A theme
which resonates throughout the National Council of Teachers' of Mathematics
Curriculum and Evaluation Standards for School Mathematics (NCTM, 1989) is that
of empowerment.
1. All
students should be empowered to actively do meaningful mathematics.
2.
Ambitious new goals are proclaimed for all students.
3. All
students should value mathematics, have confidence in their ability to do
mathematics, become mathematical problem solvers, reason mathematically, and
communicate mathematically.
4.
Motivating many recommendations in these national standards is the
constructivist learning theory - the idea that students actively construct
their own knowledge.
Technology
can serve at least four roles in the teaching and learning of mathematics.
Specifically, technology can aid in
(1)
Mathematical concept and skill development.
(2)
Mathematical problem solving.
(3)
Mathematical reasoning.
£Technology as an Aid in Mathematical Concept and Skill Development
Specifically
in the realm of mathematical concept and skill development,
(1)
Technology empowers students to deal with multiple representations.
(2)
Enhances ability to visualize.
(3)
Increases opportunity to construct mathematical knowledge.
(4)
Enhances opportunity for individualized and customized diagnosis, remediation
and evaluation (Kimmins, 1995).
With
graphing calculators and computer algebra systems, students can explore
symbolic, numeric, and graphical representations of functions instead
concentrating on the symbolic.
In the
realm of mathematical problem solving, technology provides students
(1)
Enhanced ability to focus on the process of problem solving instead of the
computational aspect.
(2)Enhanced
ability to solve realistic problems instead of being restricted t o contrived
problems having "nice solutions."
(3)
Enhanced opportunity to be introduced to interesting problems and associated
mathematical subject matter much earlier than before possible.
(4)
Increased opportunity to develop mathematical modeling skills .
£Technology as an Aid in Mathematical Reasoning
In the
context of mathematical reasoning, technology has the potential to
(1) Empower
students to gather data in order to form conjectures and apply inductive
reasoning.
(2)
Motivate students to think logically in the context of programming a calculator
or computer to perform a desired task.
£Technology as an Aid in Mathematical Communication
In the
realm of mathematical communication, technology can enhance
(1)
Motivation to communicate mathematics precisely.
(2)
Ability to present mathematical ideas both orally and in writing.
(3)Precise
language is essential when programming a calculator or a computer to perform a
desired task.
The
Department of Mathematical Sciences at Middle Tennessee State University has
initiated a three-pronged approach:
(1)
Development of a new Emphasis in Mathematics Education at the undergraduate
level required of mathematics majors preparing to teach secondary school
mathematics,
(2)
Development of a new course, Technology in School Mathematics required of all students
in the Mathematics Education Emphasis,
(3)
Integration of technology into mathematical content courses in which
prospective secondary school mathematics teachers are enrolled.
The Use of Technology in the Learning and Teaching of Mathematics
Position
Technology
is an essential tool for teaching and learning mathematics effectively; it
extends the mathematics that can be taught and enhances students' learning.
Recommendations
- Every school
mathematics program should provide students and teachers with access to
tools of instructional technology, including appropriate calculators,
computers with mathematical software, Internet connectivity, handheld
data-collection devices, and sensing probes.
- Preservice and
in-service teachers of mathematics at all levels should be provided with
appropriate professional development in the use of instructional
technology, the development of mathematics lessons that take advantage of
technology-rich environments, and the integration of technology into
day-to-day instruction.
- Curricula and
courses of study at all levels should incorporate appropriate
instructional technology in objectives, lessons, and assessment of
learning outcomes.
- Programs of
preservice teacher preparation and in-service professional development should
strive to instill dispositions of openness to experimentation itch
ever-evolving technological tools and their pervasive impact on
mathematics education.
- Teachers should
make informed decisions about the appropriate implementation of
technologies in a coherent instructional program.
Aims
Here are some early thoughts on what we expected people to gain from participating in WGA11.
Here are some early thoughts on what we expected people to gain from participating in WGA11.
Find out about
international issues and trends in this area:
- Educational issues (e.g. curriculum developments
incorporating the Internet)
- Political issues (e.g. banning of calculators in
schools)
- Technical issues (e.g. principles of instructional
design for software)
Share experiences
related to these kinds of issues:
- Practical experiences (e.g. effective forms of
professional development)
- Research observations and conclusions (e.g. evaluating
student use of software)
- Advice offered to others (e.g. inclusion of dynamic
geometry software in curricula)
Be informed about recent
developments:
- Emerging trends in practice (e.g. use of graphics
calculators in public examinations)
- Demonstrations of new kinds of significant technologies
(e.g. affordable computer algebra)
- Emerging consensus (e.g. the Internet will continue to
be important)
Technology
- Calculators (basic calculators, scientific calculators
and graphics calculators)
- Computers (computer algebra systems (CAS),
spreadsheets, data analysis programs, CAS-capable graphics calculators)
- Tools designed for educational use (such as function
graphers, probability simulators, dynamic geometry software)
- Learning environments, simulations and micro worlds
designed for educational use
- Integrated multimedia and tool software (such as
hypertext tools, micro worlds)
- Internet and telecommunications (World Wide Web, List
servers, Email, Java)
Type and focus of
contribution
- Presentations
and project reports: Reflective
software presentations, presentation of classroom materials (including
assessment), report on teaching experiments, courses or broader innovative
projects [We do not expect that significant time will be made available
for "show-and-tell" demonstrations of software as part of the
WGA itself, although it is likely that other parts of the Congress will
provide this opportunity. At the least, the commercial areas of the
Congress will do so to an extent.]
- Visions: What do we expect, what do we wish for
technology-supported mathematics teaching in 2015?
- Software
reflections and evaluations of existing programs and programs to be
developed: What are the merits of various types of software? What software
do we need in the future? What do we expect? Principles for designing
software and multimedia.
- Curriculum
development issues associated with technology: reflections on goals
and appropriate mathematical content in technology-rich settings, new
curricular emphases, new societal demands, cultural aspects. Contributions
might focus on specific domains, such as new goals, contents, materials
and teaching methods for algebra, statistics or geometry.
- Principles
of instructional design (including didactical engineering, teacher development
and assessment) specific for the integrated use of computers, calculators
and telecommunications in mathematics education
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