Editing Procedural knowledge (section)

== Interaction with conceptual knowledge ==
The most common understanding in relation to the procedural and conceptual knowledge is of the contrast of ''knowing how'' and ''knowing that''.<ref>{{Cite book|last=Ryle|first=G.|title=The concept of mind|year=1949}}</ref> Some see the distinction as a contrast between the tacit knowledge of technology and the explicit knowledge of science.<ref>{{Cite book|last1=Cross|first1=A.|title=Technology in schools: a reader|last2=McCormick|first2=R.|year=1986}}</ref> Conceptual knowledge allows us to explain why, hence the distinction of "know how" and "know why".<ref>{{Cite book|last=Plant|first=M.|title=How is science useful to technology.|year=1994}}</ref>  Conceptual knowledge is concerned with relationships among items of knowledge, such that when students can identify these links, it means they have conceptual understanding. Cognitive psychologists also use the term ''declarative knowledge'' to contrast it with procedural knowledge, and define it as "knowledge of facts".<ref>{{Cite book|last=Anderson|first=J.R.|title=Cognitive psychology and its implications|year=2005}}</ref> However, declarative knowledge may be a collection of unrelated facts, whereas conceptual knowledge puts the focus on relationships.<ref>{{Cite book|last1=Heibert|first1=J.|title=Conceptual and procedural knowledge: The case of mathematics.|last2=Lefevre|first2=P.|year=1986}}</ref> Also, declarative knowledge is an inert form of knowledge which contrasted with procedural knowledge as an active form, but conceptual knowledge can be part of an active process. Therefore, it is important to know that conceptual knowledge is not simply factual knowledge but consists of ideas that give some power to thinking about technological activity.

Evidence from mathematics learning research supports the idea that conceptual understanding plays a role in generation and adoption of procedures. Children with greater conceptual understanding tend to have greater procedural skill.<ref>{{Cite journal|last1=Hiebert|first1=James|last2=Wearne|first2=Diana|date=1996|title=Instruction, Understanding, and Skill in Multidigit Addition and Subtraction|url=http://dx.doi.org/10.1207/s1532690xci1403_1|journal=Cognition and Instruction|volume=14|issue=3|pages=251–283|doi=10.1207/s1532690xci1403_1|issn=0737-0008|url-access=subscription}}</ref>  Conceptual understanding precedes procedural skill.<ref>{{Cite journal|last1=Gelman|first1=Rochel|last2=Meck|first2=Elizabeth|date=1983|title=Preschoolers' counting: Principles before skill|url=http://dx.doi.org/10.1016/0010-0277(83)90014-8|journal=Cognition|volume=13|issue=3|pages=343–359|doi=10.1016/0010-0277(83)90014-8|pmid=6683141 |s2cid=5070684 |issn=0010-0277|url-access=subscription}}</ref> Instruction about concepts as well as procedures can lead to increased procedural skill.<ref>{{Cite journal|last1=Hiebert|first1=James|last2=Wearne|first2=Diana|date=1992|title=Links between Teaching and Learning Place Value with Understanding in First Grade|url=http://dx.doi.org/10.2307/749496|journal=Journal for Research in Mathematics Education|volume=23|issue=2|pages=98|doi=10.2307/749496|jstor=749496 |issn=0021-8251|url-access=subscription}}</ref> And increasing conceptual knowledge leads to procedure generation.<ref>{{Cite journal|last=Perry|first=Michelle|date=1991|title=Learning and transfer: Instructional conditions and conceptual change|url=http://dx.doi.org/10.1016/0885-2014(91)90049-j|journal=Cognitive Development|volume=6|issue=4|pages=449–468|doi=10.1016/0885-2014(91)90049-j|issn=0885-2014|hdl=2027.42/29108|hdl-access=free}}</ref><ref name=":6">{{Cite journal|last1=Rittle-Johnson|first1=Bethany|last2=Alibali|first2=Martha Wagner|date=1999|title=Conceptual and procedural knowledge of mathematics: Does one lead to the other?|url=http://dx.doi.org/10.1037/0022-0663.91.1.175|journal=Journal of Educational Psychology|volume=91|issue=1|pages=175–189|doi=10.1037/0022-0663.91.1.175|issn=0022-0663|url-access=subscription}}</ref> However, this relationship is not unidirectional. Conceptual and procedural knowledge develop iteratively, but the conceptual knowledge may have a greater influence on procedural knowledge than the reverse.<ref name=":6" /><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> Conceptual instruction led to increased conceptual understanding and to generation and transfer of a correct procedure. Procedural instruction led to increased conceptual understanding and to adoption, but only limited transfer, of the instructed procedure.