Problem solving and Creativity
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Cebu Normal University**We aren't endorsed by this school
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EDUCATION 575975
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Computer Science
Date
Dec 20, 2024
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7
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Problem Solving‘Ana's food catering business has been profitable, asthere is no competitor. Lately, a new catering groupwas put up, offering as good services similar tohers. With the presence of the competitor, someclientshaveshiftedtothenewprovider.Anainquires on how to sustain her customers' loyalty.This situation illustrates a problem.Aproblemariseswhenthereisadifferencebetween where you are now (e.g., the presence ofAna's competitor) and where you want to be (e.g.,Ana's desire to sustain customer loyalty).A distinguishing feature of a problemis that there isa goal to be reached through some action on yourpart,buthowtogetthereisnotimmediatelyapparent. There is an obstacle or a gap betweenwhereyou are now and where you want to be(Robertson, 2015). In Ana's case, her goal is tosustain the customer clients, but the solution is notthere yet (current state).A necessary element of a problemis the presenceof an obstacle or block toward the attainment ofthat goal. For this reason,problem-solving happenswhen an individual strives to eliminate the obstaclethat hinders the attainment of the desired goal. "Ifnoobstaclehindersprogresstowardagoal,attaining the goal is no problem" (Reese, 1994).Figure11 illustrates the elements of a problemscenario.Elements of the problem scenario:●Current State●Block/ obstacle●Desired GoalProblemsolvingreferstocognitiveprocessingdirected at achieving a goal for which the problemsolver does not initially know a solution method(Mayer, 2013). This definition consists of four majorelements (Mayer, 1992; Mayer & Wittrock, 2006),namely:1.Cognitive -Problem solving occurs within theproblem solver's cognitive system and can only beinferredindirectlyfromtheproblemsolver'sbehavior(includingbiologicalchanges,introspections, and actions during problem solving).2.Process-Problemsolvinginvolvesmentalcomputations in which an operation is applied to amental representation, sometimes resulting in thecreation of new mental representation.3.Directed- Problem solving is aimed at achieving agoal.4.Personal-Problemsolvingdependsontheexisting knowledge of the problem solver so thatwhat is a problem for one problem solver may notbe a problem for someone who already knows asolution method.Types of ProblemsProblemscan be classified in many ways. For one,itcouldeitherbeawell-definedorill-definedproblem.Robertson(2015)describedawell-defined problemas one that "provides all theinformation required to solve it." Jonassen (1997)considered it as a problem requiring the applicationofadefinitenumberofconcepts,rules,andprinciples being studied to a constrained problemsituation. The problem tells you everything you needto know to solve it or whether you need to work outfor yourself what you are supposed to do. Likewise,it tells you whether or not there is only one answeror solution or there are many solutions.For example, in the problem 4+3 = 7, you are certainthat you are to add the two numbers and there isonly one correct answer. You also know that you are100%rightorwrong.Nevertheless,thereareinstances that you have everything to know to solvetheproblem,butyoucannotstillarriveattheanswer. In Mathematics, for instance, you know theMDAS(multiplication,division,addition,andsubtraction) rule, but applying them may not beclear to you.Anill-defined problem, meanwhile, is one where theinitial state of the problem is given but what the goalstate looks like is not provided (Robertson, 2015). Itis typically situated in and emergent from a specificcontext, where an aspect or aspects of the problemscenarioarenotwellspecified,theproblemdescriptionsarenotdefinite, or the informationneeded to solve it is not expressed in the problemstatement (Chi & Glaser, 1985). Because of thissituation, there may be many correct answers as thelearnershavedivergentcircumstancesandexperiences related to the emergent context. Anexample of an ill-defined problem is, "You notice thatthepopulationofyourtownistremendouslyincreasingandyouarealarmedoftheconsequences. What could you do?" This problem is
