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Graphing

Transformations

View working prototype

Note: This is a semi-live demo that shows the main parts of the graphing system. Some parts are interactive, but other parts like the table are better demonstrated with the graphing prototype.

  

Design Overview

  • Allows the user to enter parameters in the equation template pertaining to the equation type selected (linear, quadratic, or custom)
  • Adjust the parameters dynamically on the graphing screen.

Motivation

  • 27 teachers use graphing calculators for linear graphs.
  • 8 teachers vary coefficients to teach slope and intercepts.
  • 2 Algebra 1 teachers mentioned that students have problems understanding slope and relating multiple representations.
  • 5 teachers use tables in conjunction with graphs.

We decided to first focus on a model for graphing linear equations, which can be extended to quadratics.

Major findings

  • 15/16 teachers who tested this feature appreciated this idea of relating the equation and graphical representation.
  • By the last iteration, 6/7 students were able to adjust the slope and y-intercept.
  • Next step: Incorporating fractions. One teacher also expressed interest in entering fractions to demonstrate perpendicular slopes to students
  • Next step: Including axes labels. If users cannot see the points/graphs, it is unclear what went wrong because there is no indication of what each tick mark represents.

Past iterations and user tests

See Evolution of Prototypes

 

Design Background

This design came out of some brainstorming we had about how we could use the calculator to be more of an educational tool. Later we found that some of the TI calculators support functionality like this, but it is very hard to get to, and not obvious at all how to use it without reading the instruction manual. In any case, our idea from the start was to make this functionality readily accessible as a feature, since there were teachers who indicated they taught slope and intercept in a similar way.

Look at Evolution of Prototypes to see how this evolved into our final design.

 

Detailed Design

1.

To start graphing, the user selects the "y=" option.
2.

The user may first choose from a menu with equation “templates” with forms of different types of equations, including linear and quadratic.

Note: This part of the prototype is not implemented dynamically.
3.

In the y= screen, the user can fill in the blanks for the parameters for the equation, and then view the graphical form of the equation by pressing on the “Graph” button.
4.

To adjust a linear equation dynamically, the user may use the left/right keys to move between the slope and the y-intercept fields, and they can use the up/down keys to increase or decrease the parameter in focus. Fractions, though not prototyped in this interface due to time constraints, would be a part of the design for future work.
5.

To view the corresponding table of values, the user can press on the “Table” button.