EpsilonWriter 

Dynamic algebra

Dynamic algebra is making calculations with the mouse, is direct manipulation on formulas, preserving the signification.


Principle

Dynamic algebra rely on a gesture of the user. From this gesture, EpsilonWriter can propose several operations. The user validates one of these propositions. EpsilonWriter display the operation done and give an explanation. The result of the operation is available for any new operation of the user. The user can thus chain several operations very smoothly.

Gestures of the dynamic algebra

Detailed example of equivalent drag&drop

Given 2x=5   selection of 2 and drag before 5:

image image6 

We see what we shall obtain if the mouse button is released here.

If the button is released, we obtain the explanation and the result:

red 2x=5 green ⇝x=5/ red 2 

Division of both sides by 2 


x=5/2 

Examples of equivalent drag&drop

3x²  is dragged over 4x²  :

red 3x²+2x+4x²  green ⇝  2x+7x² 

The first x  is dragged in the parenthesis:

red x(x²-2x-1)  green ⇝  x³-2x²-x 

a²  is dragged a bit on the left:

red a²+ab+b²  green ⇝  a²(1+ab/a²+b²/a²) 

 

Other drag&drop: substitution

x=a+2 and y=2a-1  is dragged over  (2x+y)/(x-y)  which provides :

(2(a+2)+2a-1)/(a+2-(2a-1... 

Other drag&drop: addition/subtraction of equations

2x+3y=z-3   is dragged over  5x-y=z+2  which provides either:  7x+2y=2z-1  or  3x-4y=5 

The choice is presented in a popup menu.

Calculation by click on a selection

Given image image4  a Ctrl+Clic is applied on the selection, giving 2*22 

Given image image5  a Ctrl+Clic is applied on the selection, giving 3x^5y   This is a multiplication of like factors.

Calculation by click on an operator

Given 3*2x+3y  a Ctrl+Clic is applied on *  , giving 6x+3y 

Given 3(x-1)+(x-1)/2  a Ctrl+Clic is applied on +  , giving 7(x-1)/2  . This is an addition of like terms.



Dynamic algebra and description of gestures

 

All the dynamic algebra actions have a mathematical explanation, some have in addition a gesture description.

Given -2x≤3  ,   -2  is dragged before 3  . If the "Describe the dynamic algebra gesture" setting is on, one gets:

 

red -2x≤3  green ⇝  x≥3/( red -2) 

Gesture: Multiplicative move of a negative expression to the other side, the factor becomes divisor, the inequality sign is reversed

Explanation: division of both sides by -2 


 

 


Pedagogical Dynamic Algebra

This is the name of Dynamic Algebra when there limitations to basic gestures and indications of some refused gestures.

When the setting Pedagogical Dynamic Algebra is active, given (2+6)/5  if one tries to dropt 2  before the fraction, the action is refused with the message: No basic additive output of the numerator.

When the setting is inactive, the action is accepted with the result: 2/5+6/5  and the explanation: Transforming into a sum of 2 fractions or with 2 been factored out.

The idea is that there is no simple action allowing to bring 2  out of the numerator and obtaining an equivalent expression, but that there are two complex actions.

 

See a demo of pedagogical dynamic algebra

 

Dynamic Algebra for the teacher: make math of the 21th century on interactive whiteboard

 

Make some of your calculations on an interactive whiteboard with epsilonwriter, have sometimes students doing so.

 

 

Use Dynamic Algebra to write solved exercises. You can delete lines, delete some explanations, and modify others. You will soon have the possibility of modifying the texts used by epsilonwriter for the explanations and descriptions.

 

Dynamic Algebra is also a more flexible way for typing and modifying formulas. To be used to write documents with formulas.

 

Dynamic Algebra for the student: understand and learn

 

Use Dynamic Algebra:

-  To learn the correct gestures with their explanations and their descriptions,

-  To learn erroneous gestures, learn what we cannot do,

-  To understand that we cannot make a gesture if we do not know it is correct or not,

-  To understand that certain gestures are complex and that if we make them in a rough way, we make errors. In algebra, it is necessary to be very precise.

 

Dynamic Algebra for the student: calculate and write

 

Use the dynamic algebra to make your calculations more easily. It is you who decide on what you want to do, it is the computer which makes it.

Draft your exercises with epsilonwriter, customize your work.

 

Dynamic Algebra and distance work

Dynamic Algebra: is included in epsilonwriter, software allowing several persons working on a document. Using Skype in addition, it is ideal for distance tutoring and collaborative work.