Cognition and Instruction/Problem Solving, Critical Thinking and Expertise

Introduction

We are constantly surrounded by ambiguities, challenges or situations in our daily lives that require our problem solving skills, critical thinking and expertise, our chapter seeks to provide an overview of these three topics. We will discuss the qualities of each topic, their relation to each other, the experience for the learner, applications to the classroom and potential issues that arise when engaging in cognition. Since, critical thinking and expertise enable us to draw upon efficient techniques to come up with effective solutions in problem solving, we will discuss their relationship to one another at the end of the problem solving chapter.

Problem Solving

In everyday life we are surrounded by a plethora of problems that require solutions and our attention to resolve them to reach our goals . We may be confronted with problems such as: needing to determine the best route to get to work, what to wear for an interview, how to do well on an argumentative essay or needing to find the solution to a quadratic equation. A problem is present in situations where there is a desire to solve the problem, however the solution is not obvious to the solver. Problem solving is the process of finding the solutions to these problems. . This chapter on problem solving will first differentiate between well-defined and ill-defined problems, then explain uses of conceptualizing and visually representing problems within the context of problem solving and finally we will discuss how mental set may impede successful problem solving.

Well-defined and Ill-defined Problems

Problems can be categorized into two types: ill-defined or well-defined . A well-defined problem has specific goals, defined steps to find the solution, one guaranteed correct solution, and a guaranteed method of finding that particular solution. A well-defined problem can be solved through applying the appropriate algorithm to the problem at hand. An example of a well-defined problem is an algebraic problem (ex: 2x - 29 = 7) where one must find the value of x. Another example may be converting the weight of the turkey from kilograms to pounds. In both instances these represent well-defined problems as there is one correct solution and a clearly defined way of finding that solution.

In contrast, ill-defined problems represent those we may face in our daily lives, the goals are unclear and they have information that is conflicting, incomplete or inconclusive . An example of an ill-defined problem may be “how do we solve climate change?” or “how should we resolve poverty” as there is no one right answer to these problems. These problems yield the possibility to many different solutions as there isn’t a universally agreed upon strategy for solving them. People approach these problems differently depending on their assumptions, application of theory or values that they use to inform their approach. Furthermore, each solution to a problem has its own unique strengths and weaknesses..

Ill-Defined	Well-Defined
Given state is not clearly specified , unclear goal state, unclear set of allowable procedures and multiple solutions .	Given state is clearly specified, there are clearly specified goals, clearly specified set of allowable procedures and one clear solution.
For example: How should we resolve global warming?	For example: 5x=10
Argumentation, attitudes and "metacognition highly predicted problem-solving score	Domain knowledge and justification skills highly predicted problem-solving scores.

Table 1. Summarizes the difference between well-defined and ill-defined problems.

Differences in Solving Ill-defined and Well-defined Problems

In earlier times, researchers assumed both types of problems were solved in similar ways , more contemporary research highlights some distinct differences between processes behind finding a solution.

Kitchener (1983) proposed that well-defined problems did not involve assumptions regarding epistemological beliefs because they have a clear and definite solution, while ill-defined problems require these beliefs due to not having a clear and particular solution. In support of this idea, Schraw, Dunkle and Bendixen conducted an experiment with 200 participants, where they found that performance in well-defined problems is not predictive of one's performance on ill-defined problems, as ill-defined problems activated different beliefs about knowledge.

Furthermore Shin, Jonassen and McGee (2003), found that solving ill-defined problems brought forth different skills than those found in well-structured problems. In well-structured problems domain knowledge and justification skills highly predicted problem-solving scores, whereas scores on ill-structured tasks were predictive of argumentation, attitudes and metacognition in an astronomy simulation.

Aligned with these findings, Cho and Jonassen (2002) found that groups solving ill-structured problems produced more argumentation and problem solving strategies due to the importance of considering a wide variety of solutions and perspectives. In contrast, the same argumentation technique distracted the participant's activities when they dealt with well-defined problems. This research highlights the potential differences in the processes behind solving ill-defined and well-defined problems.

