Some key points to remember…
q
It's a good idea to
look at something teachers and learners really struggle with and then look at how
a technology may be of use. Instead of just believing Technology is going to
make us better thinkers! ask yourself…
How
can technology help me and my students become better thinkers?
How can I use technology to find more resources about the concept?
How
can I use technology to recognize the concept?
How
can I use technology to explain the concept?
How can I use technology to help my students see the components of the concept (i.e., the part-to-whole relationships)?
How
can I use technology to allow my students to experiment with the concept?
How
can I use technology to help my students create their own versions of the
concept?
How can I use technology to help my students evaluate their ability to use the concept?
q
Computer usage must
be about quality--not quantity. Technology is, after all, only a tool
in the educational process, not terribly unlike a pencil.
q
What makes some programs
more successful than others? Most of the successful programs described in
recent studies have found three factors in common:
o
The software used was
carefully selected as an educational supplement integrated into a well
thought-out program of classroom instruction. Technology was one important tool
among many; teachers taught concepts and then used technology to reinforce,
enhance, and elaborate on that instruction.
o
Teachers received
ample training and support in using the software.
o
Students had ready access
to up-dated software and well-functioning computers.
q
High school algebra
and geometry students who use commercially available problem-solving software
score significantly higher on tests of mathematics content than groups of
students who do not use the software. The students using software also made
significant gains in problem-solving ability.
q
Technology can have
positive benefits if used in mathematics instruction. However, the benefits
depend on how the technology is used.
q
Technology has more
of an impact in middle schools than it does in elementary schools.
q
In eighth grade,
where computers are often used for simulations and applications, students have
higher test scores than where computers are used for drill and practice.
q
Students of teachers
who have appropriate professional development in computers score one-third of a
grade level higher than students whose teachers do not.
q
The essential
conditions necessary to maximize student achievement:
o
Better Access to
Technology--In order to become an
integral part of students' learning, computers need to be available for
individual student use during extended periods of time. Currently, student
access to computers is estimated to be less than one hour per week (4 percent
of total instructional time).
o
Updated Systems--Electrical and communication systems must be
updated in order to maximize the benefits of computer technology.
o
Learning
Environments--Computers must be
viewed as learning environments with multiple capabilities to support and
enhance student learning as an important medium for instruction.
o
Professional
Development--Teachers must be
provided with instruction and practice in integrating the curriculum with the
technology and become familiar with hardware and software.
q
Using computers to
increase classroom resources is both an impetus for and outcome of transforming
the role of the teacher in the classroom. Once known as the sole disseminator
of information, teachers now identify themselves as guides, mentors, and
facilitators whose roles are to motivate students and engage them in discussion
and reflection.
q
Gateway concepts are
those concepts so important to a content area that failure to understand them
has a severe impact on learning of that subject matter. Teachers are the
Gatekeepers of knowledge and wisdom. It is not enough to give students
knowledge. As teachers, we have to help students understand how to wisely apply
what has been learned.
Useful
Sites for Math Teachers
|
Title |
Description |
Web
address |
|
A+ Math |
This web site was developed to help students improve
their math skills interactively. |
|
|
The ExplorerTM |
If you are a math teacher or know a math teacher or
parent who needs some real-world, fun math lessons, you must see this
site! The ExplorerTM is a
collection of educational resources (instructional software, lab activities,
lesson plans, student created materials ...) for K-12 mathematics and science
education. You may browse through mathematics and science education curricula
(they plan to expand to other curricula) or conduct searches that focus on
specific interests. Many resources are available in the Adobe Acrobat format
that is readable by Macintosh, Windows and other operating systems. The
ExplorerTM is being developed jointly by the Great Lakes
Collaborative and the University of Kansas UNITE group to involve educators
and students in creating and using multimedia resources for active learning
and "on time" delivery. The U.S. Department of Education OERI
office has supported the Explorer research and development efforts. The
Explorer was first posted on the World Wide Web on June 21, 1993. |
|
|
Abstract Algebra On Line |
The site contains many of the definitions and theorems
from the area of mathematics generally called abstract algebra. It is based
on the two books Abstract Algebra and Abstract Algebra, II by by John A.
