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Volume 1, Issue 2 ISSN 1528-5804
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Browning, C.A., & Klespis, M. (2000). A
reaction to Garofalo, Drier, Harper, Timmerman, and Shockey.
Contemporary Issues in Technology and Teacher Education,
[Online serial], 1 (2). Available:
http://www.citejournal.org/vol1/iss2/currentissues/mathematics/article1.htm
A Reaction to Garofalo, Drier, Harper, Timmerman, and
Shockey
CHRISTINE A.
BROWNING
Western Michigan University
MARK L.
KLESPIS
Sam Houston State University
Teacher preparation programs cannot ignore their important role
in providing many positive and instructive experiences with using
technology in the teaching and learning of mathematics. This role
is critically important when research points to the lengthy process
of teachers developing competence and confidence in teaching with
technology themselves (Dwyer, Ringstaff, & Sandholtz, 1991;
Means & Olson, 1994).
Graduating preservice teachers (PSTs) should not need in-service
training the moment they leave the college halls. Thus, we concur
with Garofalo, Drier, Harper, Timmerman, and Shockey (2000) that an
effective way to bring about enhanced student learning of
mathematics through technology is to prepare PSTs to incorporate
into their teaching an array of activities that engage students in
mathematical thinking facilitated by technology.
The authors make this point even stronger by indicating that it
is the most direct and effective way to bring about a positive
change in student understanding, where “student” means
a school student. Research is needed to document the relative
impact on PSTs having such experiences, as compared to the other
suggestions presented in the paper for incorporating technology in
teacher education.
The activities the PSTs complete, as described by Garofalo et
al., are designed for secondary mathematics students, and most (not
all) of the mathematics they engage in is “old”
mathematics for the PSTs. Granted, PSTs may have forgotten some of
the mathematics they learned. The PSTs claim that, had they been
presented the material in a fashion similar to the current
mathematical activity, they would have understood it far better and
retained it far longer. However, the “nagging” memory
of how they first encountered and constructed the mathematical
ideas typically prevails when confronted with their initial
teaching experiences and a traditional text (Benkin & Wilson,
1998). Fine and Fleener (1994) found, too, that just having
experiences with calculators did not cause PSTs to think
differently about mathematics but that they need to be engaged with
mathematics learning in a new way. In fact, if PSTs are not
prepared properly for the appropriate use of technology, they may
see its incorporation as an added and possibly unnecessary stage in
learning new mathematical content. We believe the PSTs need to be
engaged in more activities that are designed for their level
of understanding, present new mathematics, and are
facilitated by the use of technology in their initial
constructions, so the PSTs can determine the impact of technology
on their own “first” learning versus a
“revisited” learning.
Jones (1995) noted that learners must develop an
“intelligent partnership” with the technology they use.
A follow-up on the PSTs retention of the concepts related to
fractals and other new mathematical ideas from the activities would
have been useful to include. Many of these types of experiences
need to occur outside of their mathematics education courses. We
are not saying that activities focusing on secondary school
mathematics should not be included. Those activities are also a
necessary component of preparing the PSTs, but we believe they need
to go beyond that type of experience and include those in which the
initial mathematical constructions were facilitated by
technology.
Garofalo et al., stated that “in the course of completing
these activities, PSTs not only learn how to use the technology,
but also how to incorporate technology into their teaching.”
We would like to see more evidence of this claim. Based on our
personal experiences, students are not prepared to incorporate
technology into their teaching after being engaged in such
activities. Their understanding of some mathematical concepts has
improved dramatically, but the design of lessons making appropriate
use of technology remains a challenge.
For example, when presented with crafting a lesson on linear
functions and their graphs, the PSTs now may think of incorporating
graphing calculators and motion detectors, but the assessment tasks
will likely maintain a traditional focus on skill development. They
may ask students to find the slope, but they will not connect the
value back to the context of the problem. When students raise
questions about other types of graphs, the PST falls back to the
linear function objective and squashes further student learning.
They do not know what types of questions to ask the students during
the task to assess their understanding of x - y
coordinates, their motion, slope, intercepts, etc. The actual
development of questions was only a small part of (or perhaps
nonexistent in) the PSTs’ technology activities from their
teacher education program. The inclusion of assessment design for
lessons was not evident in the paper but perhaps it is a part of
the activities presented. We believe that this aspect needs to be
addressed more clearly.
The authors use five guidelines to shape the development of the
activities: introduce technology in context, address worthwhile
mathematics with appropriate pedagogy, take advantage of
technology, connect mathematics topics, and incorporate multiple
representations. These five guidelines encompass critical areas of
concern when implementing technology in either content or
methodology courses. We are curious about the assessment of the
PSTs’ understanding of the five guidelines. This connects
back to the PSTs incorporating technology into their own lessons.
Are they aware of how they are making use of the technology when
they design a lesson?
The activities presented are great examples of how to make
effective use of technology and include a variety of platforms,
software, and mathematical topics. The authors have provided a good
resource of ideas for others to implement in their mathematics
teacher education programs.
References
Benkin, B., & Wilson, M. (1998, October). The Impact of a
secondary preservice teacher’s beliefs about mathematics on
her teaching practice . Paper presented at the Annual Meeting
of the North American Chapter of the International Group for the
Psychology of Mathematics Education, Raleigh, NC.
Dwyer, D.C., Ringstaff, C., & Sandholtz, J.H. (1991).
Changes in teachers’ beliefs and practices in technology-rich
classrooms. Educational Leadership, 48 (8), 45-52.
Fine, A., & Fleener, M.J. (1994). Calculators as
instructional tools: Perceptions of three preservice teachers.
Journal of Computers in Mathematics and Science Teaching
.
Garofalo J., Drier, H., Harper, S., Timmerman, M., &
Shockey, T. (2000). Promoting appropriate uses of technology in
mathematics teaching . Contemporary Issues in Technology and
Teacher Education [On-line serial], 1 (1). Available:
Hostname: http://www.citejournal.org/
Directory: vol1/iss1/currentissues/ mathematics/article1.htm
Jones, P.L. (1999). Realising the potential of the graphics
calculator. In E.L. Laughbaum (Ed.), Hand-held technology in
mathematics and science education: A collection of papers.
pp.68-71. Columbus, OH: Teachers Teaching with Technology College
Short Course Program at The Ohio State University.
Means, B., & Olson. K. (1994). Tomorrow’s schools:
Technology and reform in partnership. In B. Means (Ed.),
Technology and the education reform (pp. 191-222). San
Francisco: Jossey-Bass.
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