Implications Of The Classroom Environment

The fundamental differences between well-structured and ill-structured problems implicate that solving ill-structured problems calls for different skills, strategies, and approaches than well-structured problems. Meanwhile, most tasks in the educational setting are designed around engaging learners in solving well-structured problems that are found at the end of textbook chapters or on standardized tests.. Unfortunately the strategies used for well-defined problems have little application to ill-defined problems that are likely to be encountered day to day as simplified problem solving strategies used for the well-structured designs have been found to have almost no similarities to real-life problems

This demonstrates the need to restructure classrooms in a way that facilitates the student problem solving of ill-structured problems. One way we may facilitate this is through asking students questions that exemplify the problems found in everyday life. This type of approach is called problem-based learning, in this type of classroom structure students are given the opportunity to address questions by collecting and compiling evidence, data and information from a plethora of sources. In doing so students learn to analyze the information,data and information, while taking into consideration the vast interpretations and perspectives in order to present and explain their findings.

Structure Of The Classroom

In problem-based learning, students work in small groups to where they explore meaningful problems, identify the information needed to solve the given problem, and devise effective approaches for the solution . Students utilize these strategies, analyze and consider their results to devise new strategies until they have come up with an effective solution. The teacher’s role in this classroom structure is to guide the process, facilitate participation and pose questions to elicit reflections and critical thinking about their findings. In addition teachers may also provide traditional lectures and explanations that are intended to support student inquiry.

In support of the argument to implement a problem-based approach to problem solving, a meta-analysis conducted by Dochy, Segers, Van den Bossche, & Gijbels (2003), found problem-based learning to be superior to traditional styles of learning though in supporting flexible problem solving, application of knowledge, and hypothesis generation. Furthermore, Williams, Hemstreet, Liu, and Smith (1998) found that this approach fostered greater gains in conceptual understanding in science. Lastly Gallagher, Stepien, & Rosenthal (1992), found that in comparing traditional vs. project-based approaches students in problem-based learning demonstrate an ability to define problems. These findings highlight the benefits of problem-based learning on understanding and defining problems in science. Given the positive effects of defining problems this education approach may also be applied to our next sub-topic of conceptualizing problems.

Steps to Problem Solving

There have been five stages consistently found within the literature of problem solving: (1) identifying the problem, (2) representing the problem, (3) choosing the appropriate strategy, (4) implementing the strategy, and (5) assessing the solutions. This overview will focus on the first two stages of problem solving and examine how they influence problem solving.

Conceptualizing Problems

One of the most tedious and taxing aspects of problem solving is identifying the problem as it requires one to consider the problem through multiple lenses and perspectives without being attached to one particular solution to early on in the task. In addition it is also important to spend time clearly identifying the problem due to the association between time spent "conceptualizing a particular problem and the quality of one's solutions".

For example consider the following problem:

Becka baked a chocolate cake in her oven for twenty five minutes. How long would it take her to bake three chocolate cakes?

Most people would jump to the conclusion to multiply twenty five by three, however if we place all three cakes in the oven at a time we find it would take the same time to bake three cakes as it would take to bake one. This example highlights the need to properly conceptualize the problem and look at it from different viewpoints, before rushing to solutions.

Research also supports the importance of taking one's time to clearly identifying the problem before proceeding to other stages. In support of this argument, Getzel and Csikszentmihalyi found that artist students that spend more time identifying the problem when producing their art were rated as having more creative and original pieces than artists who spent less time at this stage. These researchers postulated that in considering a wider scope of options during this initial stage they were able to come up with more original and dynamic solutions.

Furthermore, when comparing the approaches of experienced teachers and novice post-secondary students studying to be teachers, it was found that experienced teachers spent a greater amount of time lesson planning in comparison to post-secondary students when in a placed in a hypothetical classroom. In addition these teachers offered significantly more solutions to problems posed in both ill-defined and well-defined problems. Therefore it is implicated that successful problem solving is associated with the time spent finding the correct problem and the consideration of multiple solutions.

Instructional Implications

One instructional implication we may draw from the literature that supports that the direct relationship between time spent on conceptualizing a problem and the quality of the solution, is that teachers should encourage students to spend as much time as possible at this stage. In providing this knowledge and by monitoring student’s problem solving processes to ensure that they “linger” when conceptualizing problems, we may facilitate effective problem solving.

