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Graph Transformations

Evolution of Prototypes

 

Initial Design

 

Try prototype

The initial prototype only included one screen where the user can interact with the equation and see changes on the graph dynamically.

The purpose of this prototype is to test the desirability of this feature in a graphing calculator.

The right arrow indicates that the user may press the right arrow key to switch the focus to the y-intercept field. The up and down arrows indicate that the user may use the up or down arrow keys to increase or decrease the value of the slope parameter.

 

 

Iteration 1

Try prototype

Design change: Extend interface

  • The linear equation graphing interface is extended to combine with a table of values view.
  • User may choose to enter equations or data.
  • The table view shows the corresponding values of the entered equation.
 
   

Rationale

7/8 students

Most teachers at TTT conference mentioned that this would a great tool to introduce slope and y-intercept to students in Algebra 1. Once users see the pattern of how to change the slope and y-intercept, they all expressed delight.

1/4 users

One user indicated that some students may assume the initial selection is the correct answer of the problem. It is also unclear which box is in focus.

Design Change: Remove horizontal arrows

  • The horizontal arrows that users found confusing were eliminated on the graph screen, and only the active field is highlighted.
   

Rationale

8/8 teachers

All teachers were confused about the vertical and horizontal arrows, since every cursor movement would cause both fields to be highlighted, and it is not clear which field is active.

 

Iteration 2

Try prototype

Design change: Directly enter numbers

  • The intermediate step for selecting y1 or y2 and then pressing enter to change the numbers is eliminated.


  • In this prototype, the user can enter the slope and y-intercept parameters directly.
   

Rationale

2/4 students

Users found the default highlighted y1=2x+1 confusing, and were hesitant to press “Enter” to modify the equation. One user attempted to directly enter an equation to overwrite the “2x+1”.

This introduced a trade-off, because eliminating this step would take away the ability of using the up and down arrow keys to adjust the numbers. Since users had a tendency to directly enter numbers in the y= screen in previous tests, we decided to remove the ability to adjust the values with up/down keys when the graph is not yet visible.

Users were confused by the initial “2x+1” (top). They did not know how to get to the editing screen (right) by pressing “Enter”, where the user may use the up and down keys to adjust the parameters.

 

Iteration 3

More Findings

6/7 students

Almost all students successfully figured out how to use the up/down keys to change slope and y-intercepts. They were able to verbally explain the effects of changing the “m” and “b” terms.