The Vision for the
Future
Where We Are Going: The Classroom
Vision
If you can imagine a classroom where
students prove mathematical equations using experiments they perform
themselves, then you can imagine the classroom where students derive
mathematical formulas from their own collected data. With today's
computer-interfaced data collection tools, students can gather data
in a fraction of the time it took scientists and mathematicians in
the past. The data is more accurate and is plotted visually on the
computer screen as the events occur in real time. Students are
motivated to get better results because it is convenient and
appropriate to repeat an experiment. Error calculations become more
meaningful because students can compare graphs quickly. They can also
participate in collaborative experimentation and pooled data
collection with networked computers. This inductive approach to
understanding the meaning behind an algebra equation is compelling
because it resembles the methods used by the mathematicians who
discovered the equations. Instead of memorizing equations, students
learn how equations are derived.
Young students have difficulty transferring
skills learned in mathematics classrooms to real-life situations.
Establishing connections is a challenge for even the best teachers.
It takes relentless effort and an understanding that "covering" it
once is not enough. It is less important that students remember all
of the mathematical equations and laws themselves. It is more
important that they grasp something of the process of discovering
such laws. For example, students collect data on the pressure-volume
relationship, and then using trial and error in data manipulation
derive the mathematical equation that best describes the observed
behavior. Students need practice "playing" with data in this manner.
They need to work through graphical analysis lessons many times
before they can easily manipulate data in quadratic, inverse,
logarithmic and exponential relationships. These curve fitting
techniques can only be introduced in Algebra I. This powerful method
of real data analysis must be a strand evident throughout the
mathematics program. Students must be encouraged to recognize
mathematical patterns in the real world. Once the dawning comes, it
will certainly be a powerful connection for the mathematics
student.
In Coalition classrooms funded by this
proposal, teachers will utilize a variety of teaching methods
relating instruction to real-world situations incorporating the
latest state-of-the-art technology. Enrichment and enhancement of
standards-based curriculum from the National Council of Teachers of
Mathematics (NCTM) with SA-USI and Brooks AFB programs will result in
an increase of mathematical, scientific and technological
achievement.
In such a classroom, at the end of a
concept-unit (i.e. ratio and proportion) teachers will be able to
follow the National Science Educational Standards by having students
create a project to demonstrate their understanding of the concept
and relate it to previous knowledge. Students employ available
technology to gather, sort, analyze, synthesize and illustrate their
understanding of the information in both formal and informal
presentations. From such methods, the students gain not only the
knowledge of a specific mathematical concept, but also the
development of higher order thinking skills. This ability to relate
information from one source to concepts learned in the classroom
results in students who are able to transfer this knowledge to other
disciplines.
When you walk into a San Antonio Technology
in Education Coalition mathematics classroom, you will see each
student using a graphing calculator, a pod of six computers loaded
with graphical analysis, image processing and analysis software, and
probeware to connect to either the computers or calculators. Other
appropriate equipment will be available to print in color and project
from the computer screen to a TV. Software will be available for
spreadsheet-based simulations and analysis. In addition,
computer-interfaced probes will be available to explore mathematical
concepts.
Where We are Going: The Mathematics
Vision
This Coalition recognizes that our schools
have a responsibility to incorporate newer technologies to provide
improved methods of instruction. The traditional methods of
instruction have concentrated on rote memory, utilizing formulas, and
solving numerical problems. We seek to go to the next level: to
develop higher level thinking skills by using the tools available
from modern technology.
The opportunity for all students to
experience a program based on these goals is at the heart of our
vision of a quality technology-enhanced mathematics program. We see
classrooms as places where interesting problems based on important
math ideas are regularly explored. One should expect to see students
using technology to record measurements of real objects, to collect
information and describe their properties using statistical tools,
and to explore the properties of a function by examining its
computer-generated graph. Our vision sees students studying the same
mathematics concepts currently being taught, but with a different
emphasis on how they learn it. The Coalition plans to use several
types of technology tools to enhance mathematics instruction.
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