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Factoring

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Design Overview

  • A structured environment for factoring trinomial expressions without giving answers away. Could aid in learning to factor by taking the tedious nature out of factoring.
  • A simple way for students to check to see if they factored a trinomial correctly.

Motivation

  • Factoring is one of the major topic covered in Algebra 1
  • 4 teachers indicated students initially have difficulty, but eventually become comfortable, with factoring.
  • 4 Algebra tutor experts said that factoring is difficult for students.
  • 3 teachers would like calculators to have a feature to help with factoring.

Major Findings

  • Students who knew factoring found all different designs helpful. Students who could not factor were not able to use the interfaces to guess an answer.
  • 7/7 users found trinomials with the a coefficient greater than 1 more difficult.
  • Giving instant feedback by incorporating the checking step and showing intermediate progress seemed to help for 2/2 users that it was tested on.
  • 3/7 users appreciate the binomial structure.

Past Iterations and User Tests

See Evolution of Prototypes

Design Background

Teachers that we interviewed stressed the importance of being able to teach their students a memorable step-by-step process for math concepts. We also learned that teachers had difficulty teaching this process for factoring. We felt that it was important to scaffold commonly utilized procedures within our factoring design to reinforce the factoring concept by reminding students of the relationships between different numbers. Because teachers indicated that students initially have trouble with picking up factoring, we felt that our design should check their answers using the FOIL procedure so that students can make sure that their answers are on the right track.

 

Design Walkthrough

1.

User enters the trinomial in the form provided.

2.

No automation to assist user to determine the correct combination of factors.

Structured to show the FOIL relationship early instead of in the checking process.

There are two modes: trinomials with first term coefficient as 1 or greater than 1. In the first case, only the guide lines that have to be considered would be shown.
3.

For trinomials with the first term coefficient greater than 1, the screen would show all of the guide lines that the user would need to consider.