Sketch2Go - encourages visual exploration of phenomena by providing qualitative indication of the ways in which the sketch drawn by the user changes. The sketch is a diagrammatic representation that attempts to help the viewer focus on the principles rather than on tedious details of the represented phenomenon. Phenomenon can refer to processes outside of mathematics (e.g., physical temporal phenomena) or to mathematical phenomena (e.g., a function with three extrema). Moving students beyond plotting and reading points to interpreting the global meaning of graphs and the functional relationships that they describe has been identified as a major goal of mathematics education.

Tools like Sketch2Go enable the bypassing of algebraic symbols as the only channel into mathematical representation, and motivate students to experiment with a given situation, analyze it, and reflect upon it, even when the situation is too complicated for them to approach symbolically. The visual analysis that emerges from work with such tools is different from that which arises from work with algebraic symbols or numerical tables.

Features

Sketch2Go is a qualitative graphing tool. Graphs are sketched using seven icons representing constant, increasing, and decreasing functions that change at constant, increasing, or decreasing rates. It is based on original R&D carried out by Schwartz and Yerushalmy (1995) and Shternberg & Yerushalmy (2001), who propose an intermediate bridging representation based on the function and its vocabulary. The seven graphic icons describe the change in both the function and its rate of change. Sketch2Go is a version of the Qualitative Derivative Grapher programmed by Alexander Zilber for CET (Centre for Educational Technology).

Mathematical modeling cannot be fully accomplished by this qualitative sign system of constant, increasing, and decreasing functions. But the set of seven signs supports forming a mathematical construction with language developed from acquaintance with physical scenarios, helping lay the foundations of learning pre-calculus and calculus. Sketch2Go supports the abstraction of everyday phenomena using a small set of mathematical signs that can be manipulated on screen as semi-concrete objects.

Suggested Activities

a modeling problem

a car is moving at a speed of 20 meters per second when the driver sees a ball rolling on the road. The driver's reaction time is one second (reaction time is the time that passes between identifying the ball and pressing the brakes.) During that time the car continues at its constant speed. After the driver presses the brakes, the car decelerates for 7 seconds until it stops.

* Describe in a graph the distance the car traveled during from the time the driver saw the ball until the car stopped.
* What does the lower graph describe in this story?
* How would your graph change in each of the following situations: (1) the driver drove faster; (2) the driver was drunk; (3) it was a rainy day.

Using sketches to prove derivative rules

Sketch examples of functions that would fulfill the constraints listed below.

Write the properties that the functions represent or argue why you could not find such functions:

* Continuous functions whose derivatives are increase monotonically
* Continuous functions that have derivative functions with exactly a single maximum
* Continuous functions with derivative functions that have a discontinuity or some sort
* Functions with discontinuity that have continuous derivative functions
* Functions that have continuous derivative functions and a second derivative with discontinuity

Requirements:· Java Enabled (J2ME) Phone - Profile/MIDP-2.0 Configuration/CLDC-1.1
· Screen Resolution: 128 x 96 and above

Other Java Freeware of Developer «Math4Mobile»:

Graph2Go Graph2Go - Graphing calculators are instrumental in teaching and learning mathematics. It is an environment that supports conceptual understanding of functions in general, and school algebra and real analysis in particular. Especially, it enhances connections between graphic and symbolic representations

Quad2Go Quad2Go - Explorations with Quad2Go are especially appropriate for 11-12 year old students. Teaching geometry to students of this age focuses on the critical attributes of quadrilaterals and on the hierarchical relations among them. Learning means identifying critical attributes and non-critical attributes

Fit2Go Fit2Go supports exploration and modeling activities. It supports data collection by proposing a model that can appropriately describe the user's data. The tool highlights the numeric aspects of a phenomenon. Together, Sketch2Go and Fit2Go provide a comprehensive view of models and modeling

Solve2Go Solve2Go - supports solving equations and inequalities by means of conjectures based on visual thinking. Conjectures can be refuted or supported by examples provided by the tool, and should be proved using symbolic manipulations on paper.
Equations: when we want to know for which values of x the two functions are equal

Greenfish Plot Greenfish Plot - This program is an advanced curve plotting application for mobile Java devices. It supports plotting multiple explicite, polar or parametric function curves. It can also perform numeric calculations such as calculating the value, derivative, integral, roots, minimum or maximum of a given function

MobileMaths MobileMaths - MobileMaths Version 2.0 contains the most powerful tools for your handset and included the following programs: 1. Professional Calculator 2. Equation Solver 3. Definite Integration 4. Function Solver 5. Linear System Solver 6. Powerful Graph 2D 7. Powerful Graph 3D 8. Powerful Curve Fitting (Regression) 9. Statistics 10. Matrix Operations 11

TVH-72g Graphing Calculator TVH-72g Graphing Calculator - TVH-72g Graphing Calculator is a low-cost introductory & disposable graphing calculator for the educational use of schools and students who may have difficulty, are unable or may not wish to acquire a stand-alone feature-laden graphing calculator

Graph (Java) Graph calculates mathematical expressions and draws function graphs on the screen of J2ME mobile devices

sodBrain MathEasy sodBrain MathEasy is a brain-trainer, a free java-based mobile application that allows you to accelerate your brain by solving basic mathematical and logical problems

matrixmobile linear equations matrixmobile linear equations application compatible with most java enabled cell phones. It helps you solving systems of linear equations up to 9 unknown, working with matrices (inverse, transpose, multiply)

sodBrain MathEasy Free SodBrain MathEasy is a brain-trainer, a free java-based mobile application that allows you to accelerate your brain by solving basic mathematical and logical problems. (English and French Versions)

TouchMaths 5 TouchMaths is a revolutionary mathematical tool for mobile phones. The program is must-have for students, engineers and researchers. TouchMaths program includes many applications with many features. The famous TouchMaths is designed in order to fulfill the needs of everyone (student, engineer, researcher...)

PRIMElet A simple application for integer operations.
Factorization, Primality Testing, modPower, modInverse, Next Pr. Prime, Random

Comments on Sketch2Go:

Comments not found

JavaMobiles - Free Java games download for mobile phones. Java Applications, Software, JAR, Apps for Nokia, Samsung, touch screen, 240x320 screen