ill-defined as it is a complex problem. The solutiontotheproblemismultifacetedasthereisaninterplayofsocial,political,religious,andpsychological issues to consider in arriving at thesolution. The solution is one town varies to anothertown as their circumstances are different. Thus,thereisthepossibilityofgettingmany correctresponses.Approaches to Problem SolvingSeveral approaches have been advanced toexplain the problem-solving abilities of individuals(Anderson, 1996). One is the behaviorist approach,reproducing a previous behavior to solve a problem.A person faced with a problem situation is likely touse the same solution previously used and waseffective in the past. To prepare the garden beforeplanting, pick mattock is traditionally used becausethe Crop Science teacher told it so.In contrast to the reproductive approach advocatedby behaviorists, theGestaltist approachto problemsolvingisaproductiveprocess.Kohler'sexperimentswithapesunderscoredtheroleofinsightintherestructuringofaperson'srepresentationof the problem. As the individualponders upon how to solve a problem, a flash of anidea comes to mind, which eventually provides thebestsolutiontotheproblem.ThissituationillustratestheEurekamoment,the"momentaperson realizes or solves something." A Sciencestudentsaw a rural folk using akapulko extract(CassiaalataLinn.),locallyknownasandadasi(Iloko), as an antifungal treatment. The extract wasused on his face to treat tinea dead cells in the face.The student concluded that the plant extract alsohas exfoliating effect. flava. After three days oftreatment, the extract did not only treat the mainproblem, but it also peeled off dead cells in the face.The student concludedconcluded the plant extractalso has an exfoliating effect.Problem-solving CycleProblem solving is a complex process. It isnot a single skill, but rather an overlapping of somethinking skills, as logical thinking, lateral thinking,synthesis,analysis,evaluation,sequencing,decision- making, research, and prediction are likelyto be involved (Teare, 2006). Metacognitive thinking,creativity, and transfer of learning interplay in theprocess. These cognitive and metacognitive skillsare expressed in the several models proposed toundertakeproblemsolving.TheIDEALmodel(Bransford & Stein, 1993) is adopted to explain theprocess of problem solving. Figure 12 indicates thespecific steps to solve a problem.The IDEAL problem solving processStep1: Identify the problem and opportunities.Problem solving initially identifies the problem orpotential problems. Determining the causes of theproblem is necessary to pinpoint the major cause toprioritizeinresolvingtheproblem.Consideringproblemswithapositiveoutlookservesasopportunitiestodosomethingcreative.Whenproblems are treated as opportunities, the result isoften an unexpected solution or invention. It can bebeneficial to actively attempt to identify problemsthathavegoneunnoticed.Peoplewhoidentifyimportant problems and treat them as opportunitiesare often among the most successful in their fields.For instance, your parents have informed you that inthe next semester you will stop for the meantime asthey are financially incapable to send you to college.Itisjustonesemestermore; just the PracticeTeachingthatyouneedtofulfilltofinish yourdegree. The problem is how would you financiallysupport your last semester in school. This dilemmais the current state of the situation.Step 2: Define goals.The second aspect of the model requires you tocarefully define your goals in the problem situation.This is different from identifying the problem. For aproblem situation, a group of people could identifythe existence of a general problem and agree that itrepresents an opportunity but still disagree aboutwhat their goals should be. Different goals oftenreflectdifferencesinhowpeopleunderstandaproblem. For the problem situation above, the goalis to continue with your college education because it
is just one semester before graduation. Anotherstudent with the same problematic situation mayhaveadifferentgoal.Differentgoalscanleadpeopletoexploreverydifferentstrategiesforsolving a problem.Step 3: Explore possible strategies.This step involves looking back at your goals andfinding possible strategies to solve the problem. Itentailstherecallof procedural knowledge fromlong-term memory. As you think of alternative w tosolvetheproblem,ascertainthatthechosenalternative fits the goal set. Bransford and Stein(1993) Some strategies in problem solving are verygeneral and apply to almost any problem, whereasthere a argued that even when people explicitly tryto solve problems, they often fail to use appropriatestrategies.strategiesthatareveryspecific