Considerations for Appropriate
Technology
Abstract

Mathematics programs must take full advantage of the power of calculators and
computers at all levels ( NCTM, 1980)
 Changes in technology and the broadening of
the areas in which mathematics is applied have resulted in growth and changes
in the discipline of mathematics itself (NCTM, 1989)
 Technology is essential in teaching and learning
mathematics; it influences the mathematics that is taught and enhances
studentsÕ learning. (NCTM, 2000. p.24)
ÒTechnology
in education is not a new issue nor a recent phenomenon.Ó (Eisele & Eisele,
cited by Donald, 1998) As stated above, technology is considered a critical
component in mathematics education. Mathematics teachers should use technology
for their teaching. The problem of technology is not that technology is used or
not in school, but what the appropriate use is. In this paper I examine the
appropriated use of technology and the reason why technology does not work, and
consider what we should do to use technology appropriately.
What is technology in
mathematics education?
The National Academy of
Sciences (2001) stated Òtechnology is the process by which humans modify nature
to meet their needs and wants.Ó The National Academy of Sciences (2001) declared technology is not only the
artifacts, such as computers and software, aircraft, and microwave ovens, but
the knowledge and processes used to create and to operate technological
artifacts are also the part of technology.
I
refer to software available in K12 schools, colleges and universities. Wilson
described the software tools: spreadsheet, hand held calculators, graphing,
dynamic Geometry, communication tools and the website. In details, Òa
spreadsheet is a tool for organizing and analyzing data (Chapin, Illingworth,
Landau, Masingila, and McCracken, 2001, p.12).Ó Microsoft Excel is generally
used as a spreadsheet. Wilson considered handheld calculators, for example
TI81, TI82, TI83, having the function of computations. Generally, handheld
calculators are used in computations or in clarifying a square root or in
making a graph. Graphing programs are diversely used in different levels. For
example, there are Algebra Xpresser, Theorist, Mathematica, Maple, or MatLab
and Graphing Calculator. Dynamic geometry programs are GeometerÕs Sketchpad,
Cabri, and Geometric Supposer. These tools provide visual effects and
explorations for the middle grades. Communication tools are for communication
or presentation with other students or the teacher. For instance, word
processors, spreadsheets, Internet browsers ( Netscape Navigator, Microsoft
Explorer, etc.) web page tools ( Adobe PageMill, Clarisworks HTML, etc.), and
Email are usually used. Teachers and students can communicate out of school
through the Internet web page and email. The website can be built by
participants on the server or by the mathematics teachers after the courses. It
also helps to develop the understanding of concepts and skills in teaching and
learning. Kaput and Thompson (1994) called the computer or calculator the electronic
technologies. Here I consider all software and skills available in mathematics
education as technology.
.
What is appropriate
technology
in mathematics education?
One
of the misunderstandings for technology is that Òpaper and pencilÓ is not
technology. ÒPaper and pencil is one of the innovative tools for school.Ó
(Personal communication in Dr. Choe, 2004) The important thing when mathematics
teachers consider technology is what is appropriate uses of technology in their
teaching and studentsÕ learning.
As
stated above, technology is not just tangible products. To talk about the appropriate
technology
in mathematics education, we should first think about the goal of teaching and
learning. The appropriate technology indicates that the technology is used
effectively in accordance with the educational goal. To judge the effectiveness
of technology, we ought to know the goal using technology. ÒJudging the impact
of any particular technology requires an understanding of how it is used in the
classroom and what learning goals are held by the educators involved, ÉÓ
(Honey, 1999) When the technology is used effectively, Òtechnology applications
can support higherorder thinking by engaging students in authentic, complex
tasks within collaborative learning contextsÓ (Means, Blando, Olson, Middleton,
Morocco, Remz & Zorfass, 1993, cited by Honey, 1999). Talking about the
impact of technologies, Honey (1999) mentioned Òresearchers need to think about
what kind of technologies are being used in the classroom and for what
purposes.Ó North Central Regional Educational Laboratory (NCREL) made clear the
appropriate uses of technology recommended in NCTM as follows:
♦Appropriate calculators be available to
all students.
♦A computer be available in every
classroom for demonstration purposes.
♦Every student have access to a computer
for individual and group work.
♦Students learn to use the computer as a
tool for processing information and performing calculations to investigate and
solve problems.
(http://www.ncrel.org/tplan/guide/intmath.htm)
To
sum up the appropriate uses of technology in mathematics education, mathematics
teachers should have their teaching goal and then, use appropriate
technology
for their teaching and studentsÕ learning.
