Karen C. Brown
EDUC 685-194-06F
Dr. Fred Hofstetter
November 28, 2006
Working in a school that has an abundance of technology has proven out the reality that an increased presence of computers in a school does not guarantee the adoption or infusion of technology and multimedia applications into classroom instruction. One wonders why these tools are not quickly implemented and utilized when the advantages seemingly outweigh any disadvantages that may be encountered with the implementation. Students not only become more engaged when technology is utilized, but classroom management improves as students become more involved with the lesson. Concepts and applications can be quickly investigated using technology, thus allowing for deeper or broader research. Current curriculum publications attempt to incorporate technology allowing teachers an idea of how implementation aligns with mathematical concepts. Multimedia is the avenue of information that intrigues students and draws them in to the subject encouraging them to inquire and discover. Yet, many teachers seem to hesitate to utilize these tools in the classroom for instructional purposes.
In addressing various educational technology myths in Myths and Realities about Technology in K-12 Schools, Kleiman (2000) states that, “technology can affect what needs to be taught, how it can be taught, how classrooms are organized and managed, and the roles and expectations of both teachers and students.” Waxman and Huang (1996) found that instruction in classroom settings where multimedia applications were not often used tended to be whole-class approaches, in which students generally listened or watched the teacher. Instruction in classroom settings where technology was moderately used had much less whole-class instruction and much more independent work. Another important finding from the Waxman and Huang (1996) study is that students in classrooms where technology was moderately used (more than 20 percent of the time) were found to be on task significantly more of the time than students from the other two groups—in which technology was infrequently used (less than 10 percent of the time) or in which technology was slightly used (11 percent to 19 percent of the time) (Waxman, Lin, and Michko, 2003). Yet, infusing technology can be a daunting proposition for many teachers – new and veteran – as they change their instructional practices and classroom environments to utilize these new multimedia application tools.
Sandoltz, Ringstaff, and Dwyer (1997) address the confidence levels of teachers and
their willingness to experiment as factors that slow the adoption of technology
into classrooms. Low confidence levels can derail new activities – especially
when many students may be more technologically advanced than the teacher.
Unwillingness to contend with the discipline issues arising with technology use
of the Internet prevents teachers from incorporating Internet activities.
Changing one’s instructional beliefs on how students learn affects technology
implementation as classrooms evolve away from the traditional classroom
environment into classrooms where students begin to construct their own
knowledge. Slow administrative support of these instructional changes hinders
teachers from changing their classroom practices (Solomon, Allen, & Resta, 2003). The issues of time, administrative support, addressing assessment concerns,
changes in classroom management and discipline are each authentic concerns for
the classroom teacher which may slow the adoption of multimedia applications in
the classroom. Roschelle, Pea, Hoadley, Gordin, and Means (2000) in their article, Changing How and What Children
Learn in School with Computer-based Technologies,
acknowledge that teachers who finally succeed in using technology often make
“substantial changes in their teaching style and in the curriculum they use,”
and that making these changes can be difficult without administrative support
and commitment.
If the
American educational system is the interlocking jigsaw puzzle described by
Roschelle, et al (2000), it is little wonder that teachers are slow to adopt
technology. These authors point to the necessity of structuring computer
based technology within a “coordinated approach to
improving curriculum, pedagogy, assessment, teacher development, and other
aspects of school structure.” These are the same issues Kleiman (2000)
addresses: “the need for professional development, technical support,
and the availability of appropriate software, classroom management, and
curriculum integration.” According to Bain and Smith
(2000), “the excellent curricular use of technology came about by
rethinking the way we teach, how we build curriculum and the way we support and
evaluate faculty.” Adopting multimedia applications is made possible through
supportive professional development, curriculum
design or redesign, changing assessment methods, and a school’s capacity for reform,
not the presence of computers.
In opposition to these apparent
difficulties are many merits for implementing technology into the mathematics
curriculum. Integrating Technology into Middle School Mathematics is an
excellent article by Denise Jarrett (1998) offering examples and ideas to
challenge teachers at all levels of technology implementation. Jarrett begins
by stating that technology is a “necessary component for success in the 21st
century.” She believes that “technology tools can engage students in authentic
learning opportunities that enhance the development of higher-order and basic
skills.” This is important in mathematics since many students struggle with
basic skills. However, many classroom teachers utilize technology only to improve
students’ basic skill levels, and Jarrett cautions teachers against making that
the sole purpose of technology usage. Even though students need improvement in
basic skills, Jarrett offers many ideas of how that practice can be integrated
into problem-solving activities that reach critical thinking skills. The
Internet offers a plethora of interactive sites that allow students to practice
a basic math concept in a problem-solving scenario. This is a necessity if
those students are not to be left behind as the remainder of the class forges
ahead into deeper realms of mathematics in problem solving activities.