Representing the Problem

Problem representation refers to how the known information about a particular problem is organized. There are two ways to represent a problem: abstract or tangible. In abstract representation of a problem, we merely think or speak about the problem without externally visually representing. In representing a problem tangibly this is done by creating a visual representation on paper, computer, etc. of the data though graphs, stories, symbols, pictures or equations. These visual representations may be helpful they can help us keep track of solutions and steps to a problem, which can particularly be useful when encountering complex problems.

Buddhist monk

For example if we look at Dunker's Buddhist Monk example:

In the morning a Buddhist monk walks outside at sunrise to climb up the mountain to get to the temple at the peak. He reaches the temple just prior to sunset. A couple days later, he departs from the temple at sunrise to climb back down the mountain, travelling quicker than he did during his ascent as he is going down the mountain. Can you show a location along the path that the monk would have passed on both at the exact time of the day?

In solely using abstraction, this problem is seemingly impossible to solve due to the vast amount of information, how it is verbally presented and the amount of irrelevant information present in the question. In using a visual representation we are able to create a mental image of where the two points would intersect and are better able to come up with a solution .

Kaninchen und Ente

Research supports the benefits of visual representation when confronted with difficult problems. Martin and Schwartz found greater usage of external representations when confronted with a difficult task and they had intermittent access to resources, which suggests that these representations are used as a tool when problems are too complex without external aids. Results found that while creating the initial visual representation itself took up time, those who created these visual representations solved tasks with greater efficiency and accuracy.

Another benefit is that these visual representations may foster problem solving abilities by enabling us to overcome our cognitive biases. In a study conducted by Chambers and Reisberg, participants were asked to look at the image below then close their eyes and form a mental image. When asked to recall their mental image of the photo and see if there were any alternate possibilities of what the photo could be, none of the participants were able to do so. However when participants were given the visual representation of the photo they were quickly able to manipulate the position of the photo to come up with an alternate explanation of what the photo could be. This shows how visual representations may be used in education by learners to counteract mental sets, which will be discussed in the next section.

Instructional Implications

As shown above, relying on abstraction can often overload one’s cognitive resources due to short- term memory being limited to seven items of information at a time. Many problems surpass these limits disabling us being able to hold all the relevant information needed to solve a problem in our working memory. Therefore it is implicated that in posing problems teachers should represent them written or visually in order to reduce the cognitive load. Lastly another implication is that as teachers we may increase problem-solving skills through demonstrating to students different types of external representations that can be used to show the relevant information pertaining to the problem. These representations may include different types of graphs, charts and imagery, which all can serve as tools for students in coming up with an effective solution, representing relevant information and reducing cognitive load

Challenges of Problem Solving

As discussed above there are many techniques to facilitate the problem solving process, however there are factors that can also hinder this process. For example: one’s past experiences can often impede problem solving as they can provide a barrier in looking at novel solutions, approaches or ideas.

Mind set

A mind set refers to one's tendency to be influenced by one's past experiences in approaching tasks. Mental set refers to confining ourselves to using solutions that have worked in the past rather than seeking out alternative approaches. Mental sets can be functional in certain situation as in using strategies that have worked before we are quickly able to come up with solutions. However, they can also eliminate other potential and more effective solutions.

Functional Fixedness

Functional fixedness is a type of mental set that refers to our tendency to focus on a specific function of an object (ie. what we traditionally use it for) while overlooking other potential novel functions of that object.

The Candle Problem

A classic example of functional fixedness is the candle problem . Consider you are at a table with a box full of tacks, one candle, and matches, you are then asked to mount the lit candle on the wall corkscrew board wall as quickly as possible, and make sure that this doesn't cause any wax to melt on the table. Due to functional fixedness you might first be inclined to pin the candle to the wall as that is what tacks are typically used for, similar to participants in this experiment. However, this is the incorrect solution as it would cause the wax to melt on the table.

