20140410040555_Topic 4 Development of Problem Solving

8/10/2019 20140410040555_Topic 4 Development of Problem Solving

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INTRODUCTION

Georgie (a two-year old) wants to throw rocks out of the kitchen window. Thelawnmower is outside. Dad says that Georgie cant throw rocks out of thewindow because he might "break the lawnmower with the rocks. Georgie saysI've got an idea. He goes outside, brings in some green peaches that he had

been playing with, and says: They wont break the lawnmower.

(Waters, 1989, p. 7)

TTooppiicc

44 Development

of ProblemSolving

LEARNING OUTCOMES

By the end of this topic, you should be able to:1. Explain what is meant by strategic development in problem solving;

2. Describe representational development in problem solving;

3. Explain the use of external representations as tools for problemsolving;

4. Describe the role of language and planning in problem solving;

5. Identify the various specialised representations employed inproblem solving;

6.

Explain the role of interaction in problem solving;

7. Describe the importance of self-monitoring in problem solving; and

8. Compare and contrast problem-solving abilities between childrenand adolescents.


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TOPIC 4 DEVELOPMENT OF PROBLEM SOLVING78

The example above as quoted from Sternberg, R. J. (1998), explains thefundamental nature of problem solving where you have a goal, an obstacle andachievement of the goal. Problem solving in social contexts have indeed become

an important field of interest of cognitive psychologists in the recent years. Anincrease in the amount of research on the way children think about otherindividuals reasoning (Wellman, 1990; Feinman, 1992; Siegler, 1993), on howchildren solve problems together (Brown et al., 1989; Resnick et al., 1991) andhow social relationships impact thinking development (Azmitia & Perlmuter,1989; Rogoff, 1990). In this topic, three different aspects of the development ofproblem solving will be discussed formation strategies, representation andself regulation.

THE DEVELOPEMENT OF PROBLEM

SOLVINGWe will now focus on three aspects of the development of problem solving:

(a) Formation of strategies;

(b) Representation; and

(c) Self-regulation.

It is found that different aspects are more significant at different stages of life, assummarised in Table 4.1.

Table 4.1: Significant Stage in Life for the Three Aspects in the Development of

Problem Solving

Aspect Significant Stage in life

Formation strategies Plays a vital role from infancy (birth to 12months)

Employment of varied representations(such as language, maps and models)

Shows more prominence duringtoddlerhood (one through three years)

Cognitive self-regulation Becomes more important during the pre-school years (three to five years) aschildren have more varied strategies andrepresentations from which to select andgreater cognitive resources to dedicate toplanning, self-monitoring, and otherregulatory processes.

4.1


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TOPIC 4 DEVELOPMENT OF PROBLEM SOLVING 79

4.1.1 Strategic Development

Problem-solving strategies can be defined as procedures that overcome obstacles

and achieve goals. According to researchers, such strategies exist since birth(Butterworth & Hopkins, 1988; Willats, 1990). This can be observed when young

babies communicate their desires to draw caregivers closer to obtain comfort andfood. Nevertheless, the above observation may be difficult to be told in theabsence of language or other behavioural criteria, whether their actions implyintention to achieve goals or the actions are merely carried out without anyintentions.

One of the most promising evidence for representation of goals in the first sixmonths of life is illustrated in the experiment carried out by Rovee-Collier (1987).

In her experiment (Figure 4.1), infants learned very quickly that the act of kickingmade the mobile (attached to their leg by a string) move in different ways.Various ways of evaluating the infants thinking abilities included varying thecharacteristics of the mobile as well as the setting in which the mobile waspresented, and the amount of time between the sessions.

Figure 4.1: Rovee-Collier's experiment

Source: http://psycnet.apa.org

The study carried out by Mast et al. (1980) revealed that infants as young as threemonths maintain a representation of a reinforcement contingency for up to 24hours, and at the same time become emotionally disturbed when they could onlyobtain a poor estimation of their original goal. In a separate study, Tronick (1989)reported that the behaviours of infants are a kind of problem solving strategy,and that the degree to which they engage in them indicate how successful theyare likely to be. Case (1985) suggested that the ability to represent how an actionmeets a goal affects attainment of novel strategies. Although when there is amodel to copy and the actions are within the infants range of tasks, infants areable to use other individuals, especially their mothers, to help them as tools in


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problem solving (Papousek & Papousek, 1987). This is in line with the findings ofRogoff et al. (1992) where infants exhibited strategies to obtain the help of adultsin manipulating objects in ways that would have been impossible for the infants

themselves to do. Infants have the ability to use simple forms of means-endanalysis in the second half of the first year as reported by Wilats (1989).

