procedures that students possess probably are chains of prescriptions for manipulating symbols. In their definition, procedural knowledge includes algorithms, which means if one executes the procedural steps in a predetermined order and without errors, one is guaranteed to get the solutions, but not includes heuristics, which are abstract, sophisticated and deep procedures knowledges that are tremendously powerful assets in problem solving. Therefore, Star (2005) proposed a reconceptualization of procedural knowledge, which suggesting it can be either superficial, like ones mentioned in Hiebert and Lefevre (1986), or deep. Deep procedural knowledge is associated with comprehension, flexibility and critical judgement. For example, the goals and subgoals of steps, the environment or type of situation for certain procedure, and the constraints imposed upon the procedure by the environment. Researches of procedural flexibility development indicates flexibility as an indicator for deep procedural knowledge. Individuals with superficial procedural knowledge can only use standard technique, which might lead to low efficiency solutions and probably inability to solve novel questions. However, more flexible solvers, with a deep procedural knowledge, can navigate their way through domain, using techniques other than ones that are over-practiced, and find the best match solutions for different conditions and goals. Development The development of procedural knowledge is always entangled with the development of declarative knowledge. Researchers suggested that initial problem solving involves explicitly referring to examples, participants start with pure example-based processing. The examples illustrate the solution of a similar problem and the problem solver analogically maps the solution of the example onto a solution for the current problem. People make extensive reference to examples even when they are initially taught the rules and principles. It is believed that when people acquiring cognitive skills, firstly an example is encoded as a declarative structure. When participants are tested on their first problems, they have two possible ways to respond. If the example matches the problem they learned, they can simply retrieve the answer. However, if it does not match, they must analogically extend the example. With repeated practice, general rules develop, and the specific example is no longer accessed. In this way, knowledge transitions from a declarative form (encoding of examples) to a procedural form (productions rules), which is called the adaptive control of thought—rational (ACT-R) theory. However, in certain occasions, procedural and declarative knowledge can be acquired independently. Researches with amnesic patients found that they can learn motor skills without the ability to