When technology does not
work and the solutions
NCREL
described technology as a tool in mathematics education for:
¬Acquiring, evaluating,
and processing numeric information.
¬Performing calculations
and interpreting trends.
¬Graphing and
communicating numeric information.
¬Investigating and
solving problems with mathematical premises.
¬Creating and running
models and simulations.
¬Scaffolding higher
levels of abstraction.
(http://www.ncrel.org/tplan/guide/intmath.htm)
Playing
those roles in mathematics education, technology has some problems.
There
are three categories of problems in working with technology in mathematics
education:
1.
Technology itself.
2.
The user of technology.
3.
A lack of curriculum.
The first problems
are technology is outdated or programs are not proper in mathematics classroom.
In the former case, administrators in schools and inventors of software have
responsibility. To use technology appropriately, administrators should decide
to set budgets for fast Internet environment and newest materials in school.
Valdez (1995) pointed out, in the critics of Internetbased mathematics
classroom, Òbecause of the expense and problems of access associated with the
Internet, many mathematics teachers argue that tools such as graphing
calculators are a better use of limited fund.Ó Using computer in a classroom is
as effective as using calculators in teaching and learning. If schools use the
Internet effectively, they need newest computers and software. Also, that Òthe
software presents mathematics content in an inappropriate, inaccurate, or
overpromising wayÓ (Valdez, 1995) is one critic of technology materials. To
overcome this problem, inventors should cooperate with mathematicians and
mathematics educators. They can create software with the appropriate
mathematical content through working with expertise of mathematical knowledge.
The second problem is about
teachers. Generally, mathematics teachers complain the lack of time and limited
resources using technology in a classroom. The most important thing in using
technology is the teachersÕ knowledge for technology. ÒTeachers and researchers
play an active role in interpreting technologies as tools for reforming schools
and in supporting and sometimes guiding the change process.Ó (Honey, Culp,
& Carrigg, 1999) Teachers should plan lessons to teach mathematical content
with technology, not technology itself. Honey (1999) stated Òstudents cannot be
expected to benefit from technology if their teachers are neither familiar nor
comfortable with it.Ó Recent teachers did not explore the computers and
software in their school days. Hence they do not know how to work by using
technology and what the technology affects to studentsÕ learning. For those
reasons, teachers need to explore technologies themselves by several workshops
or their own efforts. Cradler (1996) recommended Òinvolve educators in the
development of individualized instructional applications of technology as part
of the overall school level planning processÓ for educational technology
planners, developers, and implementers. Teachers bear in mind the
recommendation as implementers of technology.
The third problem is about
curriculum. In a case study at middle Tennessee State University (2001), one
faculty talk about the effect of technology, Òit is neither important or
unimportant; how it is used is what makes any technology workable and
effective.Ó The talking means how technology is used determines effectiveness
of technology. However, this problem is not only an implementerÕs
responsibility. That is, we do not have to blame the task of how technology is
used in mathematics curriculum upon the teacher only. To use technology
effectively, the change of mathematics curriculum is necessary. Teachers need a
guide for using material in their teaching. Not just ÒUse technologies.Ó
Mathematics curriculum should make the clear guidance of using technology for
teachers. It can enhance the development of teaching and the appropriate
technology.
Conclusion
Donald (cited in Sorensen,
1996) stated Òthe modern mathematics classroom is no longer necessarily
restricted to the chalkboard and the physical walls surrounding the studentsÓ
by the use of technology. Appropriate technology in mathematics
education means technology consistent with an educational goal. ÒIn order to be
effective, innovative and robust technological resources must be used to
support systematic changes in educational environments that take into account
simultaneous changes in administrative procedures, curriculum, time and space
constraints, schoolcommunity relationships, and a range of other logistical
and social factors.Ó (Honey, et al. 1999) To work with appropriate
technology,
program inventors should improve software in accordance with mathematical
knowledge and studentsÕ understanding. Kaput and Thompson (1994) stated one
power of electronic technologies that enable a change in mathematics education
lies Òin the control available to designers of learning environment.Ó It means
teachers can control the environment using technology, and can influence
studentsÕ learning more deeply than before. Hence, teachers should try to
develop the knowledge of technology and of how it works on studentsÕ
understanding. The mathematics curriculum is also reformed with the change of technologybased
classroom. It should indeed lead the change using technology appropriately in
mathematics education. This change might improve both of the professional
development of teachers and improvement of mathematics curriculum.
References
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