Interactive math sites allow students to progress at their own
pace while receiving valuable feedback about their performance. These sites
offer individualized and differentiated instruction as well as online tutorials
and practice worksheets. They encourage students to “explore mathematics in an interactive
constructivist manner” (Mhairi, 2001). “The interactive, hands-on atmosphere of the class encourages them
to explore mathematical ideas, learn some mathematics, discuss different ways
of teaching mathematics, and generally enables these students to overcome their
anxieties and arrive at a place of confidence in their learning and teaching of
mathematics, using technology as a teaching or learning tool” (Mhairi). Students become engaged in meaningful
learning; actively involved in reaching the goal of processing information,
integrating new concepts with prior knowledge, and evaluating the application
of those concepts into their own lives. Student conversation and collaboration
center on these activities, and the use of reflective journals solidify their
understanding and evaluation of mathematical concepts (Jonassen, 2005).
Collaborative Internet Projects, CIPs, allow students the opportunity to publish their multimedia projects on the Internet. Susan Silverman, in her chapter describing her experience as a CIP coordinator, states, “Research suggests that performance improves when students write to authentic audiences” (Karchmer, Mallette, Kara-Soteriou, & Leu, Jr., 2005). Using the Internet to publish projects provides students with an authentic audience beyond the classroom, parents, and hallway exhibits. Inviting other middle school students to join the project offers all students an opportunity to publish their work, view and constructively critique others, communicate feedback, and reflect upon their own learning by graciously receiving feedback. CIPs also open pathways that allow for teacher collaboration beyond the classroom as teachers communicate about the projects and network concerning the student exhibits.
Another classroom Internet implementation is a blog, which according to Wikipedia, is “a website where entries are made in journal style and displayed in a reverse chronological order.” Given that many blogs should probably not be utilized in the middle school classroom, in the article “Using Blogs to Integrate Technology in the Classroom,” Crie (2004) introduces an entirely different perspective. Collaboration on a blog can expand instruction beyond the classroom walls incorporating the community, field experts, and home bound students. The possibility of including a homebound student in the interaction between students within his or her class provides the benefits of being able to seek information from and interact with peers. While teachers have relied upon emails for student-expert communication, this is ineffective when compared to the possibilities that abound when using a blog. Blogs allow for multiple writers and readers to interact as a community of learners not limited by the individual email accounts but able to respond as a group (Crie, 2004). One drawback to be considered is the realization that using blogs will require students to understand the etiquette of Internet communication and the school’s policy, procedures, and guidelines for using the Internet.
Graphing calculators and
computer software programs are another way to implement technology and achieve
the differentiation aspect of instruction as they offer a variety of tools for
the students to use in problem solving. “More advanced technological tools in mathematics take
the form of computer applications, calculators, and languages (e.g., Logo; see
Connell, 1998). These more advanced tools continue to offer the external memory
supports of less advanced tools, but afford numerous other advantages,
including access to expert performances and modeling of processes (Koedinger
& Anderson, 1998), collaborative construction of knowledge (Piburn &
Middleton, 1998), and coaching and scaffolding (Jonassen & Reeves, 1996).” Many schools have TI-83 graphing calculators, small, portable graphing
devices offering access and mobility. The TI Interactive, a computer graphing
software, ties a student to the computer; however, it offers a myriad of other
possibilities that extend beyond those of the graphing calculator. Tables and
graphs can easily be incorporated into a document allowing students to see a
side-by-side comparison of the data – an extreme advantage in problem solving
whether a visual learner or not. “Using computers as cognitive tools to
assist students in learning powerful mathematics that they could not have
approached without the technology should be a key goal for research and
development—not only learning the same mathematics better, stronger, faster,
but also learning fundamentally different mathematics in the process” (Jonassen
& Reeves, 1996; Pea, 1986). The
graphing calculator, TI Interactive, and other mathematics software are tools
that could be extremely advantageous to enriching the data analysis aspects of
mathematical instruction.