It has been found that the development of problem-solving strategies followsmarked different courses when children have extensive experience with a taskthan when they do not. Tasks or problems in which children have littleexperience are usually accomplished by employing a single strategy. On theother hand, multiple strategies are used in tasks in which children haveconsiderable experience.

Inhelder & Piaget (1958) employed the balance scale model as a means ofexamining formal operation reasoning (Figure 4.2). One reason for thewidespread interest in balance scales is the simple, hierarchically relatedsequence of rules through which children of different ages progress on the task(Siegler, 1976), summarised in Table 4.2.

Figure 4.2: The balance scale the problem shown is a distance problem, with equalnumbers of weights placed at different distances from the fulcrum.

Source:Inhelder & Piaget, 1958


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Table 4.2: Rules Employed by Children at Different Ages on the Balancing of the Scale

Rule Description

No rule used The majority of the 3-year-olds do not employ any systematic rule;they either guess or switch frequently among alternative approaches.

I A few 3-year-olds and more 4-year-olds employ a partially systematicapproach (Richard & Siegler, 1981).

More advanced 4-year-olds and a majority of 5-year-olds employ aconsistently systematic approach (Siegler, 1976).

II Most 8 or 9-year-old children employ more sophisticated rules thattake into account of the weight on each side as well as the distancefrom the fulcrum (Siegler, 1976).

III An approach whereby only the distance is considered when the weighton both the sides is equal.

IV An approach whereby understanding of the relative weight anddistance of both the weights from the fulcrum has been achieved.

In 1992, Trudge instructed children to work:

(a) alone;

(b) with a partner who initially used a same rule; and

(c) with a partner who initially used a different rule.

He concluded that:

(a) In the absence of feedback, pairs of beginners do not usually move to amore advanced level.

(b) In the absence of feedback, the only children who make progress arebeginners that are paired with relative experts.

(c) When one partner is more expert than the other one, the highest ruleachieved is that of the more advanced partner.

(Miller & Brownel, 1975; Mugny & Doise, 1978; Mackie, 1983; Russell et al.,1990; Radziszewska, 1993).

A majority of the studies involving collaborative problem solving did not furnishchildren with feedback on the correct answer. Generally, feedback provides a

basis for choosing among alternative perspectives and also provides an attractivemethod for children to adopt an approach without seeming to give in to thechild or children who generated it. Ellis et al. (1993) worked on the beneficialeffects of collaboration in combination with feedback that stressed on childrens


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comparisons of the relative sizes of decimal fractions. These researchers observedthat:

(a) About 50% of the children who worked with a partner and obtained

feedback constantly performed the post-test correctly.

(b) Less than 25% of those who worked on their own and received feedbackdid similarly well.

(c) None of the children (either working alone or with a partner) who did notreceive feedback fared well.

Thus, students who worked with a partner and received feedback, performedbest. This translates to the fact that feedback may be critical both for thegeneration of good ideas and their adoption. Ellis et al. (1993) also reported that

children who worked with a partner who employed the correct rule on bothoccasions were expected to adopt the correct rule on their own during the post-test as compared to those with a partner who used the correct rule only at a lateropportunity (67% versus 15%). This is due to the fact that partners whoemployed the correct rules on both instances exhibited higher convincingarguments for it; whereas children who used the correct rule only during thelater occasion and also debated in favour of it, however appeared less expressiveand convincing in motivating the less expert partner to adopt it. This indicatesthat feedback is not compulsory for beginners to adopt a new, superior approachto solving mathematical problems. In addition, it also points out that eitherexternal evidence of the validity of the better approach (provided by feedback) orconvincing arguments (made by children who employed the correct rule on bothoccasions) appear important for good strategies to constantly win out.