The most effective solution requires you to view the box containing the tacks as a platform for the candle rather than its traditional use as a receptacle. In emptying the box, we may use it as a platform for the candle and then use the tacks inside to attach the box to the wall. It is difficult to initially arrive at this solution as we tend to fixate on the function of the box of holding the tacks and have difficulty designating an alternate function to the box (ie. as a platform as opposed to a receptacle). This experiment demonstrates how prior knowledge can lead to fixation and can hinder problem solving.

Techniques to Overcome Functional Fixedness

As proposed by McCaffrey (2012), one way to overcome functional fixedness is to break the object into parts. In doing so we may ask two fundamental questions “can it be broken down further” and “does my description of the part imply a use”. To explain this we can use McCaffrey’s steel ring figure-8 example. In this scenario the subject is given two steel rings, a candle and a match, they are asked to make the two steel rings into a figure 8. Looking at the tools provided to the subject they might decide that the wax from the candle could potentially hold the two pieces of steel together when heated up. However the wax would not be strong enough. It leaves them with a problem, how do they attach the two steel rings to make them a figure eight.

In being left with the wick as a tool, and labelling it as such we become fixated on seeing the primary function of the wick as giving off light, which hinders our ability to come up with a solution for creating a figure-8. In order to effectively solve problem we must break down our concept of the wick down further. In seeing a wick as just a waxed piece of string, we are able to get past functional fixedness and see the alternate functions of the string. In doing so we may come to the conclusion and see the waxed string as being able to be used to tie the two rings together. In showing the effectiveness of this approach McCaffrey (2012) found that people trained to use this technique solved 67% more problems than the control group.

Instructional Implications

Given the effectiveness of this approach, it is implicated that one way we may promote divergent thinking is through teaching students to consider: "whether the object may be broken down further" and "whether the description of the part imply a use" in doing so we may teach students to break down objects to their purest form and make salient the obscure features of a problem. This connects to the previously discussed idea of conceptualization where problem solving effectiveness can be increased through focusing time on defining the problem rather than jumping to conclusions based on our own preconceptions. In the following section we will discuss what strategies experts use when solving problems.

Novice Versus Expert In Problem Solving

Many researchers view effective problem solving as being dependent on two important variables: the amount of experience we have in trying to solve a particular category of problems, which we addressed earlier by demonstrating that in practicing problem solving through engaging in a problem-based approach we may increase problem solving skills. However, the second factor to consider is the amount of domain-specific knowledge that we have to draw upon. Experts possess a vast amount of domain knowledge, which allows them to efficiently apply their knowledge to relevant problems. Experts have a well-organized knowledge of their domain, which impacts they notice and how they arrange, represent and interpret information, this in turn enables them to better recall, reason and solve problems in comparison to novices.

In comparing experts to novices in their problem strategies, experts are able to organize their knowledge around the deep structure in important ideas or concepts in their domain, such as what kind of solution strategy is required to solve the problem. In contrast novices group problems based on surface structure of the problems, such as the objects that appear in the problem.

Experts also spend more time than novices analyzing and identifying problems at the beginning of the problem-solving process. Experts take more time in thinking and planning before implementing solutions and use a limited set of strategies that are optimal in allowing them to richer and more effective solutions to the given problem.

In addition experts will engage in deeper and more complete problem representation novices, in using external representations such as sketches and diagrams to represent information and solve problems. In doing so they are able to solve problems quicker and come up with better solutions.

Given the literature above it is evident that problem solving and expertise overlap as the key strategies that experts utilize are also provided as effective problem solving strategies. Therefore, we may conclude that experts not only have a vast knowledge of their domain, they also know and implement the most effective strategies in order to solve problem more efficiently and effectively in comparison to novices. In the next section we will discuss the connection between problem solving and critical thinking.

Critical Thinking

Critical thinking is an extremely valuable aspect of education. Although they are related, critical thinking differs fundamentally from problem solving. Critical thought is actually a process that can be applied to problem solving. For example, students may find themselves engaging in critical thought when they encounter ill-defined problems that require them to consider many options or possible answers. In essence, those who are able to think critically are able to solve problems effectively . The ability to think critically often increases over the lifespan as knowledge and experience is acquired, but it is crucial to begin the process of this development as early on as possible. Research has indicated that critical thinking skills are correlated with better transfer of knowledge, and a lack of critical thinking skills has been associated with biased reasoning . Before they even begin formal schooling, children are developing critical thinking skills at home thanks to interactions with parents and caregivers . As well, critical thinking appears to improve with explicit instruction . Being able to engage in critical thought is what allows us to make informed decisions in situations like elections, where candidates are presenting skewed views of themselves and the other candidates. Without critical thinking, people would fall prey to fallacious information and biased reasoning. It is therefore incredibly important that students are introduced to critical thought and encouraged to utilize critical thinking skills as they are faced with problems.