andapplicable only to a few or limited cases. Manystrategies are suggested to make problem solvingeasier; however, the two main strategies used areheuristicandalgorithm.Heuristicisa"ruleofthumb, a mental shortcut that works for solving aproblem," especially those about decision-makingtasks. Although there is no 100% certainty that thestrategyis successful or adequate to solve theproblem, it is most of the time effective and efficientin solving the problem. Because of its efficiency,heuristiccanlessen the time to solve and canreduce cognitive load. A student who is always lateto class may use the alarm clock in the cellphone tosignal it is time to wake up. It may work effectivelyat times, but if one is in deep slumber, the personmay not be awakened by the alarm. In anotherexample,aMathematics student may know theapplication of the mnemonics FOIL (First Outside -InsideLast)andcansolveproblemsinvolvingsimple numbers, but may not be able to answercorrectly because he or she does not know themultiplicationrulesof signed numbers. Besides,Newell and Simon (1972) suggested three generalproblem-solving heuristics for moving from a givenstate to a goal state: random trial and error, hillclimbing, and means-ends analysis.Random trialand error involvesrandomly selecting a legal moveand applying it to create a new problem state andrepeatingthatprocessuntilthegoalstateisreached.Randomtrialanderrormayworkforsimple problems but is not efficient for complexones.Hillclimbinginvolvesselectingthelegalmove that moves the problem solver closer to thegoal state. Hill climbing will not work for problemsin which the problem solver must take a move thattemporarily moves away from the goal as is requiredinmanyproblems.Themeans-endsanalysisinvolves creating goals and seeking moves that canaccomplish the goal. If a goal cannot be directlyaccomplished, a sub-goal is created to remove oneor more obstacles. The second major strategy is analgorithm, the use of a series of steps to solve aproblem.Theelementsofanalgorithm includeclarity of what is to be done, defined inputs, outputs,results, and preconditions. Computer programmingis a classic example using an algorithm. The use of"If... then..." propositions tells the precondition forthe next step to progress. If the next step does notsatisfy the condition, it will not result in the expectedgoal.Doingthestandardalgorithmsforthefundamentaloperationsin Mathematics requiresdoing the same steps repeatedly with each placevalue column in a given problem. For instance,In teaching origami (the art of paper folding), thesteps presented should be followed one at a time loarrive at the correct art piece. When withdrawingmoney using the ATM card, one needs to follow theelectronic cues to succeed.Step 4: Anticipate outcomes and act.Onceastrategyisselected,thepersonmustanticipatewhatoutcomeswilllikelybe.Theexpectation is the solution to the problem. Whenassured that the goal will be solved, the person actsor implements the planned strategy. For example, alearner anticipates that the answer to the problem23 × 21 should be more than 400 but not 500. Itshould not be less than 400 because 20 x 20 isalready 400. This assurance gives the person theconfidencetoimplementtheplannedstrategy.When a person withdraws money through the ATM,the anticipation is that money will be churned out bythe machine. That motivates the person to followthe steps as cued by the machine.Step 5: Look back and learn.What transpired after the planned strategy to solvetheproblemisproofofitseffectiveness.Inmetacognition, this step is the evaluation of theactions or solutions implemented. If the results givethe correct answer, then the strategy used is goodandeffective.Iftheansweriswrong,thenmetacognitivelyask,"Whatwentwrong?"Theanswers could be in the details missed during theanalysis of the problem, the inappropriateness oftheheuristicoralgorithmstrategy,orinthemiscalculations.Realizingtheerrorscommitted
