Finding Common Ground, Indianapolis, March 2006
Technology Group Report
Our use of “technology” concerns information technologies focused substantially on
- numeric and data processors
- graphing and geometric visualizers
- symbol manipulators and the like.
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.
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
Content & Sequence
- Technology and algorithms
- Examples and proof
- Should computational skills always precede equivalent technology
- Are there conditions under which use of technology should replace
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
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
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.
- 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
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
A lack of technology acceptance or adoption in university departments
- fails to take advantage of students’ prior technology-supported
- can miss opportunities to develop students’ understandings,
- can adversely affect understandings of educational applications
of technology by prospective teachers enrolled in courses in those
- 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