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Use of Technology in Mathematic

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.
ROLES OF TECHNOLOGY IN THE TEACHING AND LEARNING OF MATHEMATICS
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.
(4) Mathematical communication (Kimmins, 1995; Kimmins and Bouldin, 1996).
£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.
£Technology as an Aid in Mathematical Problem Solving
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.
TECHNOLOGY AND TEACHER PREPARATION IN MATHEMATICS
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.
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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