INTRODUCTION

Current reform movements in mathematics education have proposed
infusing the mathematics curriculum with technology and creating
technology-intensive instructional environments. The technologies
proposed and supported within technology-intensive instructional
programs are appropriate for mathematics education such as powerful
graphing calculators and data collection devices, the Internet and
the World Wide Web, Spreadsheets, and Computer Algebra Systems.
__The Principles and Standards for School Mathematics: Discussion
Draft__ (1998) from the National Council of Teachers of Mathematics
(NCTM) outlines six Guiding Principles for School Mathematics
Instructional Programs. According to NCTM's Technology Principle:
"Mathematics Instructional programs should use technology to help all
students understand mathematics and should prepare them to use
mathematics in an increasingly technological world." (Page 40)

And NCTM's Equity Principle affirms: "Mathematics instructional
programs should promote the learning of mathematics by __all__
students." (Page 23) NCTM promotes mathematics for all, challenging
the notion that some students are just not proficient in mathematics.
By "all" NCTM means that mathematics programs should be promoted for
students who have traditionally done well in mathematics as well as
those that have not done as well or have not been given the same
opportunity to learn substantial mathematical concepts. Mathematics
curricular programs should promote students who are seen as low
performing students as well as high performing students. Note that
the use of the term "performing" denotes a dynamic view of the
students as active learners and that students do not exist within a
set of static descriptors.

Some students have been disenfranchised by the traditional mathematics curriculum. This has happened in a variety of ways that include subtle reinforcement by educational systems or more overt displays of ability tracking, a practice in which students are sorted into different instructional sequences that often results in inequitable educational opportunities and outcomes for students (NCTM, 1998). The practice of sorting, tracking, or ability grouping is another inequitable example describing and sorting students into static categories.

Furthermore, NCTM emphasizes that technology be used to promote the understanding and use of mathematical concepts. NCTM also describes the technology tools that should be included in the mathematics instructional program to be calculators, computers, micro-computer/calculator based laboratories, Internet technology, and the World Wide Web. NCTM supports the implementation of technology in mathematics instructional programs but warns against the possible reliance on technology as replacements for basic understandings.

Finally, NCTM recommends preparing students to use mathematics in an increasingly technological world. The twenty-first century is rapidly approaching and the jobs that today's students will hold will become increasingly more infused with technology, such as sophisticated computer programs and data collection devices.

This research is designed to address the following questions:

- How can hand-held calculator technology help low performing and high performing middle school students identify more with the mathematics they are learning?
- How does technology-intensive instruction help high performing and low performing middle school mathematics students learn new mathematics, and improve their attitudes toward mathematics?

Students in low-tracked classes and low performing students may demonstrate negative attitudes toward mathematics and begin to disidentify or actively choose to not identify with mathematics. Technology and technological tools might help low and high performing students identify with mathematics and actively choose to respond positively toward mathematics.

In order to answer these questions a technology intensive mathematics unit was created and used in an instructional period with middle school students at two different ability levels. The goals for this research project were for students to explore the concept of rate, and reading and interpreting graphs as well as to study the attitudes toward mathematics in a basic mathematics class and algebra class in a middle-school setting. Hand-held calculator technology was introduced into a basic mathematics class and an algebra class at the eighth grade level over a two-week period of instruction.

There have been many advances in hand-held calculator technology; these include graphing capabilities, symbolic representation, and real-world data collection. These advances are transforming the landscape of mathematics education by creating the possibility for all students to access powerful technology and technology tools for exploration and analysis in a manner similar to scientists and mathematicians. Hand-held calculator technology offers a few unique advantages over computers as the technological tools of choice for this study. The smaller size and lower cost than computers grant more opportunities for each student to handle and operate calculator equipment. This means a greater number of students have opportunities to experiment and explore the mathematical concepts, emphasizing the students as dynamic participants and much more like scientists. An arrangement of calculator and data gathering devices offers a more lab-like environment to facilitate the exploration of mathematics concepts within group collaboration and configurations.

This section will distinguish between the different pieces of technology used in this study. Throughout the rest of this study terms will be used to describe the technology setting of instruction these terms are defined here.

__Technology-Intensive Instruction__

Technology-intensive instruction used in this study takes a cue from the 1997 report from The President’s Committee of Advisors on Science and Technology (PCAST) which emphasizes more instruction with technology at the K-12 levels.

This instruction is conducted through technological tools and explorations within a laboratory environment in cooperative teams and with the instructor as the facilitator instead of the fountain of knowledge. Students interact with the equipment pose conjectures, test, make decisions, and explain results to others and the instructor.

__Calculators and Calculator Technology__

Calculators referred to in this document are Graphing Calculators except where specifically noted as four-function calculators. In this research the calculators used were Texas Instruments Model 82 or the TI-82.

__Hand-Held Technology__

This term is used to explicitly mean graphing calculator technology and associated data collection tools. This term does not apply to newly developed hand-held computers and similar devices.

__Data-Collection Devices__

This term applies to devices that when attached to the Texas
Instruments graphing calculators through a Calculator Based
Laboratory (CBL) unit create a laboratory environment where
real-world data can be collected and displayed graphically. The
Calculator Based Ranger^{TM}
(CBR^{TM}) is a stand-alone version of
the motion sensor. The CBR^{TM} does
not need the CBL unit but there are other devices available aside
from a motion detector.