Visualization of Bugs in Subtraction with Black-Box Model

In this paper, an error-awareness learning environment targeting the bugs of multi-digit subtraction is described. We, first, introduce the block -box model where the minuend is embodied as blocks and the subtrahend is embodied as boxes. In the block -box model, the process of subtraction is embodied as concrete manipulation of putting the blocks in the boxes. The bugs in multi-digit subtraction can be visualized as irregular manipulation of the blocks and boxes. We have developed a learning environment where a learner subtracts a multi-digit number described with blocks and boxes by direct-manipulation. The learner then can reconstruct an erroneous subtraction including a bug with irregular manipulation of the blocks and boxes. Through this reconstruction, we expect that a learner will increase his/her understanding about the procedure of subtraction. In this paper, an experimental evaluation of the learning environment is also described.