Defining Critical Thinking

In general, critical thinking can be defined as the process of evaluating arguments and evidence to reach a conclusion that is the most appropriate and valid among other possible conclusions. Critical thinking is a dynamic and reflective process, and it is primarily evidence-based . Thinking critically involves being able to criticize information objectively and explore opposing views, eventually leading to a conclusion based on evidence and careful thought. Critically thinking students are skeptical of information given to them, actively seek out evidence, and are not hesitant to take on decision-making and complex problem solving tasks . Asking questions, debating topics, and critiquing the credibility of sources are all activities that involve thinking critically. As outlined by Glaser (1941), critical thinking involves three main components: a disposition for critical thought, knowledge of critical thinking strategies, and some ability to apply the strategies . Having a disposition for critical thought is necessary for applying known strategies.

Critical Thinking Disposition

It has been suggested that critical thinking skills alone are not sufficient for the application of critical thinking – a disposition for critical thinking is also necessary . A disposition for critical thought differs from cognitive skills. A disposition is better explained as the ability to consciously choose a skill, rather than just the ability to execute the skill . Having a disposition for critical thinking can involve things like genuine interest and ability in intellectual activities. Perkins et al. (2000) expanded on the idea of the necessity for a critical thinking disposition and indicated three aspects involved in a disposition for critical thinking . It was suggested that this disposition included an inclination for engaging in intellectual behaviours, a sensitivity to opportunities where such behaviours may be engaged, and a general ability for engaging in critical thought . Halpern (1998) suggested that this critical thinking disposition must include factors like a willingness to continue with tasks that seem difficult, an openmindedness, and a habit of planning . In fact, in a study done by Clifford et al. (2004) when cognitive skills were controlled for, they found that a disposition for critical thinking was associated with better overall critical thinking skills .

Critical Thinking Strategies

The application of critical thinking strategies is closely related to the presence of a disposition for critical thinking. Part of a disposition includes having an ability for critical thinking . Without a disposition for critical thinking, the application of appropriate strategies may not be possible. Psychologists and educators have discovered many different strategies for the development of critical thinking. Among these strategies are some that may be very familiar, such as concept maps or Venn diagrams, as well as some that may be less familiar, such as appeal-question stimuli strategies . Concept mapping is particularly useful for illustrating the relationships between ideas and concepts, while Venn diagrams are often used to represent contrasting ideas .

Concept map

Venn diagrams are used frequently in elementary grade levels and continue to be used as a contrast/compare tool throughout secondary school. An example of a situation in which a Venn diagram activity may be appropriate is during a science class. Instructors may direct students to develop a Venn diagram comparing and contrasting different plants or animals. Concept maps may be introduced in elementary grades, although they are most often used in the secondary and post-secondary levels. Concept maps are an interactive and versatile way to encourage students to engage with the course material. A key aspect of concept mapping is how it requires students to reflect on previously learned information and make connections. In elementary grades, concept maps can be introduced as a project, while later, possibly in college or university, students may use them as a study strategy. At the elementary level, students can use concept maps to make connections about the characters, settings, or plot in a story they have read. When introducing concept maps, teachers may provide students with a list of words or phrases and instruct the students to illustrate the connections between them in the form of a concept map. Asking questions can also be a simple and engaging way to develop critical thought. Teachers may begin by asking the students questions about the material, and then encouraging students to come up with their own questions. In secondary and post-secondary education, students may use questions as a way to assess the credibility of a source. At the elementary school level, questions can be used to assess students' understanding of the material, while also encouraging them to engage in critical thought by questioning the actions of characters in a story or the validity of an experiment. Appeal-question stimuli, founded by Svobodová, involves a process of students asking questions regarding their reading comprehension .

