The goal of mathematics interface design (MID) is to enable the learner to perform tasks with as much mathematical understanding as possible by encouraging the learner to think about the task at hand. The goal of user interface design (UID) is different; it is to accomplish tasks as quickly and effortlessly as possible.
June Lester, is an advocate for mathematical interface design principles. She expresses the need for mathematical ideas to be communicated in a clear, intuitive and appropriate way, in the design of learning object.
The example that June Lestor uses to show the difference between the two interface designs is the use of tangrams to teach children geometric transformations, such as rotations, reflections and translations. If the goal of the learning object was to solve the tangram puzzle as a game then good UID would make the movement of pieces easy and the use of visual spatial skill of primary importance. An example of good MID would have the user decide on the most appropriate center for rotation and apply a value for the angle of rotation in order to move the piece. In this case, the movement of pieces is slower than that of UID, but the learning object takes on elements of a learning exercise rather than a puzzle.
One of the challenges in creating mathematical learning objects is including aspects of good user interface design, but making sure that it did not conflict with sound mathematic interface design.