A back-end computing system configured to determine i) a first mathematical operation a user may carry out on a first mathematical expression and ii) a second mathematical operation the user may carry out on the first mathematical expression. To minimize processing loads on a user computing device, the system also provides to a mathematics application operating on the user computing device instructions to allow the user to attempt to carry out the first mathematical operation and the second mathematical operation. Further, the system determines i) an accurate outcome and an inaccurate outcome of performing the first mathematical operation and then provides the accurate outcome and the inaccurate outcome to the mathematics application. The system then receives an indication of a second mathematical expression from the mathematical application, where the second mathematical expression is based on the first mathematical operation and a selection of the inaccurate outcome by the user.