ROWAN
UNIVERSITY
Department
of Mathematics
Syllabus
Math 01.205
Technological Tools for Discovering Mathematics
Catalog
Description:
Math 01.205
Technological Tools for Discovering Mathematics 2
s.h.
(Prerequisites:
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)
This
course will use mathematicsspecific 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 mathematicsspecific
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
precalculus,
calculus, geometry, and statistics.
Essence
of the Course and Outline:
The
emphasis in this course will be on mathematicsspecific technologies and
on the discovery of mathematics using such tools. Throughout the course,
students will become aware of the broad range of mathematicsspecific technologies
available and become proficient in the use of several of these. Some objectives
of the course follow:

Programming:
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.

Data
Collection:
Students will use calculator based probes to gather and analyze data, creating
appropriate mathematical models to fit the data.

Internet:
Students will use geometry software to discover theorems in Geometry.

Algebraic
Symbolic Manipulation:
Students will compare handheld technology (TI92 & TI89) with symbolic
algebraic manipulation capabilities to a computer application (Mathematica).

Courseware:
Students will evaluate commercially available mathematics software and
examine shareware and public domain software available on the Internet.
Required
Technologies:

Geometry
discovery software  Geometer's Sketchpad & Tesselmania  for discovering
geometry properties and developing spatial visualization skills.

Mathematica
 emphasis
on mathematics modeling.

Using
spreadsheets as a tool for investigation statistics, discovering mathematics,
and problem solving.

Mathematics
word processing (Math Type or Equation Editor)

Graphing
calculators  emphasis on using programming for problem solving and on
the utility of programming in forcing logical thinking and precise mathematical
communication.

CBL
Calculator Based Laboratory) or CBR (Calculator Based Ranger)  for data
collection and discovering the relationship between reality and mathematics
modeling.

Resources
for mathematicians available on the Internet.
Optional
Technologies:

Additional
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).

Other
computer algebra & numerical systems

SPSS,
Fathom or other statistical software programs
Texts:
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 TINspire, 2009, Key Curr. Press & Texas Instruments
Ameis, Jerry, Mathematics on the Internet: A Resource for K12 Teachers, 3/E, 2006, Pearson/Merrill/Prentice Hall..