along the way will make the person understand themistakes committed. Learning from the experiencewillmakethe person more careful next time asimilar task is given.Barriers to Problem SolvingIn the search for alternative strategies to solve theproblem, the individual finds difficulty in coming withapotentialsolutionbecauseofvaried reasons.Anderson (1996) listed some of these and they upare as follows.1.Mentalset.Thesituationwhenthepersonbecomesfixatedontheuse of a strategy thatpreviously produced the right solution, but in thenewsituationitisnottheapplication.Inmetacognitivethinking,thisisconditionalknowledge. An English language learner may befixated on the rule that the past tense of the verb isusually formed by adding -d, -ed to the base form.Thus, given an irregular verb like GO, the answergiven could be "goed." Moreover, a Mathematicslearner could not get the sum of three-digit numbersthat require carrying over because he or she isfixated to the addition of numbers without carryingover.2.Functionalfixedness.Thisis a phenomenonwhen individuals fail to recognize that objects canhave other purposes, aside from the traditional usethey were made for. A learner may think that aspoon is only used for eating. However, in instanceswhennobottleopeneris available, a spoon isusually used to open a bottle of soda drink.3.Failuretodistinguish relevant and irrelevantinformation.This happens when a situation arisesduring the analysis of a problem when an individualcannot discern the relevant information needed inplanning the strategy to solve a problem. When theirrelevant information is given more emphasis in theprocess, it will lead to a wrong solution to theproblem.Anexampleisaproblemofwhat toinclude in a bulletin announcement to help someonewho lost a bunch of keys. Children were askedwhich details to include were relevant, like whereand when it was lost, how many keys were there inthe keyholder, which keys were these, who owned it,wherethe key holder was bought, when it wasbought. Some children may not be able to identifythe relevant from the irrelevant ones.Varied theories explain how creativity is developed(Kozbelt et al., 2010)1.Developmental theory-whichadvocatesthatcreativitydevelops over time (from potential toachievement). It is mediated by aninteractionofpersonandenvironment.-It emphasizes the influence of theplaceand family structures - roleplayandsupportduringthetransitions.2.cognitive theory of creativity-statesthatideationalthoughtprocessesarefoundationaltocreativepersonsandaccomplishment.-Individualswhodiscernremoteassociation,andaregoodatdivergent/convergentthinkingandconceptualcombinationandmetacognitive processes are likelyto be more creative.3.Thestageandcomponential process ofcreativity-pointoutthat creative expressionproceeds through a series of stagesorcomponents.Theprocesscanhave linear and recursive elements.-Ithighlightstheimportanceofpreparation, incubation and insight,andverificationandevaluationincreative thinking.Guilford’s first model of creativity-Heconsideredcreativityasdivergentthinking and the result of several processes:fluency, flexibility, originality and elaboration.Fluency- the ability to produce a great number ofideas or problem solutions in a short period.Flexibility- the ability to simultaneously propose avariety of approaches to a specific problem.Originality -refers to the ability to produce new,original ideas, as well as products.Elaboration- the ability to to systematize ideas andorganize the details of an idea in one’s headandcarry it out.
The creative process follows certain stages1.Preparation -gathering material2.Incubation-subconscious working on theidea3.Illumination-Eureka moment, AHA, lightbulbmoment)4.Verification- idea into formPreparationistheinitialstageofthecreativeprocess. It involves becoming passionate about anwhichmotivatesyoutogathermaterials(read,observe, compare). The information gathered seepsperiodintoyoursubconsciousness,eventuallyremaining there momentarily.Incubationis where you unconsciously continue towork on the idea, but there is no active attempt tosolve the. The mind just wanders until an idea takesform.Illumination, a sudden idea pops out in your mind.The subconscious thoughts find the connection withthe consciousness, resulting in the AHA and Eurekamoments. Once the idea is concretized, it needs tobe verified.Verification, the final stage of the creative process,involves working with the idea into a form that canbetestedand,onceproven,itcouldbecommunicated to others.AresearchconductedbyCalubaquib(2013)illustrates the creative problem solving. One time,she heard from a fellow teacher about the parents'personalexperienceaboutthepotencyofcat'swhiskersorbalbaspusa(OrthosiphonaristatusLinn.) as antihypertension treatment. As it soundedinteresting to her, she read more about the plant andthe use of its extract. She wondered about whatother studies could be made out of the plant extract.At this stage, she was in the preparation stage.While thinking of a novel use for the balbas pusaextract, she was informed by the fellow teacher aftertwo weeks that not only did her blood pressurestabilize, but