Editing Procedural knowledge (section)

== Definition ==
Procedural knowledge is the "know how" attributed to technology defined by cognitive psychologists, which is simply "know how to do it" knowledge. Part of the complexity of it comes in trying to link it to terms such as ''process'', ''problem solving'', ''strategic thinking'' and the like, which in turn requires distinguishing different levels of procedure.<ref>{{Cite journal|last=McCormick|first=Robert|date=1997-01-01|title=Conceptual and Procedural Knowledge|url=https://doi.org/10.1023/A:1008819912213|journal=International Journal of Technology and Design Education|language=en|volume=7|issue=1|pages=141–159|doi=10.1023/A:1008819912213|issn=1573-1804|url-access=subscription}}</ref> It is the ability to execute action sequences to solve problems. This type of knowledge is tied to specific problem types and therefore is not widely generalizable.<ref>{{Cite journal|last1=Rittle-Johnson|first1=Bethany|last2=Siegler|first2=Robert S.|last3=Alibali|first3=Martha Wagner|date=2001|title=Developing conceptual understanding and procedural skill in mathematics: An iterative process.|url=http://dx.doi.org/10.1037/0022-0663.93.2.346|journal=Journal of Educational Psychology|volume=93|issue=2|pages=346–362|doi=10.1037/0022-0663.93.2.346|issn=1939-2176|url-access=subscription}}</ref> Procedural knowledge is goal-oriented and mediates problem-solving behavior.<ref>{{Cite journal|last1=Corbett|first1=Albert T.|last2=Anderson|first2=John R.|date=1995|title=Knowledge tracing: Modeling the acquisition of procedural knowledge|url=http://dx.doi.org/10.1007/bf01099821|journal=User Modeling and User-Adapted Interaction|volume=4|issue=4|pages=253–278|doi=10.1007/bf01099821|s2cid=19228797 |issn=0924-1868|url-access=subscription}}</ref>

The concept of procedural knowledge is also widely used in mathematics educational researches. The well-influential definition of procedural knowledge in this domain comes from the introductory chapter by Hiebert and Lefevre (1986) of the seminal book "Conceptual and procedural knowledge: The case of mathematics", in which they divided procedural knowledge into two categories. The first one is a familiarity with the individual symbols of the system and with the syntactic conventions for acceptable configurations of symbols. The second one consists of rules or procedures of solving mathematical problems. In other words, they define procedural knowledge as knowledge of the syntax, steps conventions and rules for manipulating symbols.<ref name=":0">{{Cite book|last=Hiebert|first=James|title=Conceptual and procedural knowledge: The case of mathematics.}}</ref> Many of the 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 knowledge that are tremendously powerful assets in problem solving. <ref>{{Cite journal|last=Schoenfeld|first=Alan H.|date=1979|title=Explicit Heuristic Training as a Variable in Problem-Solving Performance|url=http://dx.doi.org/10.2307/748805|journal=Journal for Research in Mathematics Education|volume=10|issue=3|pages=173–187|doi=10.2307/748805|jstor=748805 |issn=0021-8251|url-access=subscription}}</ref> Therefore, Star (2005) proposed a reconceptualization of procedural knowledge, suggesting that it can be either superficial, like ones mentioned in Hiebert and Lefevre (1986), or deep.<ref name=":1">{{Cite journal|last=Star|first=Jon R.|date=2005|title=Reconceptualizing Procedural Knowledge|journal=Journal for Research in Mathematics Education|volume=36|issue=5|pages=404–411|doi=10.2307/30034943|jstor=30034943 |issn=0021-8251|doi-access=free}}</ref><ref name=":0" /> 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.<ref>{{Cite book|title=The Development of Mathematical Thinking|year=1983|pages=253–290}}</ref> Research on 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. <ref>{{Cite book|last=Star|first=Jon R.|url=https://eric.ed.gov/?id=ED471762|title=Re-Conceptualizing Procedural Knowledge: The Emergence of "Intelligent" Performances among Equation Solvers|date=2002|publisher=ERIC/CSMEE Publications, 1929 Kenny Road, Columbus, OH 43210-1080|language=en}}</ref><ref name=":1" /><ref>Star, J. R. (2013). {{Citation|title=On the Relationship Between Knowing and Doing in Procedural Learning|date=2013-04-15|url=http://dx.doi.org/10.4324/9780203763865-22|work=International Conference of the Learning Sciences|pages=92–98|publisher=Psychology Press|doi=10.4324/9780203763865-22 |isbn=978-0-203-76386-5|s2cid=9793860 |access-date=2020-12-08}}</ref>