It is important for students to understand the goals and the criteria for success when learning in the classroom. Often teachers will introduce learning goals to their students before a lesson, but will not do an effective job in distinguishing between the end goals and what the students will be doing to achieve those goals. "When teachers start from what it is they want students to know and design their instruction backward from that goal, then instruction is far more likely to be effective". In a study done by Gray and Tall, they found that 72 students between the ages of 7 and 13 had different experiences when learning in mathematics. The study showed that higher achieving students looked over mathematical ambiguities, while the lower achieving students tended to get stuck on these misunderstandings. An example of this can be seen in the number formula_1. Although it is not explicitly stated, the operation between these two numbers is addition. If we look at the number formula_2, here the implied operation between formula_3 and formula_4 is multiplication. Finally if we take a look at the number formula_5, there is a completely different operation between the 6 and 1. The study showed that higher achieving students were able to look past this while other students were not.