Beachy and William D. Blair. |
|
|
Algebra On-Line |
Welcome to Algebra Online! Algebra Online is a free service designed to allow students,
parents, and educators throughout the world to communicate. This includes free private tutoring, live
chat, and a message board, among many other features. Questions and discussions relating to all
levels of mathematics (not just Algebra) are welcome. Algebra Online is the future in education! |
|
|
Animated Proof of the Pythagorean Theorem |
It’s just too cool! Check it out! |
|
|
Computers and Maths Teaching |
Suggestions for teaching with functions, spreadsheets,
assessment, modelling, shareware, and graphics. The author, Pete Hobson
leaves in Canberra, Australia. |
|
|
Cornell Math-Science Gateway |
This site provides links to resources in mathematics and
science for educators and students in grades 9-12, although teachers of other
levels may find these materials helpful. |
|
|
David Eppstein's Recreational Mathematics Page |
A site that contains a mixture of puzzles, silliness,
curious/useless math, and quite serious (but not overly technical) math. Check
out the Geometry Junkpile! |
|
|
Educational JAVA programs |
The idea behind this site is to give a student
challenging and motivating problems and have her use the tools provided in
this site to explore new concepts, discover new ideas, and improve her
abilities to solve problems. The developer hopes that the programs provided
here will make the students stronger in their conceptual understanding, basic
skills, and problem solving abilities. With the advent of the Internet and Java™ it is possible
to not only have the ability to use these tools both at school and at home
but also to enhance the collaborative aspects of learning, where students can
work independently but share ideas and jointly build knowledge. |
|
|
Educational Standards, Technology, Applications and
Resources (EdSTAR) |
Good description of mathematical concepts and
applications |
|
|
Eisenhower National Clearinghouse |
This is one huge Math resource site sponsored by the
U.S. Department of Education, Office of Educational Research and Improvement.
The nationally recognized information source for K-12 mathematics and science
teachers. |
|
|
Enchanted Mind |
The purpose of this site is to create a daily experience
of humor, inspiration and creative problem solving. The combination of these
three elements, if practiced daily, will open the mind, allowing creative
genius to blossom. With this method you can stimulate creative thinking
habits and add a little delight to your day. Pretty lofty, huh? Still, it’s
worth a look—really! |
|
|
Eric Weisstein's World of Mathematics |
A rare and, probably, the most comprehensive collection
of mathematical information available on the Web. This is a dynamic extension
of Eric's hardcopy Encyclopedia of Mathematics. There are close to 9,000
entries each with book references and links to related Web sites. Some topics
are covered better than others, but in most cases you may expect to glean a
good deal of information on a huge variety of topics in Mathematics |
|
|
ExploreMath.com |
Very good interactive demonstrations of slope, linear
equations, and other algebraic equations. |
|
|
Frequently Asked Questions in Mathematics Web Site |
The name says it all! It is a collection of mathematical
essays maintained at the University of Waterloo. The site covers many topics
in history, algebra (mostly higher), number systems and Number Theory and
more. Special pages describe Famous problems in Mathematics. |
|
|
FSU’s Math WWW Virtual Library: Education |
This is a site place where a math teacher can spend
hours traveling back and force between various links. |
|
|
Math In Daily Life |
The next time your students ask, “How are we ever gonna
use this?” send them to this web site. |
|
|
Math for Decision Making |
The next time your students ask, “How are we ever gonna
use this?” send them to this web site. It explores how math is used in making
important decisions (in business). Each activity comes with a lesson plan and
downloadable activity sheets. |
|
|
Geometry Center |
This site is maintained by the Center for the Computation
and Visualization of Geometric Structures, a National Science Foundation
Science and Technology Center at the University of Minnesota. It's a site
that is hard to compete with. Many facets of Geometry are represented on
their pages. Check out the Java section! |
|
|
Harcourt Brace Multimedia Math Glossary |
This is a MUST-SEE site! It could go a long way toward
helping students who need a better grounding math fundamentals. |
|
|
Cyber Exchange Math Lessons |
Not many lessons but what they do have is kind of cool! |
|
|
AutoMaths—Online math activities |
Kind of silly but still a useful place. |
|
|
Figure This Out—Math Challenges for Families |
Web site designed by the US government that encourages
families to work together to solve math problems. Hey, it could happen! |
|
|
iMath |
This is a site where you can get a free download of the
iMath communicator that provides math symbols. Using iMath students and
teachers can discuss math with each other over the Internet. iMath provides
user accounts which enable you to send and receive math pages. It’s like a
math chatroom! |
|
|
Impossible Things |
Want to stump your know-it-all students? Take a gander
at this page for some inspiration. |
|
|
Interactive Activities Index |
The activities on this site are designed for either
group or individual exploration into concepts from middle school mathematics.
