were designed and how they operate. The
student will have many Web sites to view about how other companies and
universities have developed their own robotics research departments. While learning about the different types of
robots, the student will be asked questions that prompt creative thinking about
how that information could be used if they wanted to design their own robot for
a space or Earth environment. The final
area will lead the student to make choices about how they would design their
own robot and point them to some companies that provide the tools for them to
actually build it. Then it is up to them
if they want to order the parts and create their own version of Will Robinson’s
“Lost in Space” Robot. This Web Quest is
for any 11th and 12th grade high school student who has
had some basic trigonometry and can understand 3D coordinate systems (both
Cartesian and Polar).
http://www2.mcdaniel.edu/slm/student/vaskisc/webqstop.htm
Submission Log
Submission Log
– Records all assignments turned in and the grades received.
http://www2.mcdaniel.edu/slm/student/vaskisc/sublog.htm