The following guidelines were developed at the Center of Technology and Teacher Education at the University of Virginia for secondary preservice mathematics teachers (http://www.teacherlink.org/content/math/). I found them extremely usefull to create my projects for future elementary teachers. My goal is to create ready-to-use projects which integrate technology and mathematics.
Introduce
technology
in context
Address
worthwhile
mathematics with appropriate pedagogy
Take advantage
of technology
Connect
mathematics
topics
Incorporate
multiple
representations
Introduce
technology
in context
Features of technology, whether mathematics-specific
or more generic, should be introduced and illustrated in the context of
meaningful content-based activities. Teaching a set of technology or
software-based
skills, and then trying to find mathematical topics for which they
might
be useful, is comparable to teaching a set of procedural mathematical
skills
and then giving a collection of "word problems" to solve using the
procedures.
Such an approach can obscure the purpose of learning and using
technology,
make mathematics appear as an afterthought, and lead to contrived
activities.
The use of technology in mathematics teaching is not for the purpose of
teaching about technology, but for the purpose of enhancing mathematics
teaching and learning with technology. Furthermore, in our experience,
teachers who learn about technology while using it to explore
mathematics
topics are more likely to see its potential benefits and use it in
their
subsequent teaching. This guideline is in accord with the first
recommendation
of the President's Committee of Advisors on Science and Technology,
Panel
on Educational Technology (1997): "Focus on learning with technology,
not
about technology" (p. 7).
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Address
worthwhile
mathematics with appropriate pedagogy
Content-based activities using technology should
address
worthwhile mathematics concepts, procedures and strategies, and should
reflect the nature and spirit of mathematics. Activities should support
sound mathematical curricular goals and should not be developed merely
because technology makes them possible. Indeed, the use of technology
in
mathematics teaching should support and facilitate conceptual
development,
exploration, reasoning and problem solving, as described by the
National
Council of Teachers of Mathematics [NCTM] (1989, 2000).
Technology should not be used to carry out procedures without appropriate mathematical and technological understanding (e.g., inserting rote formulas into spreadsheets). Nor should it be used in ways that can distract from the underlying mathematics (e.g., adding too many bells and whistles in a PowerPoint presentation that the mathematics gets lost). In other words, mathematical content should not be compromised.
Another way to prevent technology use from
compromising
mathematics is to encourage users to connect their experiential
findings
to more formal aspects of mathematics. For example, students using
software
to explore geometric shapes and relationships should be asked to use
previously
proved theorems to validate their empirical results, or use their new
findings
to propose new conjectures. In other words, technology should not
influence
students to take things at face value or to become what Schoenfeld
(1985)
referred to as "naive empiricists." This guideline is in accord with
the
second recommendation of the President's Committee of Advisors on
Science
and Technology, Panel on Educational Technology (1997): "Emphasize
content
and pedagogy, and not just hardware" (p. 7).
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Take
advantage
of technology
Activities should take advantage of the capabilities
of technology, and hence should extend beyond or significantly enhance
what could be done without technology. Technology enables users to
explore
topics in more depth (e.g., interconnect mathematics topics, write
programs,
devise multiple proofs and solutions) and in more interactive ways
(e.g.,
simulations, data collection with probes). Technology also makes
accessible
the study of mathematics topics that were previously impractical, such
as recursion and regression, by removing computational constraints.
Using technology to teach the same mathematical topics, in fundamentally the same ways, that could be taught without technology does not strengthen students' learning of mathematics and belies the usefulness of technology. Furthermore, using technology to perform tasks that are just as easily or even better carried out without technology may actually be a hindrance to learning. Such uses of technology may convince teachers and administrators that preparing teachers to use technology is not worth the considerable effort and expense necessary to do so.
This guideline supports the technology principle
of
NCTM Principles and Standards of School Mathematics: "Teachers should
use
technology to enhance their students learning opportunities by
selecting
or creating mathematical tasks that take advantage of what technology
can
do efficiently and well- graphing, visualizing and computing" (NCTM,
2000,
p. 25).
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Connect
mathematics
topics
Technology-augmented activities should facilitate
mathematical connections in two ways: (a) interconnect mathematics
topics
and (b) connect mathematics to real-world phenomena. Technology "blurs
some of the artificial separations among some topics in algebra,
geometry
and data analysis by allowing students to use ideas from one area of
mathematics
to better understand another area of mathematics" (NCTM, 2000, p. 26).
Many school mathematics topics can be used to model and resolve
situations
arising in the physical, biological, environmental, social, and
managerial
sciences. Many topics can be connected to the arts and humanities as
well.
Appropriate use of technology can facilitate such applications by
providing
ready access to real data and information, by making the inclusion of
mathematics
topics useful for applications more practical (e.g., regression and
recursion),
and by making it easier for teachers and students to bring together
multiple
representations of mathematics topics. This guideline supports the
curriculum
standards of the NCTM (1989, 2000).
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Incorporate
multiple representations
Activities should incorporate multiple
representations
of mathematical topics. Research shows that many students have
difficulty
connecting the verbal, graphical, numerical and algebraic
representations
of mathematical functions (Goldenberg, 1988; Leinhardt, Zaslavsky &
Stein, 1990). Appropriate use of technology can be effective in helping
students make such connections (e.g., connecting tabulated data to
graph
and curves of best fit, generating sequences and series numerically,
algebraically,
and geometrically). "We, as mathematics educators, should make the best
use of multiple representations, especially those enhances by the use
of
technology, encourage and help our students to apply multiple
approaches
to mathematical problem solving and engage them in creative thinking"
(Jiang
& McClintock, 2000, p. 19).
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References
Goldenberg, E.P. (1988). Mathematics, metaphors, and human factors: Mathematical, technical, and pedagogical challenges in the educational use of graphical representations. Journal of Mathematical Behavior, 7, 135-173.
Jiang, Z., & McClintock, E. (2000). Multiple approaches to problem solving and the use of technology. Journal of Computers in Mathematics and Science Teaching, 19(1), 7-20.
Leinhardt, G., Zaslavsky, O., & Stein, M.K. (1990). Functions, graphs, and graphing: Tasks, learning and teaching. Review of Educational Research, 60(1), 1-64.
National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: Author.
President’s Committee of Advisors on Science and Technology, Panel on Educational Technology. (1997). Report to the President on the use of technology to strengthen K-12 education in the United States.
Schoenfeld, A. (1985). Mathematical problem
solving.
New York: Academic Press.
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Updated: 08/21/2003
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