They are arranged according to the NCTM Principles and Standards for School
Mathematics and the NCEE Performance Standards for Middle School. This is one
you MUST see! |
|
|
Interactive Mathematics Activities |
Learning starts from wondering. A purpose of this site
is to serve as a resource for things, simple but curious, related to
Mathematics. |
|
|
JAVA Applets |
The material presented on this site is for middle school
students, high school students, college students, and all who are interested
in mathematics. You can find interactive programs that you (or your students)
can manipulate. There is also a lot of animation that helps students grasp
the meaning of mathematical ideas. Attention: To use the resources here, you’ll need to use
Microsoft Internet Explorer 4.5/5.0 NOT Netscape. |
|
|
Joe’s Surfin’ Safari Math Links |
Developed by an Effingham County Middle School teacher,
this site houses an enormous amount of math related links. It’s definitely
worth your time to browse here. |
http://members.tripod.com/MR_LEGO_JOE/math_1.htm
and |
|
Key Topics |
A lot—and I mean A LOT--of things related to
mathematics. If your students have ever said, “How are we going to use this
later on in our lives?” or “hey, what else is there we need to know when
learning algebra?” then this is a site for you! |
|
|
King's List of On-line Math Activities |
A mega-list of all kinds of math-based activities. |
|
|
MacTutor History of Mathematics Archive |
This is a most remarkable and well-organized site. There
is plenty of information (not all of which is actually historical).
Information can be accessed (and, therefore, searched for) in a variety of
ways - several indices, chronologies, birthplace map. There is also a page of
Famous Curves. |
|
|
Math Archives (K-12 Resources) |
This place contains Internet sites that contain significant collections of materials which can be used in the teaching of mathematics at the K-12 level. The site is organized into the following categories: q
Lesson Plans q
Software q
Topics in Mathematics q
Contests and Competitions q
Professional Societies q
Other |
|
|
Math For Morons Like Us |
Surprisingly useful web site developed by (*gulp*) math
students with an attitude. Hey, every little bit helps! Check it out! |
|
|
Math Forum |
The Math Forum is a leading center for mathematics and
mathematics education on the Internet. The Math Forum's mission is to provide
resources, materials, activities, person-to-person interactions, and
educational products and services that enrich and support teaching and
learning in an increasingly technological world. Their online community
includes teachers, students, researchers, parents, educators, and citizens at
all levels who have an interest in math and math education. The site is the
hub of the math education activity on the Web |
|
|
Math Teacher Home Page: Technology |
The focus of
this site is on using technology (Computers, Multimedia, the Internet,
Graphing Calculators) to improve learning and teaching. The author states,
“Although learning takes place in a technological environment the focus is on
the mathematics and not the technology. The computer and the graphing
calculator are tools to facilitate knowledge not goals in themselves. Please
remember that the teacher is the best technology present.” |
|
|
Math.com |
The world of math, on-line! |
|
|
Maths Online |
A well organized collection of topics each illustrated
by one or more applets. A gallery of topics from introductory Calculus that
are suitable for high school students and teachers and college freshmen. The
authors have even managed to illustrate the notion of derivative with simple
but entertaining puzzles. |
http://www.univie.ac.at/future.media/moe/
and |
|
MegaMathematics! |
This is a site from the Los Alamos National Laboratory.