she also observed that there wereintestinal worms in her stool. This phase was theincubation stage. As Calubaquib was intrigued, abright idea came to her mind. Balbas pusa cannotonlyactasantihypertensionbutalsobeanantihelminthic. This is the illumination stage as sherealizedabout the possibility of using the plantextract to expel internal parasites. Following thatidea,sheplannedusingswineasexperimentalanimals to prove the antihelminthic potency andefficacy of the plant extract, a study for her master'sdegree in chemistry. This is the verification stage ofthe creative problem-solving process.TransferofLearninginProblemSolvingandCreativityProblem solving is made easier if the learner canretrievedeclarativeknowledge,proceduralknowledge,andconditionalknowledge from thelong-termmemory.Iftheproblem-solvingtaskrequires convergent answers, problem solving canbe quite easy if the learner has mastered algorithmtechniques.Nevertheless,eveniftheproblem-solving tasks require divergent thinking, iftherehavebeenexperiencesinthepastthatenabled the learner to answer such task, solvingthem could be successfully done. The phenomenonthatpastexperiencesinsolvingproblemsarecarried over or used in solving new problems isreferred to as the transfer of learning. Transfers oflearning are categorized into the following:1. Near transfer and far transfer.When learners apply their knowledge and skills insituations and contexts that are very close to thosein which the learning occurred, it isnear transfer.When learners perform a skill in a context very muchdifferent from the context, it was learned, itis fartransfer(Johnson, 1995). Learners find it easier toadd three-digit numbers after they have learned thelesson (near transfer). However, they find difficultyemployingthesameskillwhenthetaskistransformedintoawordproblemsolving(fartransfer).2. Positive transfer and negative transferWhenlearnerscanusepriorknowledgeorexperience in solving problems a new problem, it isapositive transfer.When the previous learning orskill obstructs the acquisitionof a new skill orsolving of a problem, it is anegative transfer. Usinga new model of the same brand of Android phone iseasyasthefeaturesarealmost alike (Positivetransfer). However, when a new phone using IOStechnologyis bought, there will be difficultyinusing it the first time (Negative transfer).3. Vertical transfer and lateral transferWhen the learners use their learning at a lower levelto a higher level of cognitive task, vertical transferoccurs. It is the goal of spiral progression in theK-12 curriculum. When learners use the same skill tosolve a related but different problem of comparablelevel of difficulty after learning it, it is lateral transfer.
For example, Ruben finds it easy to add five-digitnumbers as he has mastered adding numbers withorwithoutcarryingoverinthepreviousgrade(verticaltransfer).Likewise,Ruben relies on hisknowledgeoffindingratiosinMathematicsinacquiring the skill of finding the seed germinationrate in a Science laboratory task (lateral transfer).4. Neutral or zero transfer.This happens when past learning or prior experiencedoes not enhance or hinder the acquisition of a newskill or in the solution of a problem.In the transfer of learning, Glass and Holyoak (1986)stated that "the problem-solving process involvesseveral aspects from which three major facets tendtoemerge:thesolver'srepresentationoftheproblem, the solver's background experiences, andthe solver's understanding of the problem." Theyexplainedthatthelearnerbeginstheproblem-solvingprocessassoonasenoughinformation about the problem space is generatedtogainanunderstandingoftheproblem.Theprocessinvolvesassociatingconceptsfromprevious experiences to solve a similar problem.The learner is prompted by the potential answerwhen he or she recognizes similarities between theprevious experience and the new task.Several theories explain how learning is transferredfrom one situation to another (Woolfolk, 2017).Thetheoryofidenticalelementsby Thorndikemaintains that the quality of transfer depends on theidentical elements that are common in both pastand new situations. If the content, method, goal, andattitude in the two situations are similar, the transferis facilitated.The theory of generalization, developed by Judd,states that skills learned are transferrable to othersituations. It argues that if the learner has fullyunderstoodthelessonandmasteredthecompetency, there is a greater likelihood that suchskill can be transferred to a similar situation.The theory of configuration,anchored