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Integrating IT Into Each Subject Area

IT-Using Mathematic Educators

The roots of IT lie in mathematics, and IT is now a common tool throughout mathematics. Computational mathematics, along with Pure and Applied Mathematics, are three common ways of "doing" math.

One of the purposes of this Webpage is to support a Virtual Community of IT-Using math educators. Click here to find out how to participate in an IT in Math Education Virtual Community.

This Webpage is a "Work in Progress." Here is a list of topics that are currently being developed.

Brain Science and Computer Technology in Math Education

Computer Algebra Systems

Elementary School Mathematics Education

History of Calculators & Computers

Middle School Mathematics Education

Secondary School Mathematics Education

Virtual Manipulatives

General References Not Included in the Above

 

Join the Oregon IT in Math E-mail Distribution List

or-it-math is an interactive E-mail distribution list (anybody can join, anybody can post) in Math Education. It serves as a communication vehicle for a community of educators interested in IT in mathematics education.

To join the Math list and the general OTEC list, send an E-mail message to:

majordomo@lists.uoregon.edu

In the body of the message (NOT in the subject line) enter the text:

subscribe or-it-math
subscribe ocite
end

After you join the or-it-math E-mail Distribution List, send a message to the list talking about some of the good things you are doing and/or are aware of uses of IT in Math Education. If you are aware of really good websites that Oregon IT-Using Math teachers might find useful, share this information.

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General Math Education References

Association of Mathematics Teacher Educators (AMTE) [Online]. Accessed 11/18/00: http://www.ceemast.csupomona.edu/amte/.

The AMTE is a non-profit organization created to promote the improvement of mathematics teacher education in all its aspects.

Bonn, K.L, and Grabowski, B.L. (January 10, 2001). Generative Learning Theory: A Practical Cousin to Constructivism [Online]. Accessed 3/1/01: http://www.math.mtu.edu/~klbonn/GLT_in_New_Orleans.html. Quoting from the Website:

Abstract

The K-16 mathematics education community has embraced the philosophy of constructivism, yet instructors continue to struggle with practical applications of this philosophy. We suggest that constructivist researchers and practitioners study and employ a theory of learning proposed by Merlin Wittrock in 1974--generative learning theory. While Grabowski's 1996 article gives the general audience a thorough description of Wittrock's theory, the purpose of this article is to highlight the main points of generative learning theory for the mathematics education community in hopes that they will see it as a viable theoretical framework for future research in the teaching and learning of mathematics.

International Conference on Technology in Collegiate Mathematics [Online]. Accessed 7/15/01: http://archives.math.utk.edu/ICTCM/. Quoting from the Website:

Welcome to the home site of the Electronic Proceedings of the International Conference on Technology in Collegiate Mathematics (EPICTCM), an annual conference sponsored by Addison-Wesley. These Proceedings are published on the World Wide Web by the Math Archives.

Jones, Rebecca (1998). Solving problems in math and science education [Online]. Accessed 7/15/01: http://www.asbj.com/199807/0798coverstory.html.

This article contains a number of suggestions for how to improve science and mathematics education in the United States. It is based on an analysis of results from TIMSS. Quoting from the Website:
Researchers often lament the scarcity of longitudinal studies in math and science education. But the Third International Math and Science Study (TIMSS) and other studies now under way hold out tantalizing clues about ways to improve math and science instruction

K-12 Mathematics Curriculum Center [Online]. Accessed 7/15/01: http://www.edc.org/mcc/about.htm. Quoting from the Website:

The K-12 Mathematics Curriculum Center was established in 1997 by Education Development Center, Inc., with funding from the National Science Foundation. Its mission is to support school districts as they build an effective mathematics education program using curriculum materials developed in response to the National Council of Teachers of Mathematics' Curriculum and Evaluation Standards for School Mathematics.

Math Forum: Home of the Internet Math Library [Online]. Accessed 4/15/01: http://forum.swarthmore.edu/mathed/index.html.

This site provides links to a a large number of websites of interest to math educators.

Mathematics Education: Constructivism in the Classroom [Online]. Accessed 4/15/01: http://forum.swarthmore.edu/
mathed/constructivism.html. Quoting from the Website:

"Students need to construct their own understanding of each mathematical concept, so that the primary role of teaching is not to lecture, explain, or otherwise attempt to "transfer" mathematical knowledge, but to create situations for students that will foster their making the necessary mental constructions. A critical aspect of the approach is a decomposition of each mathematical concept into developmental steps following a Piagetian theory of knowledge based on observation of, and interviews with, students as they attempt to learn a concept." -- Calculus, Concepts, Computers, and Cooperative Learning (C4L)

Math Learning Center (MLC) [Online]. Accessed 7/21/01: http://www.mlc.pdx.edu/ .

