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 students’ learning. (NCTM, 2000. p.24)

“Technology in education is not a new issue nor a recent phenomenon.” (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 “technology is the process by which humans modify nature to meet their needs and wants.” 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 K-12 schools, colleges and universities. Wilson described the software tools: spreadsheet, hand held calculators, graphing, dynamic Geometry, communication tools and the website. In details, “a spreadsheet is a tool for organizing and analyzing data (Chapin, Illingworth, Landau, Masingila, and McCracken, 2001, p.12).” Microsoft Excel is generally used as a spreadsheet. Wilson considered hand-held calculators, for example TI-81, TI-82, TI-83, having the function of computations. Generally, hand-held 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 Geometer’s 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 E-mail are usually used. Teachers and students can communicate out of school through the Internet web page and e-mail. 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.

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What is appropriate technology in mathematics education?

One of the misunderstandings for technology is that “paper and pencil” is not technology. “Paper and pencil is one of the innovative tools for school.” (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 students’ 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. “Judging 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, …” (Honey, 1999) When the technology is used effectively, “technology applications can support higher-order thinking by engaging students in authentic, complex tasks within collaborative learning contexts” (Means, Blando, Olson, Middleton, Morocco, Remz & Zorfass, 1993, cited by Honey, 1999). Talking about the impact of technologies, Honey (1999) mentioned “researchers need to think about what kind of technologies are being used in the classroom and for what purposes.” 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 students’ 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 Internet-based mathematics classroom, “because 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.” 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 “the software presents mathematics content in an inappropriate, inaccurate, or over-promising way” (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 teachers’ knowledge for technology. “Teachers and researchers play an active role in interpreting technologies as tools for reforming schools and in supporting and sometimes guiding the change process.” (Honey, Culp, & Carrigg, 1999) Teachers should plan lessons to teach mathematical content with technology, not technology itself. Honey (1999) stated “students cannot be expected to benefit from technology if their teachers are neither familiar nor comfortable with it.” 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 students’ learning. For those reasons, teachers need to explore technologies themselves by several workshops or their own efforts. Cradler (1996) recommended “involve educators in the development of individualized instructional applications of technology as part of the overall school level planning process” 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, “it is neither important or unimportant; how it is used is what makes any technology workable and effective.” The talking means how technology is used determines effectiveness of technology. However, this problem is not only an implementer’s 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 “Use technologies.” 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 “the modern mathematics classroom is no longer necessarily restricted to the chalkboard and the physical walls surrounding the students” by the use of technology. Appropriate technology in mathematics education means technology consistent with an educational goal. “In 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, school-community relationships, and a range of other logistical and social factors.” (Honey, et al. 1999) To work with appropriate technology, program inventors should improve software in accordance with mathematical knowledge and students’ understanding. Kaput and Thompson (1994) stated one power of electronic technologies that enable a change in mathematics education lies “in the control available to designers of learning environment.” It means teachers can control the environment using technology, and can influence students’ learning more deeply than before. Hence, teachers should try to develop the knowledge of technology and of how it works on students’ understanding. The mathematics curriculum is also reformed with the change of technology-based 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

Cradler, J. (1996). Implementing technology in education: Recent findings from research and evaluation studies. Available at http://www.wested.org/techpolicy/recapproach.html

Chapin, S. H., Illingworth, m., Landau M. S., Masingila, J. O., & McCracken, L. (2001). Middle grades Math Tools for success, Course 2. Illinois, NJ: Prentice Hall.

Donald J. B. (1998). Technology in Mathematics Education. Dissertation of doctoral degree in the Virginia Polytechnic Institute and State University. Available at http://scholar.lib.vt.edu/theses/public/etd-81098-21917/etd-title.html

Honey, M., Culp, K. M., & Spielvogel, R. (1999). Critical Issue: Using Technology to Improve Student Achievement. The North Central Regional Technology in Education Consortium. Available at http://www.ncrel.org/sdrs/areas/issues/methods/technlgy/te800.htm

Honey, M., Culp, K. M., Carrigg, F. (1999). Perspectives in Technology and Education Research: Lessons from the Past and Present. The Secretary’s Conference on Educational Technology-1999. Available at http://www.ed.gov/rschstat/eval/techconf99/whitepapers/paper1.html

Kaput, J. J., & Thompson, P.W.( 1994). Technology in mathematics education: The first 25 years in JRME. Journal for Research in Mathematics Education, 25(6), 626-684. Special 25^th Anniversary Edition, edited by J. Wilson.

Kimble, C. (1999). The Impact of Technology on Learning Making Sense of the Research. Mid-Continent Regional Educational Laboratory. Available at http://www.mcrel.org/PDF/PolicyBriefs/5983PI_PBImpactTechnology.pdf

Lea, L. Clayton, M., Draude, B., & Barlow, S. (2001). Revisiting the Impact of Technology on Teaching and Learning at Middle Tennessee State University: A Comparative Case Study. TN Higher Education IT Symposium 2001. Available at http://mtsu32.mtsu.edu:11139/2001paper.htm

National Council of Teachers of Mathematics. (2000). Principles and Standards for School Mathematics. Reston, VA: The Author.

North Central Regional Educational Laboratory. Integrating Technology into the Curriculum. Available at http://www.ncrel.org/tplan/guide/intmath.htm

Ptaszynski, J. G. (1997). Technology Provides New Responses to Old Problems. The Technology Source. Available at http://ts.mivu.org/default.asp?show=article&id=523

Thoms, K. J., & Junaid, N. (1997). Developing Critical Thinking Skills in a Technology-Related Class. Preceedings of 2th Annual Instructional Technology Conference. Available at http://www.mtsu.edu/~itconf/proceed97/thinking.html

Wilson, J. W. Technology in Mathematics Teaching and Learning. Paper for the course. Available at http://jwilson.coe.uga.edu/Texts.Folder/Tech/Technology.Paper.html

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