Technological Tools for Discovering Mathematics
Technological Tools for Discovering Mathematics 2
CS 01.104 Introduction to Scientific Programming, Math 01.131 Calculus II, and Math 03.150 Discrete Mathematics with a grade of C- or better in all prerequisites)
course will use mathematics-specific technologies to help students discover
mathematics and to develop a better understanding of new content. Throughout
the course students will become aware of the broad range of mathematics-specific
technologies available to mathematicians, become proficient in the use
of these, and pursue the advantages, disadvantages, and limitations of
such technologies. Students will solve problems and advance their understanding
of topics in the areas of
calculus, geometry, and statistics.
of the Course and Outline:
emphasis in this course will be on mathematics-specific technologies and
on the discovery of mathematics using such tools. Throughout the course,
students will become aware of the broad range of mathematics-specific technologies
available and become proficient in the use of several of these. Some objectives
of the course follow:
Students will develop and use programs for graphing calculators and computers
that illustrate mathematical concepts, simulate mathematical and probabilistic
events, and carry out routine computations.
Students will use calculator based probes to gather and analyze data, creating
appropriate mathematical models to fit the data.
Students will use geometry software to discover theorems in Geometry.
Students will compare hand-held technology (TI-92 & TI-89) with symbolic
algebraic manipulation capabilities to a computer application (Mathematica).
Students will evaluate commercially available mathematics software and
examine shareware and public domain software available on the Internet.
discovery software - Geometer's Sketchpad & Tesselmania - for discovering
geometry properties and developing spatial visualization skills.
on mathematics modeling.
spreadsheets as a tool for investigation statistics, discovering mathematics,
and problem solving.
word processing (Math Type or Equation Editor)
calculators - emphasis on using programming for problem solving and on
the utility of programming in forcing logical thinking and precise mathematical
Calculator Based Laboratory) or CBR (Calculator Based Ranger) - for data
collection and discovering the relationship between reality and mathematics
for mathematicians available on the Internet.
geometry Software such as Cabri Geometry, Geometry SuperSupposer software,
Logo (programming language) and other software associated with spatial
visualization (Gyrographics, The Right Turn, Building Perspective, Kaleidomania,
and The Super Factory).
computer algebra & numerical systems
Fathom or other statistical software programs
Goldberg, Kenneth, Using Technoloogy for Problem Solving in Middle and High School Mathematics: Investigations Using Scientific & Graphing Calculators, Spreadsheets, & the Geometer's Sketchpad, 2007, Pearson/Merrill/Prentice Hall.
Hicks, Jensen, Lewis, Exploring Algebra I with TI-Nspire, 2009, Key Curr. Press & Texas Instruments
Ameis, Jerry, Mathematics on the Internet: A Resource for K-12 Teachers, 3/E, 2006, Pearson/Merrill/Prentice Hall..