4.1.2 Representational Development

A majority of the progress in problem solving among children after the first yeararises from improving ability to internally represent goals, actions, objects andevents. Improvement in representational skills allows toddlers to employ a widerrange of the resources of the social world. Generally, they come up with long-term representations of the methods they have observed of other individuals'problem solving. Subsequently, they employ these methods themselves later in

ACTIVITY 4.1

Carry out a search in the internet on the ability of infants to employsimple forms of means-ends analysis in the second half of the firstyear. Briefly explain this phenomenon.


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life. In addition, improved language ability, both expressive and receptive, alsocontributes to the development of problem solving in this particular age group. Itis a rather surprising fact indeed that infants are able to alert their caretakers

regarding the problems they are facing and hope to solve, but the language skillsof toddlers provide them the opportunity to accurately indicate what they wantto achieve and why exactly they are unable to complete it themselves.

As they come closer to completing their first year of life, children show the abilityto walk or crawl to rooms or places that they cannot see at the beginning of their

journey, in order to get hold of toys or things that they are not able to see at thebeginning (Benson et al., 1989). Subsequently, by 18 months, they start takingsteps that help them maintain representations that otherwise may becomeinaccessible. Allowing toddlers to remember goal-directed actions modelled byadults or peers is one part of how increasing representation skills contribute todevelopment of problem solving (Meltzoff, 1985; Hannah & Meltzoff, 1993).Furthermore, increasingly specific and durable representations permit toddlers totake on the path to specific goals within an activity, rather than focusing on theactivity as a whole. It was found that positive affective reactions such as smilesand abrupt movement of hands and arms to accomplishment of the tasksincreased with age. It appears that part of development of problem solving in therange of one and three years of age include representing specific goals moreprominently in memory, and following the goals more single-mindedly.

The ability in solving problem improves as children become able to express

themselves using language in various circumstances and events. This is due tothe fact that language is a medium for transferring lessons gained on pastencountered problems to novel ones. This includes the improved understandingamong toddlers on what is being said to them by others. It has been found thatchildren as young as two years of age are already able to transfer strategies tonew problems similar to older ones and when children are reminded that theproblems are similar in nature (Crisafi & Brown, 1986).

Besides internal representations, toddlers also exhibit increasing ability to formexternal representations as tools for solving problems. DeLoache (1987) reported

that young childrens understanding of the correspondence between a scalemodel and a larger space is dependent upon the degree of physical similaritybetween both the spaces. These researchers carried out an experiment wherechildren between 2.5 and 3.5 years old observed as a miniature toy was hidden ina particular location in a scale model of the room. Subsequently, they were askedto find the similar toy in the actual room itself. Overall, the ability of children inlocating the toy increased as the degree of similarity between the scale model andthe room increased, even though younger children required a higher degree ofsimilarity to understand the model-room relationship as compared to olderchildren. They concluded that the level of similarity between the objects within


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the two spaces and overall size of both spaces had profound effects on thechildrens performance. Thus similarity may affect accessibility whereby theprobability that childrens representation of one space will provide access to their

representation of the other space. Hence, toddlers can use scale models as toolsfor solving problems, but have an affinity to confuse the representation as anobject in its own right with its role as symbol of another situation.

The term mental model is used to refer to the representation of a body ofknowledge in long-term memory, which may have the same sort of structure asthe models used in reasoning. Psychologists have investigated mental models ofsuch physical systems as hand-held calculators, the solar system, and the flow ofelectricity (Gentner and Stevens, 1983). They have studied how children developsuch models (Halford, 1993), how to design artefacts and computer systems forwhich it is easy to acquire models (Ehrlich, 1996), and how models of one domain

may serve as an analogy for another domain. According to Halford (1993), thecentral characteristic of mental models is that the model must accuratelyrepresent the structure of the problem. On the other hand, the success of themental model is dependent upon whether the critical structural features ofproblems are encoded. Children tend to form analogies in which the system ofrelations within the target domain resembles the system of relations within the

base. It is not necessary for the objects within each domain to have any particularsimilarities. In fact, the key to a good analogy is the similarity of thecorresponding relations in the two situations. The mental model for the classicanalogy Heat flow is like water flow stresses the parallels between thestructural relations among variables that affect the two types of flows (Gentner,1989) (Figure 4.3).

