## Finding Common Ground, Indianapolis, March 2006 Technology Group Report

Working Group:
Kathy Heid
Nicholas Jackiw
Alfred Posamentier
David Santucci
Susan Schwartz-Wildstrom
Bill Velez
Ann Watkins

Working Definition:
Our use of “technology” concerns information technologies focused substantially on mathematics.
• numeric and data processors
• graphing and geometric visualizers
• symbol manipulators and the like.

#### Overall Perspective:

In their education, workplace, and throughout their lives, all students must be able to use technology to solve problems mathematically. Mathematical preparation should include developing the ability to describe phenomena in a form in which technology can be used to solve the problem, as well as include interpreting, validating and explaining to others solutions resulting from technology use.

#### Prior Perspectives:

In these observations and recommendations, we endorse—and seek to particularize and extend—the Technology Principle as stated and discussed in the NCTM Principles and Standards for School Mathematics (2000).

#### Flashpoints: Content & Sequence

• Technology and algorithms
• Examples and proof
• Should computational skills always precede equivalent technology skills?
• Are there conditions under which use of technology should replace computational skills?

Technology and Algorithms (>)
A conceptual understanding of, and demonstration of facility with, arithmetic and algebraic processes by students is essential.

Students should be able to add, subtract, divide, and multiply rational numbers by hand, and perform these and other mathematical processes using technology.
examples and proof (I…)

Technology provides tools that enable teachers and learners to explore large numbers of examples quickly and easily. This can facilitate making conjectures and lead to conviction about the truth of one’s observations; and it can effectively identify counter-examples or deviations from presumed patterns.
examples and proof (…II)

At the same time, a preponderance of compelling examples can make it difficult to motivate appropriate discussions of mathematical proof based on conviction alone. By emphasizing the many other roles of proof in mathematics—for example: explanation, communication, revelation of structure, further discovery—teachers can continue to develop logical argument and proof as the end goal of mathematical experiment and conjecture.
Should hand-skills always precede equivalent technology skills? Are there conditions under which use of technology should replace computational skills? (>)
Students can learn important mathematical ideas without being able to do associated calculations and algorithms by hand. Therefore, technological explorations of those ideas can productively precede the development of related computational skills; and for some students, technology permits students to engage with mathematical ideas at a level that would not be accessible without technology.

#### Flashpoints: On Organization

• Resistance to incorporation of technology
• Perception that technology is too expensive and volatile
• Should we ever ban technology from the mathematics classroom?

#### Resistance to incorporating technology into mathematics teaching

We are concerned with the rate of implementation of educational technology at the K-12 level, which can reflect teachers’ lack of opportunities to explore the use of appropriate technologies. The problem can be exacerbated by inappropriate ratios of investment on infrastructure to professional development, and by the situation in mathematics departments at the university level, where there is little infrastructure, incentive, or interest in—and sometimes an explicit aversion to—using technology in the teaching of mathematics.

#### Perception that technology is too expensive and volatile

Educational technology is an essential component of mathematics instruction and bears significant costs (of hardware and software, but more importantly of professional development, support specialists, and curricular integration). We urge policymakers to commit to cost allocations and budgets that sustain educational technology investments and infrastructure over time in the way that they commit to textbook infrastructure.

#### Should we ever ban technology in the mathematics classroom?

University departments of mathematics should support unconditionally the use of appropriate technologies at least through the teaching of calculus.
A lack of technology acceptance or adoption in university departments of mathematics
• fails to take advantage of students’ prior technology-supported mathematical abilities,
• can miss opportunities to develop students’ understandings,
• can adversely affect understandings of educational applications of technology by prospective teachers enrolled in courses in those departments,
• may discourage productive technology use in K-12 mathematics.

#### Flashpoints for another day

• Perception that technology will degrade students’ mathematical skills or mathematical thinking
• Perception that technology will replace face-to-face instruction
• Perception that technology exacerbates existing socio-economic and cultural divides