The MLC is non-profit Oregon organization operating out of offices located in Salem and Portland. Quoting from the Website:
The Math Learning Center was formed in 1976 as an outgrowth of the Oregon System in Mathematics Education, a statewide experimental project to improve the teaching of mathematics. Three mathematics educators, with teaching experience ranging from grade six through university level, recognized the need to continue the work started under the project. Abandoning traditional education roles, they established an independent 501(c)(3) corporation to generate programs and advance ways of teaching and learning mathematics that enable each individual (a) to develop their mathematical abilities, and (b) to find joy in the processes of teaching and learning.

The critical role visual thinking plays in the learning of mathematics became central to The Math Learning Center in 1980 as the Center staff sought effective ways for teachers and learners to overcome math anxiety and avoidance. Literature suggesting that visual approaches to teaching and learning have universal validity was reviewed and various methods were tested with Math Learning Center audiences. Since then the Center not only incorporates visual thinking into its activities, but also contributes to the body of literature and theoretical framework of the field. Workshops and materials developed by the Center promote teaching styles and strategies emphasizing active-learning experiences, problem-solving skills, independent investigation, and the use of visual models.

National Center for Educational Statistics: Create a Graph [Online]. Accessed 3/8/02: http://nces.ed.gov/nceskids/Graphing/. Quoting from the Website:

Graphs and charts are great because they communicate information visually. For this reason, graphs are often used in newspapers, magazines and businesses around the world. NCES constantly uses graphs and charts in our publications and on the web. Sometimes, complicated information is difficult to understand and needs an illustration. Other times, a graph or chart helps impress people by getting your point across quickly and visually. Here you will find four different graphs and charts for you to consider. Maybe it will help explain what you are trying to show. Use homework problems, things you have a special interest in, or use some of the numbers you find elsewhere on this site. Have fun!

SimCalc: Democratizing Access to the Mathematics of Change [Online]. Accessed 3/21/01: http://www.simcalc.umassd.edu/.

This is a project funded by the National Science Foundation. Free software is available for both Mac and PC platforms, and it is downloadable from the Website. Quoting form the Website:
The Mathematics of Change is centrally important to living and working in a rapidly evolving democratic society. Problems involving rates, accumulation, approximations, and limits appear in everyday situations involving money, motion - virtually any situation where varying quantities appear. Yet only a small subset of students who take traditional calculus courses currently gain access to these concepts, and they do so only after a long series of prerequisites that eliminate 90% of their peers.

The SimCalc Project aims to democratize access to the Mathematics of Change for mainstream students by combining advanced simulation technology with innovative curriculum that begins in the early grades and includes powerful ideas extending beyond classical calculus.

This is MegaMathematics! [Online]. Accessed 10/27/01: http://www.c3.lanl.gov/
mega-math/menu.html.

This Website contains a number of excellent mathematical problem-solving investigations for precollege students. This materials on this Website are developed by a project supported by the Los Alamos National Laboratory, with much of the work being done by volunteers. Quoting from the Website:
Metacognition is thinking about thinking. Often when solving math problems, a solution or a means to one pops into our head so quickly that we don't know how we found it. It is not always easy to slow down our thinking, retrace the path of our thoughts and examine our hidden strategies. Doing so can help us to develop a set of strategies to try when we are utterly stumped.

That is why mathematicians are always asking themselves, "How did I figure that out?" In other words, the answer to a question is only the beginning. Understanding how you thought up that answer can help you discover the answers to much harder questions.

Weisstein, Eric. World of Mathematics [Online]. Accessed 4/4/02: http://mathworld.wolfram.com/. Quoting from the Website:

Eric Weisstein's World of Mathematics (MathWorldTM) is the web's most complete mathematical resource, assembled over more than a decade by internet encyclopedist Eric W. Weisstein with assistance from the mathematics and internet communities.

MathWorld is a comprehensive and interactive mathematics encyclopedia intended for students, educators, math enthusiasts, and researchers. Like the vibrant and constantly evolving discipline of mathematics, this site is continuously updated to include new material and incorporate new discoveries.

Although it is often difficult to find explanations for technical subjects that are both clear and accessible, this website bridges the gap by placing an interlinked framework of mathematical exposition and illustrative examples at the fingertips of every internet user.

If you find MathWorld useful, you may also be interested in the author's Treasure Troves of Science site, which contains topically similar material about astronomy, scientific biography, science books, physics, and other areas of science.