on Gestaltpsychology,emphasizestheimportantroleofperception in the transfer of learning. It argues thatwhat is learned in one situation can be shifteddirectly to another situation only when similarity incontent, method, or attitude of the two situations isperceived by the learner.ClassroomApplicationsofCognitiveLearningTheoriesTeachers can benefit from the teaching principlesassociated with cognitive learning theories. Alongwithproblemsolving,Woolfolk(2017)recommended the following:1. Ask students if they understand the problem.Letthemseparaterelevantfromirrelevantinformation.Testtheirawarenessoftheassumptions.Encouragethemtovisualizetheproblem by diagramming or drawing it. Ask them toexplain the problem to someone else.2. Encourage attempts to see the problem fromdifferent angles.Suggest several different possibilities yourself, andthen ask students to offer some. Give studentspractice in taking and defending different points ofview on an issue.3.Letstudentsthink;donotjusthandthemsolutions.Offerindividualproblemsaswellasgroupproblems, so that each student has the chance topractice. Give partial credit if students have goodreasonsfor"wrong"solutionstoproblems.Ifstudents are stuck, resist the temptation to give toomanyclues.Letthemthinkabouttheissueovernight.4. Help students to develop systematic ways ofconsidering alternatives.Tell them to think out loud as they solve problems.Ask:"Whatwouldhappenif?"Keepalistofsuggestions.5.Teachheuristics.Encouragethemtouseanalogies to solve problems.Inteachingcreativity,Woolfolk(2017)alsorecommended the following strategies in teachinglearners:1.Acceptandencouragedivergentthinking.Reinforceattemptsatunusualsolutionstoproblems even if the final product is not perfect.Offer choices in topics for projects or modes ofpresentation (written, oral, visual or graphic, usingtechnology).2.Toleratedissent.Askstudentstosupportdissenting opinions. Make sure that nonconformingstudentsreceiveanequalshareofclassroomprivileges and rewards.
3.Encouragestudentstotrusttheir judgment.When students ask questions that you think theycan answer, rephrase or clarify the questions anddirect them back to the students. Give ungradedassignments from time to time.4. Emphasize that everyone is capable of creativityin some form.Avoid describing the feats of greatartists or inventors as if they were superhumanaccomplishments.Recognizecreativeeffortsineach student's work. Have a separate grade fororiginality on some assignments.5. Provide time, space, and materials to supportcreative projects.Here are some examples: collect"found"materialsforcollagesandcreations-buttons,stones,shells,paper,fabric,beads,seeds,drawingtools,clay-andtryfleamarkets and friends for donations. Have mirrors andpicturesfordrawingfaces.Makeawell-lightedspaceavailablewherechildrencanworkonprojects, leave them, and come back to finish them.Followuponmemorableoccasions(field trips,news events, holidays) with opportunities to draw,write, or make music.6. Be a stimulus for creative thinking.Use classbrainstorming sessions whenever possible. Modelcreativeproblemsolvingbysuggestingunusualsolutions for class problems. Encourage students todelay judging a particular suggestion for solving aproblemuntilallthepossibilitieshavebeenconsidered.7. Capitalize on new technology.Ask the studentsto use free apps to create visual maps of ideas andshare their ideas with others.To promote the transfer of learning, the followingteaching-learning strategies are helpful (Woolfolk,2017):1.Keepfamiliesinformedabouttheirchild'scurriculum so they can support their learning. At thebeginning of units or major projects, send a lettersummarizing the key goals, a few of the majorassignments,andsome common problems thatstudents have in learning the material for that unit.Ask parents for suggestions about how their child'sinterestscouldbeconnectedtothecurriculumtopics.2. Give families ideas on how they might encouragetheir children to practice, extend, or apply what theylearn from school. This strategy promotes a neartransfer of learning. Ask family members to includetheir children in some projects that require schoollearning.3. Show connections between learning in schooland life outside of school. Ask families to talk aboutand show how they use the skills their children arelearningintheirjobs,hobbies,orcommunityinvolvement projects.4.Partnerwithfamiliesinpracticinglearningstrategies. Focus on one learning strategy at a time.Ask families to simply remind their children to use aparticular strategy for a homework that week.