Interaction Design: 4 Approaches to Balancing Whole Number Expressions

Mathematical Model:

A scale measures equality between two weights, represented by mathematical expressions. By adding opposites that sum to zero, expressions can be simplified. The balance responds to the relative weights in the virtual manipulative.

Problem Statement:

What is the best user experience that stays true to the mathematics, and is engaging to interact with?

1) MathPlayground (http://www.mathplayground.com/AlgebraEquations.html) offers a solution to the problem of Solving Whole Number Linear Equations (Fig. 1).

Fig. 1 Mathplayground's Algebra Equations Practice Mode

I like:

·      Realistic Functionality - balance responds to inequality

·      There is exactness to the equality of the symbols on each side

·      There is a symbolic representation of the equation
·      Tiles are in a convenient place to grab

I wish:           

·      You could scale the number of tiles you were adding/subtracting, and could have more than 20 tiles on a side

·      The game had multiple representations

o   Table

o   Graph

o   Abstract symbolic

·      That other representations could be chosen to work with and automatically updated when a move was made 
·      That the manipulatives were made into fun items that were less abstract
·      That tutorial mode was not the default user first experience, it is much more restrictive than the practice version of the manipulative. 

2) Utah State University's NLVM (http://nlvm.usu.edu/en/nav/category_g_3_t_2.html) has Algebra Balance Scales (and a Negative Integer version in Fig. 2)

Fig. 2 NLVM's Algebra Balance Scales - Negatives

I like:

·      Realistic functionality - balance responds to inequality

·      Exactness of symbols - equivalent on each side

·      Symbolic representation of the equation
·      Symbolic manipulation of the equation
·      Tiles are in a convenient place to grab, and they drop easily

I wish:           

·      Other forms of manipulation other than symbolic (The objects were still moveable after being placed on the scale)
·      You could scale the number of tiles you were adding/subtracting, and were able to have more than 10 of a given object on a side

·      The game had multiple representations

o   Table

o   Graph

o   Abstract symbolic

·      That other representations could be chosen to work with and automatically updated when a move was made 
·      That the manipulatives were made into fun items that were less abstract

3) DragonBox Algebra (http://www.dragonboxapp.com/) has a gamified approach to teaching the procedures for solving linear equations. (Fig 3)

Fig. 3 DragonBox's Algebra Equations Progression

I like:

·      The graphics are great and the functionality is intuitive
·      The symbols and operations are consistent
·      The way anti-objects are implemented, and the scaffolding pictures are slowly removed

·      The gamification elements make it an addicting experience
·      That a child will learn all of the procedures for solving linear equations without thinking they are doing math

I wish:

·      There was a relation to the real world, like the balancing of weight

·      There was a conceptual underpinning to things like dividing every term by a value
·      The game had multiple representations

o   Table

o   Graph

o   Abstract symbolic

·      That other representations could be chosen to work with and automatically updated when a move was made 

4)  Curtis Wang designed a Whole Number Linear Equation lesson that can be extended as a game concept. (Fig. 4)

Fig. 4 Curtis Wang's Solving Whole Number Linear Equation Lesson

I like:

·      The graphics and friendly design

·      The animations in the original version (https://app.box.com/s/204p4g5wnk3fr4n2pf5a)
·      That this could be more fun to play than the abstracted form

I wish:           

·      There was exactness to the symbols on each side

·      There wasn’t a change in the moment of inertia when placing objects

·      There were anti-objects like helium balloons to remove weight with

·      We could incorporate scaling (Whole number multiplication/Division)