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Elementary School Mathematics

References

Clements, D. H. (1999). 'Concrete' manipulatives, concrete ideas. Contemporary Issues in Early Childhood, 1(1), 45-60 [Online]. Accessed 3/22/01: http://www.gse.buffalo.edu/org/buildingblocks/
NewsLetters/Concrete_Yelland.htm.

The Web reference is for a slightly updated version of the original article. The discussion covers both physical manipulatives and computer-generated manipulatives. The article suggests that it is not inherently obvious that one form of manipulative is better than another, and that computer-generated manipulatives may well be superior in some cases.

Clements, D. H., & Swaminathan,S. (1995). Technology and school change: New lamps for old? Childhood Education, 71, 275-281 [Online]. Accessed 3/22/01: http://www.gse.buffalo.edu/org/buildingblocks/
NewsLetters/Tech_and_School_DHC.htm

For many years, Doug Clements has been a national leader in the field of computers and school mathematics. This 1995 article provides a good introduction to effective uses of computers in early childhood education.

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Middle School Mathematics

Show Me Project [Online]. Accessed 7/15/01: http://showmecenter.missouri.edu/showme/project.html.

A National Science Foundation project supporting implementation of standards-based middle grades mathematics curricula It focuses on five middle school sets of mathematics curriculum materials that were developed through NSF funding. One can explore each of the five curricula from the point of view of various topics, such as Technology. In general, the curricula make use of calculators, and some use computers. None aim for a deep integration of IT into the mathematics curriculum. Indeed, several note that the curriculum materials can be done without the technology.

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Secondary School Mathematics

Brief Introduction

Secondary school mathematics tends to be taught by faculty who have a keen interest in mathematics and who have had substantial formal coursework in the field. Since the National Council of Supervisors of Mathematics (in 1979) and the National Council of Teachers of Mathematics (in 1980) recommended the use of calculators in mathematics education, we have seen a slow but steady increase in the use of IT in secondary school mathematics. For example, the use of scientific calculators and graphing calculators is relatively common in secondary school mathematics. Calculator technology has led to changes in curriculum content, such as dropping the "by hand" computation of square roots from the curriculum, and students no longer learning to make extensive use of math tables.

As notes in the Computer Algebra Systems part of this web page, very powerful tools exist for carrying out mathematical computations, manipulations, and procedures. Most schools are quite far from implementing routine use of such tools into their mathematics curriculum, instruction, and assessment.

Project-based learning (PBL) (with roots lying in a constructivist approach to instruction and learning) has long been used in a variety of curriculum areas. IT-Assisted PBL is of increasing importance in all academic disciplines and grade levels in our educational system. Some math courses make use of IT-Ass sited PBL, but there is substantial room for growth in this approach to math education.

References

Specht, Jim (2001) The Last Great Race: Using Technology to Support Math Instruction. ASCD Computer Technology Quarterly [Online].Volume 10, Number 4 Summer 2001. Accessed 7/21/01: http://www.ascd.org/readingroom/ctq/framemain.html.

Jim Specht is a math teacher at Hillsboro High School in Hillsboro, Oregon., currently teaching pre-algebra, geometry, and statistics. He's also past president of the Oregon Council of Teachers of Mathematics and the author of More Than Graphs (Key Curriculum Press) about the integration of graphing calculators in classrooms. Specht can be reached via e-mail at Jim15387@email.msn.com. Quoting from the Website:
Over the years, I've enjoyed using the Iditarod race in my math classes because it has been successful with all ability levels. I believe it would work at middle school, too. It conforms with the National Council of Teachers of Mathematics standards at many levels by appropriately using technology and addressing multiple learning styles with a variety of activities. As a teacher using the Last Great Race, I truly act as the facilitator, rather than as the dispenser of knowledge.

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Computer Algebra Systems

Brief Introduction

Various functional components of today's Computer Algebra Systems (CAS) were developed on for mainframes and timeshared computers more than 30 years ago. Now, very powerful CAS is available for microcomputers, and systems of less power are available on some handheld calculators.

Very roughly speaking, our formal educational system is faced by:

  1. Very inexpensive, solar powered, 6-function handheld calculators that students can readily learn to use in elementary school.
  2. Calculators that can do what those in #1 can do, but also do arithmetic with fractions. These are suitable for students at the upper elementary school levels and above.
  3. Scientific calculators.
  4. Graphing calculators.
  5. CAS calculators.
  6. Microcomputers that can do all that items 1-5 can do, and more.