It contains hands-on lessons and resources in knot and set theories, coloring
problem, algorithms and finite state machines. The presentation is very
substantive but elementary. |
|
|
National Council of Teachers of Mathematics |
You can find conference and membership information and
online publications with plenty of entertaining math activities. Valuable
resources are provided for teachers, family, leaders, and researchers. |
|
|
National Library of Virtual Manipulatives for
Interactive Mathematics |
Check out the Virtual Library. If you don’t, well,
you’re really missing the boat! |
|
|
No Matter What Shape Your Fractions are In |
Like Visual Fractions, this site can be an invaluable
aid in teaching students how to think in terms of fractions. |
|
|
Polyhedra |
This is a site by George Hart of Hofstra University.
This is also the Internet at its best. It contains virtual reality models of
all kinds of polyhedra—something like 850 in all. There are also directions
how to create one's own paper models. |
and http://www.georgehart.com/virtualpolyhedra/classroom.html
(for classroom ideas) |
|
POPMathematics |
Did you ever wonder what made your math teacher get so
excited about some topic in Mathematics? On this page, the authors try to
collect items about Mathematics one of which hopefully may explain such weird
behavior. |
|
|
Prometeo |
Prometeo is the Spanish name of the Greek God
Prometheus, who brought fire and technology to mortal men. This project is
being developed in the same spirit, with the purpose of bringing educators
all over the world useful tools for the development of educational software
that will run on the Internet. The main purpose of project Prometeo is to create powerful
tools for the development of educational software that can be used directly
on web pages, and to make these tools readily available to educators all over
the world. Take a look at their math related software. |
|
|
WebMath |
Type in the problem and this site will show you how
to arrive at a solution. |
|
|
Varnelle Moore's Primary Math Activities |
This site hosts some activities that might be
appropriate for struggling or special education math students. |
|
|
Yahoo’s Math related links |
Often a good place to start looking, this directory is
categorized and chocked full of useful sites. |
|
|
Math Problem of the Week Web Site |
A useful web site you or your students might want to
visit. It has problems for each level of ability. |
|
|
Mathematics that are FUN! FUN! FUN! |
Name says it all—give it a try! |
|
|
Visual Fractions |
This site will help many students! It makes those often
confusing fractions easy to understand. |
|
|
PurpleMath |
According to the site, it’s “Your algebra resource” and
boy is it EVER! You simply must see the modules! |
|
|
SheppardSoftware |
Check this out! This site allows teachers to use its
software for free! They say… “Our software policy for schools: Our policy is that registered versions of our software
are completely free to teachers and schools. For students' home use,
you are welcome to hand out the shareware versions of our programs or to have
them download shareware versions at their homes. The shareware versions are
the same as the registered versions, but have nag screens asking for
purchase. To receive electronically the registered versions of the
programs simply send us an e-mail specifying which programs you'd
like. If you already have the registered version you are free to use it
throughout your school. You are even welcome to give copies of our registered
software to other school districts. We would, however, like their e-mail
addresses if possible. Frankly, we're not giving our software to schools just
because we're "good guys". We've gotten valuable feedback from
schools on how to improve our programs. Also, students who use programs in
schools are likely to want to use them at home. Finally, being in many
schools worldwide is an important selling point we have. How to get free registered copies of our software for
your school or tutoring center: Go to our Software Description Page and decide which
programs would benefit your school. Email educators@sheppardsoftware.com with your request. Include in your email your name, your position, your
school or institution, which grade you teach.” |