SELF-CHECK 4.1

In the experiment carried out by DeLoache (1987), the 2.5-year-oldsshowed difficulties in translating between the model and the room. Whatcould be the source of young childrens difficulty with the scale model?Suggest other tools that may be easier to be used than the scale model as a

representation of another object.


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Figure 4.3: Structural correspondences in the water/heat flow analogy

Adapted from: Gentner, 1989

Unlike the language, mental imagery and spatial representations that areacquired in the first two years of the childs life, specialised representations areacquired much later in life. In addition, the acquisition of specialised

representations has a tendency to be less universal and more variable in timingthan acquisition of the broadly used ones. Speech, mental imagery and spatialrepresentations observed in all children are the results of the interaction between

biological maturation and general experience. On the other hand, the ability of achild to learn how to write; to draw maps and diagrams; to understand graphsand number lines; to use conventional measurement devices; and to performcontrolled scientific experiments are dependent upon the childs particularexperiences.

Maps are one important specialised and often used representation. The functions

of maps include: A method of representing the locations and boundaries of political entities

such as cities, states and nations, or road systems.

A representation of unperceivable aspects of the universe in perceivableform.

(Liben & Downs, 1989).


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A majority of children are able to understand simple maps drawn by otherindividuals by the age of 5, and utilise these maps as a tool for finding objects(Bluestone & Acredolo, 1979; Uttal & Wellman, 1989). As their age increases, their

ability for drawing maps and including important topological relations amongthe landmarks, and the adoption of a consistent perspective come even later(Piaget & Inhelder, 1956). Besides maps, other types of specialisedrepresentations that are used by older children include rulers, scales, clocks,calendars and other cultural artefacts. It was found that the main difficultyencountered by children with the various measurement devices is not in usingthem but knowing how and when to use them. In conclusion, measurement toolsand other specialised representations significantly increase childrens potential inproblem solving. However, their usefulness naturally depends on the childsunderstanding and comprehension ability.

According to Brown et al. (1989), the main difference between school and real-world problems is the frequent difficulty in school in identifying what exactlythe problem is. Children often reinterpret problems in ways that make sense tothem rather than solving the problem as originally presented. When childrenwere presented with a hypothesis that seemed intuitively unlikely, theycircumvented the suggestion that they test the hypothesis and instead produceda more intuitively likely hypothesis and concentrated on collecting confirmatoryevidence for it. On the other hand, adults tested the hypothesis that wassuggested, regardless of its initial plausibility, and usually discovered that theseemingly unlikely hypothesis was in actual fact correct. Hence, part ofdevelopment of problem solving among older children involves accepting goalsset by the social environment when the task calls for it (Klahr et al., 1993).

SELF-CHECK 4.2

A group of children were instructed to give two turtles identicalamounts of food. They divided the food by giving one piece to oneturtle, the next piece to the other turtle, and so on. Discuss the strategythat was employed by the children in fulfilling the objective of theexperiment. As an adult, how will you guide the children inimprovising on the strategy employed?

ACTIVITY 4.2

Search information about the goal sketch hypothesis proposed by Siegler& Jenkins (1989) where children were able to make a discovery withoutany trial and error. Discuss your findings with your coursemates.


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4.1.3 Self-Regulation

The ability of children in effectively regulating their thinking activities becomes

increasingly central to their problem solving as they attain both increasingnumbers of strategies and representational capacities. One of the key self-regulatory processes is planning, as it can be employed in many differentcircumstances to prevent potentially costly errors. The Tower of Hanoi puzzlewas invented by the French mathematician Edouard Lucas in 1883 where a childis presented with a tower of five disks, initially stacked in increasing size on oneof three pegs. The main objective is to transfer the entire tower to one of the otherpegs (the rightmost one in Figure 4.4), moving only one disk at a time, never alarger one onto a smaller and using the minimum number of steps as possible.Knowing which first move is correct, nevertheless, demands working through

the problem from starting to the end. Hence, solving such a problem in acontinuous manner requires planning the entire sequence of events beforecarrying out any of them.