Concept mapping software programs, such as Inspiration, allow students the necessary opportunities to reflect upon their mathematical understandings as well. Concept maps are effective methods of assessing student knowledge, comprehension, synthesis, and evaluation (Baroody & Bartels, 2001). They afford students a platform for illustrating and sharing their mathematical proficiency with their peers. All mathematics standards require students to identify, interpret, reason, evaluate, and explain the connections and relationships between various mathematical concepts. It is imperative that students be able to express those relationships in order to consolidate and strengthen their understandings as well as further evaluate these newly acquired concepts and skills. Concept maps, if completed correctly, contain concepts, linking phrases and links, which clearly demonstrate student understanding (Novak, 2004). They are effective tools for reflection allowing students the opportunity to rethink how concepts have been illustrated. Their versatility, different methods of mapping, and diverse applications facilitate differentiated instruction (Bartels, 1995). As students use their understanding of the unit concepts to create the concept map, they communicate their conceptual understanding of and connections between mathematical concepts. Multimedia applications such as Inspiration and C-Map give students the stage for accomplishing the task of creating, revising, and publishing their maps as well as an authentic arena for presenting their mathematical connections.
Another advantage of implementing multimedia
applications in the classroom is the effect upon classroom collaboration.
Collaboration is defined by Merriam-Webster as “to work jointly with others or
together especially in an intellectual endeavor.” Considering the ways that the
mathematics classroom utilizes collaboration, one immediately thinks of
projects and class activities that focus on group work and require students to
collaborate to complete the final product. While these are valuable methods,
there are multiple ways to encourage collaboration, using technology, in the
middle school mathematics classroom. Thinking of the simplest strategy –
offering activities where students make and explore conjectures – technology
“provides a focus as students discuss with one another and with the teacher the
objects on the screen and the effects of the various dynamic transformations
that technology allows” (NCTM, 2000). This is collaboration that ensues from
student explorations and facilitates and strengthens student learning and
application. The typical mathematics classroom could achieve collaboration
around the explorations, but the technology affords a platform that quickly
facilitates these discussions, increasing the opportunities to observe and
discuss those observations. Students are engaged at high levels with the technology,
and collaboration takes new dimensions as the investigations are deepened and
strengthened by the technology. The “interactive nature of technology can also
empower students to develop such personal strengths as initiative,
problem-solving and persistence” (Jarrett, 1998) – useful traits in
collaborative exercises.
Since “technology’s greatest impact on
learning is in the area of problem-solving and higher-order thinking” (Jarrett,
1998), it should come as no surprise that many projects and activities
implement the use of technology to collaborate with experts outside the
classroom. The Buckets of Data: Aquatic Creepers and Crawlers Project
implemented at the Freewater School (Jarrett) utilizes technology and field
experts to increase and enhance the collaboration required for the project’s
completion. Students actively seek expert opinions and quickly incorporate
their findings into data reports shared on the Internet. This project
illustrates how technology can be used as an effective tool for increasing
student motivation to experience peer, parent, and expert collaboration in
order to present projects that reflect and solidifies student learning.
Research states, “middle school
students should have many opportunities to communicate their mathematical
ideas” (Jarrett, 1998). The use of multimedia applications in the mathematics
classroom becomes the avenue students can use to present their ideas and
projects. “Actively engaging students in mathematical thinking and
discovery can promote a more cohesive understanding of mathematics. Students
are provided opportunities to see the mathematics they have programmed in the
computer immediately and rapidly. These opportunities allow them to make
immediate judgments and provide convincing arguments about the validity of
results” (Dugdale, 1999). Using
PowerPoint, Inspiration, graphing technologies, and other multimedia software
allow students to create, edit and present their mathematical understandings to
the classroom and the community. Internet collaborations afford students a
worldwide showcase for their work. These opportunities not only offer authentic
audiences that all students desire, but “engage students in extended and
cooperative learning experiences that involve multiple disciplines” (Jarrett,
1998). Research indicates that “computer
supported learning can encourage rapid interaction and feedback, can encourage
students to spend extended periods on their learning task, and in some
situations, can analyze each student’s performance and provide more timely and
targeted feedback than the student typically receives in traditional
classrooms” (Schofield, 1995; Anderson et al., 1995; Roschelle et al., 2000).
Technology not only supports and
encourages collaboration; it also facilitates collaboration that provides quick
and effective feedback. The Jasper Woodbury playground project illustrates how
scientist and software programs “give students feedback about their thinking,”
“impact the quality of solutions,” and “provide rich experiences for learning”
(Bransford, 1999) as students interact with working scientists. Classtalk is an
example of a classroom communication technology that “can promote more active
learning” (Bransford) in large lecture classes. While this may not be feasible
in a middle school classroom, examples of how these technologies promote peer
feedback and collaboration cannot be dismissed. Teachers with vision could
easily utilize these technologies in smaller settings. The Internet is now a
“forum for students to give feedback to each other” (Bransford). Projects such
as the Globe Project allow students to “inspect each others’ data on the
project web site and sometimes find readings they believe may be in error”
(Bransford). This engages students in further collaboration about the data and
mathematical concepts.