There has been quite a bit of research on the use of these tools in mathematics education. Research on simple calculators (and, their decreasing price) by 1980 led the National Council of Teachers of Mathematics to recommend their use even in the elementary school math education curriculum. Such calculators are now allowed by many states in their statewide assessments, and on a variety of national exams such as the SAT.

Scientific and graphing calculators have become rather common in secondary school mathematics courses. The use of CAS calculators or computers at this level is slowly growing.

Uses of CAS as a tool for learning and doing mathematics can be divided into the categories: (a) computation (b) visualization, (c) experimentation, (d) pattern-recognition, and (e) conjecture-forming.

The references given below focus on CAS.

References

Asp, Gary and Kendal, Margaret (1999). Teaching Calculus with CAS [Online]. Accessed 7/15/01: http://www.tech.plym.ac.uk/maths/
CTMHOME/ictmt4/P01_McCr.pdf. The following abstract is quoted from the Website:

The article presents a research study on the use of a TI-92 Computer Algebra System with year 11 and year 12 Australian students taking calculus courses. The authors report favorable results in terms of student ability to deal with more complex problems.

Maple. Accessed 4/2/03: www.maplesoft.com. Quoting from the Website:

Maplesoft, which began operations in 1988, is headquartered in Waterloo, Ontario, Canada. Our mission is to increase the productivity, creativity and effectiveness of professors, researchers, students and industry professionals through the development, support and promotion of the Maple system.

The Maple system is an advanced, mathematical problem solving and programming environment. The analytical engine that powers Maple includes a powerful symbolic computation system that expresses and manipulates complex mathematics using automated mathematical formalisms and knowledge systems. The University of Waterloo's Symbolic Computation Group (Waterloo, Canada) initially developed the Maple symbolic technology.

Mathematica. Accessed 4/2/03: www.wolfram.com/products/mathematica. Quoting from the Website:

From simple calculator operations to large-scale programming and interactive document preparation, Mathematica is the tool of choice at the frontiers of scientific research, in engineering analysis and modeling, in technical education from high school to graduate school, and wherever quantitative methods are used.

Mathematica Version 1.0 was released on June 23, 1988, and was immediately lauded by the scientific and technical community, as well as the media, as a dramatic advance. Within months, there were tens of thousands of users around the world, and today Mathematica's reach continues to grow to well over a million.

Mathematica has been adopted in an unprecedented range of fields both in industry and in academia. In fact, Mathematica has been responsible for bringing advanced mathematics and computing to fields that were traditionally less technical, and in so doing it has substantially increased the market for technical software in general. A growing industry of applications, consulting services, books, and courseware serves the international community of Mathematica users.

Murphy, Lisa Denise (1999). Computer Algebra Systems in Calculus Reform [Online]. Accessed 7/15/01: http://www.mste.uiuc.edu/murphy/
Papers/CalcReformPaper.html. The following Abstract is quoted from the Website:

A history of the calculus reform movement is given, with emphasis on the roles of computers and computer algebra systems (CAS). The implications of CAS for the curriculum are considered. Early advocates of CAS in the calculus classroom stressed the opportunity to focus students' attention on concepts, with the computer taking on the burden of the algebraic manipulations that occupy so much time and attention in a traditional calculus course. Along with this change of emphasis comes the opportunity to alter the traditional sequence of topics in many ways, some of which are discussed here. In addition, CAS can be used to quickly create accurate graphs, allowing a more geometric approach to calculus. Calculus courses using CAS often involve much more student writing than traditional courses. Courses based on CAS generally use a constructivist approach, and frequently incorporate some form of cooperative learning. Evaluating these courses has been difficult because not only the methods, but also the goals, are different from those of a traditional course. Some of the evaluation techniques used by researchers are discussed. Evaluations comparing reformed calculus courses with CAS to traditional calculus courses generally favor the CAS courses, although there is some variation among CAS courses.

National Math Trail [Online]. Accessed 11/16/01: http://www.nationalmathtrail.org/front2.html. Quoting from the Website:

The National Math Trail is now in its second year, thanks to renewed support from the US Department of Education's Star Schools program, through the Satellite Education Resources Consortium (SERC), and the Verizon Foundation.

The National Math Trail is an opportunity for K-12 teachers and students to discover and share the math that exists in their own environments. Students explore their communities and create one or more math problems that relate to what they find. Teachers submit the problems to the National Math Trail site, along with photos, drawings, sound recordings, videos--whatever can be adapted to the Internet. All submissions will be posted to the site as they are submitted. They will also be indexed according to grade level and math topic and will remain on the site for access by educators, students and parents.

 

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