Figure 4.4: The Tower of Hanoi

Source: http://www.labspaces.net

Most of the problem solving activities carried out by children in their day-to-daylives take place with adults, rather than on their own. In these circumstances,adults frequently plan the activities in such a way that remove the burden ofplanning from the children, thus benefiting them. The term used to describe whathas been carried out by an adult to facilitate problem solving among children iscalled scaffolding which involves the utilisation of specific strategies focused atsimultaneously allowing children to participate, maintaining their interest and atthe same time increasing their competence. (Wood et al., 1976). In general, adultsusually carry out the most crucial and difficult part of the tasks such as dividingthe tasks into sub-goals, coming up with the plans for achieving them andkeeping track of the success of different strategies whereas children are allowed


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to carry out the parts of the task they can complete successfully (Wertsch, 1978).As the child exhibits increasing skill on the particular task, the adult slowly letsgo until the child is carrying out the task independently both the actions and the

self-regulatory aspects of the task. Studies carried out have indicated thatscaffolding is both an all-encompassing activity in the daily environment andthat it assists children to learn planning and other self-regulative skills. Adultsfrequently provide preschoolers with scaffolded instruction and modify the typeof instruction given according to the competence of the learner (Wertsch et al.,1980; Rogoff et al., 1984; Gauvain, 1992). Moss (1992) found that parents,particularly mothers, provide scaffolding where he observed three strategies:

(a) A mother instructs the child with strategies it would not otherwise knowand not able to actually manage unaided for some time.

(b)

A mother encourages the child to keep using useful strategies that the childhas demonstrated.

(c) A mother persuades the child to not implement strategies they considerdevelopmentally immature.

In addition, Conner et al. (1997) found that fathers are as good as mothers atscaffolding. They also found that children that have received scaffolding showlonger-term improvements in skills as well as immediate improvements.

Language plays an important role in regulating thinking activities and is used to

communicate to others as well as to direct childrens problem solving. In general,spontaneous self-directed speech appears in childrens problem solving aroundthe age of 4 or 5. Prior to this age, children at times do talk to themselves,although, self-directed speech is not coordinated with their problem-solving

behaviour (Luria, 1961). In contrast, older children also employ self-directedlanguage to regulate their thinking activity; however, theirs cannot be heard,unlike that of preschoolers (Frauenglass & Diaz, 1985; Berk, 1986; Bivens & Berk,1990). Children usually talk to themselves while solving problems that arechallenging but not impossibly difficult (Berk & Garvin, 1984; Behrend et al.,1989). It happens most often when children experience great difficulty in solving

a problem or following failure to solve a problem (Goodman, 1981). Self-directedspeech plays a crucial role in circumstances in which the childs problem is toresist a tempting, but non-optimal, course of action. In other words, manyproblems are tough not because it is difficult to identify what should be done but

because it is difficult to prevent oneself from employing a less desirablealternative path.


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When faced with several strategies in solving a problem, children use conscious,explicit, metacognitive knowledge about problems they are presented, availablestrategies and their own cognitive capacities (Flavell& Wellman, 1977).Generally, strategies that worked in the past are also selected. As children growup, they become increasingly skilled at monitoring their plans and adjustingthem according to the circumstances (Gardner & Rogoff, 1990). In contrast,younger children do not modify their plans according to the differentinstructions. However, several researchers have reported the failure of school agechildren to plan various tasks such as writing (Bereiter & Scardamalia, 1987)route planning (Gauvain & Rogoff, 1989), instructing other children (Ellis &Rogoff, 1986) and referential communication (Cosgrove & Patterson, 1977).Planning has both its advantages and disadvantages, as shown Table 4.3.

Table 4.3: Advantages and disadvantages of planning in problem solving

Advantages Disadvantages

Making accurate and direct solutions

possible.

Time consuming and tedious.

Allows problem to be solved in a

systematic manner.

Does not directly bring goal attainment.

Interaction with adults is one of the main factors that results in planning amongchildren. Hudson & Fivush (1991) found that children were more likely to planwhen they worked together with an adult as compared to when they worked ontheir own. In addition, the experience of planning with adults also results inmore sophisticated planning when they later solve problems by themselves

(Radziszewska & Rogoff, 1988; Gauvain, 1992). On the other hand, experiencewith peers and older children was found to be not as effective as experience withadults. This may be due to the fact that adults discuss the strategies with theyounger children than peers, reminding them frequently about the goals of thetask and monitoring their progress more closely. Furthermore, adults are moresensitive in modifying the type of help they provide according to therequirement of the child. (Rogoff et., 1984; Gauvain, 1992).

