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:
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 used in this study takes a cue from the 1997 report from The Presidents 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.
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.
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 RangerTM (CBRTM) is a stand-alone version of the motion sensor. The CBRTM does not need the CBL unit but there are other devices available aside from a motion detector.