Technology can indeed deepen and extend the mathematical problem solving
scenarios encountered by students according to the National Council of Teachers
of Mathematics (2000) under The Technology Principle. Once students
understand the basics of a problem, the right tools allow for further
investigation into realms beyond simple pencil and paper calculations. “Technological
tools help to support cognitive processes by reducing the memory load of a
student and by encouraging awareness of the problem-solving process” (Lajoie,
1993). This is most especially true with
struggling students who become so bogged down in their struggle to perform
simple calculations that they never reach the enrichment problems. A vicious
cycle ensues that eventually leads to disheartenment and frustration as well as
limits the opportunities for meaningful application for those students. “Tools
can share the cognitive load by reducing the time that students spend on
computation” (Lajoie). Technology for
more advanced students facilitates their inquiry into depths they might not
explore without the technology to do the “grunt” work; “the tools allow
students to engage in mathematics that would otherwise be out of reach, thereby
stretching students' opportunities” (Lajoie). Technology “should not be used as a replacement for basic
understandings and intuition; rather it can be used to foster those
understanding and intuitions” (NCTM, 2000). Technology tools “support
logical reasoning and hypothesis testing by allowing students to test
conjectures easily” (Lajoie, 1993). The
goal of technology and multimedia applications is to enrich and extend student
understanding and learning of the mathematics. Technology is not a substitute
for understanding the basics. However, there are times when the technology can
bring that “aha” moment for students who on seeing multiple examples of a
situation can finally connect why things are happening, and performing multiple
examples is easily accomplished with the use of technology.
Middle school students can be quite savvy about multimedia applications. The Internet and most computer applications are not new venues for many of them. These tools intrigue and engage students. Thus student access to technology offers numerous benefits. Students become more engaged and willing to participate in the investigations if technology is utilized effectively. Engagement with a problem brings inquiry and investigation which leads to ownership of the problem. When students take ownership of a problem, they spend more time making the necessary connections that further their learning of mathematics. Students are motivated to participate in activities utilizing multimedia, allowing for better classroom management. “Engagement on the part of the learner is therefore an important factor in successful achievement” (Galbraith, Haines, 1998). Student participation in a project increases when multimedia facilitates research and presentation; instruction can be easily tailored to address individual needs. Admittedly, with all these advantages, the cautions remain about the necessity to monitor student use of the Internet. Teachers must be aware of what their students are doing and whether they are off task because of the availability of the Internet. Teachers need to question why they desire multimedia applications in the classroom and consider the implication of whether or not it will be used as an instructional tool. The United States Department of Education states in the National Education Technology Plan (2005), “increased access to technology alone, however, will not fundamentally transform education.” Teachers must ask themselves whether or not technology is being used to further instruction and increase student understanding, constantly ascertaining the effectiveness of the multimedia application for increasing inquiry and problem-solving.
A plethora of technology implementations
for the mathematics classroom abound for teachers and students. As our world
changes and technology becomes more advanced, teachers need to discover ways of
implementing multimedia applications into their curriculum offering “a
secondary mathematics curriculum that takes advantage of computer technology to
assist students in becoming powerful and thoughtful problem solvers” (Waits, Demana, 1996). Research
supports the advantages to students when they are actively engaged with
authentic problem-solving curriculum. “Bringing students and teachers in
contact with the broader community can enhance their learning” (Bransford
1999). Teachers need to “make explicit efforts to facilitate group interaction
and establish social norms” (Bransford 1999). They must be “willing to assume
new or untraditional roles” (Bransford) in order to facilitate multimedia applications
within and outside the classrooms. “Business
and industry want employees who can think, read, and understand problem
situations; work cooperatively in groups; understand and use technology; and
communicate effectively with others. The appropriate use of technology in
mathematics teaching and learning helps build these important skills in
students” (Waits, Demana, 1996).
Fundamentally, teachers desire to
offer their students the best educational experiences possible. Thus it is
imperative that teachers encourage effective technology integration in the
classroom utilizing multimedia to open learning avenues and create extensions
that reach beyond one’s imaginings.
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