Blaye et al. (1991) reported that children working in pairs fared better in solvingproblems as compared to peers who worked on their own, and performed better

SELF-CHECK 4.3

Briefly discuss the reasons why self-directed speech may facilitateproblem solving.


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on an individual post-test as well. This is because when children worked in pairs,they realise the importance of dividing the problem into sub-goals, thuschannelling their thinking activity in fruitful directions. Nevertheless, children

below schooling age rarely collaborated successfully due to their difficulty inthinking analytically about the other persons reasoning (Azmitia & Perlmutter,1989; Perlmutter et al., 1989).

Skilled problem solvers usually practise several self-monitoring activitiesincluding questioning and elaborating their own knowledge, evaluating theirdegree of understanding, and thinking of counter-examples and possiblegeneralisations (Palincsar & Brown, 1984). Reciprocal teaching is a successfulexample of this type of involvement and it emphasises four strategic activitiesnamely summarising, clarifying, questioning and anticipating future questions(Palincsar & Brown, 1984; Brown & Palincsar, 1989).

SELF-CHECK 4.5

SELF-CHECK 4.4

The effects of collaboration between young children who are beginnersand older children who are more expert tend to benefit the beginnersless than when they solved the problem with adults. Discuss the abovestatement.

1. Discuss the rules employed by children of different ages on thebalancing of the scale.

2. State one benefit of feedback in collaborative problem solving.

3. Identify the factors which contribute to the success of mentalmodel.

4. State the functions of maps as a specialised representation.

5. What do you understand by the term scaffolding?

6. Identify the advantages and disadvantages of planning inproblem solving.


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Problem-solving strategies can be defined as procedures that overcomeobstacles and achieve goals.

Most of the studies involving collaborative problem solving have notfurnished children with feedback on the correct answers.

The progress in problem solving among children after the first year arisesfrom the improved ability to internally represent goals, actions, objects andevents.

The ability to solve problems improves as children become able to express

themselves using language in various circumstances and events.

Besides internal representations, toddlers also exhibit increasing ability toexternal representations as tools for solving problems.

Mental model refers to the representation of a body of knowledge in long-term memory, which may have the same sort of structure as the models usedin reasoning.

Unlike the language, mental imagery and spatial representations that are

acquired in the first two years of the childrens life, specialisedrepresentations are acquired much later in life.

Maps are one important specialised and often used representation.

The main difference between school and real-world problems is thefrequent difficulty in school in identifying what exactly the problem is.

The ability of children in effectively regulating their thinking activitiesbecome increasingly central to their problem solving as they attain both

increasing numbers of strategies and representational capacities.

Language plays an important role in regulating thinking, communicatingwith others and directing the childs own problem solving.

In solving their problems, children use conscious, explicit and metacognitiveknowledge about the problem as well as available strategies and their owncognitive capacities.


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Effective planning requires the ability to formulate actions in advance, as wellas skill at monitoring and modifying plans; as circumstances and goalsrequire.

Regulation of cognitive activities is often accomplished through interactionamong people working together rather than through the efforts of a singleindividual.

Skilled problem solvers usually practise self-monitoring activities includingquestioning and elaborating on their own knowledge; evaluating their degreeof understanding; and thinking of counterexamples and possiblegeneralisations.

Feedback

Goal sketch hypothesis

Maps

Mental models

Planning

Problem solving

Reciprocal teaching

Representational development

Scaffolding

Self-directed speech

Self-monitoring

Strategic development

1. State the three aspects of problem-solving development and thecorresponding significant stages in life.

2. Problem-solving strategies exist since birth. Explain this statement usingthe Rovee-Collier experiment. In your explanation, illustrate what is meant

by representational skills.3. The Tower of Hanoi design using a single peg and three pegs is used to

create toys for children of different age groups. Discuss the respective skilldevelopment and the suitable age group for both toys.


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