It is important to remember that there are many different factors that can either encourage or inhibit the application of critical thinking strategies. Students may be discouraged from using critical thinking strategies when parents or teachers react negatively to the students' questions or comments . Baumrind (1966) indicated that authoritarian parenting styles can also discourage children from engaging in critical thinking . The appropriate application of these strategies relies on reflection and revision of strategies - also known as metacognition. It is crucial for students to receive consistent feedback in order for them to review the strategies they have used and consider potentially better or more appropriate strategies.

Attributes	Critical Thinking Skills	Disposition
• Qualities about an individual that lend well to critical thinking • Values, beliefs, attitudes, culture	• Cognitive tools used to analyze a problem or situation • Ability to draw inferences, weigh evidence, reasoning	• Arguably the most important factor in critical thinking skills • The likelihood an individual will use critical thinking in a given situation

Table 2. Factors that interact with the use of critical thinking skills

Instructional Implications

Critical thinking skills may be taught directly or indirectly. Teachers may introduce critical thinking as a separate unit from other school subjects, or incorporate critical thinking skills into assignments and discussions within the students’ regularly scheduled subjects. In the classroom, critical thinking can be taught by both instruction and discussion. Direct instruction and inquiry-based instruction are two methods of instruction. Inquiry-based instruction is a form of minimally guided learning that allows students to construct their own understanding of the materials . Inquiry-based instruction is reliant heavily on the constructivist belief that learning is a continuous process and that involves the construction and reconstruction of knowledge . Direct instruction, on the other hand, is a guided learning approach that directly teaches cognitive skills and involves knowledge being explicitly passed from teacher to student . There are also general and infusion approaches to instruction. With a general approach, cognitive skills are taught separately from specific subjects, while infusion approach mixes cognitive skills into other subjects . Research by has indicated that students who receive direct instruction tend to show more improvements in their use of critical thinking . In order for instruction to be effective in teaching critical thinking skills, it must help foster personal dispositions in critical thinking .

Discussions

Using discussions as a way to develop students’ critical thinking skills can be a particularly valuable strategy for teachers. Peer interactions provide a basis for developing particular critical thinking skills, such as perspective taking and cooperation, which may not be as easily taught through instruction. A large part of discussions, of course, is language. Klooster (2002) suggested that critical thinking begins with asking questions . Similarly, Vygotsky has claimed that language skills can be a crucial precursor for higher level thought processes . As children develop larger vocabularies, they are better able to understand reading material and can then begin to think abstractly about the material and engage in thoughtful discussions with peers about what they understood .

Studies have indicated that cross-age peer discussions may be particularly helpful in facilitating the development of critical thinking. Cross-age peer groups can be effective because of the motivation children tend to have when working with peers of different ages . Younger children often look up to the older children as mentors and valuable sources of knowledge and experience, while older children feel a sense of maturity and a responsibility to share their knowledge and experience with younger students . These cross-age peer discussions also provide students with the challenge of tailoring their use of language to the other group members in order to make their points understandable . An example of cross-age peer groups that is relatively common in Canadian schools is the big buddy programs, where intermediate grade students are assigned a primary grade buddy to help over the course of the school year. Big buddies may help their little buddies with projects, advice, or school events. The big buddy/little buddy programs can be effective as younger students look up to their big buddies, and the big buddies feel a responsibility to help their little buddy. One important factor to be considered with cross-age peer discussions, as noted by Hattie (2006), is that these discussions should be highly structured activities facilitated by a teacher in order to ensure that students understand their group responsibilities .

The Classroom Environment

Having an environment that is a safe place for students to ask questions and share ideas is extremely valuable for creating a classroom that encourages critical thinking. It has been suggested that students are more likely to develop a disposition for critical thinking when they are able to participate in the organization and planning of their classroom and class activities . In these classrooms, students are legitimately encouraged by their teacher to engage in the decision making process regarding the functioning of the classroom . It is also important for teachers to model the desired types of critical thought, by questioning themselves and other authorities in a respectful and appropriate manner . Studies have indicated higher levels of cognitive engagement among students in classrooms with teachers who are enthusiastic and responsive . Therefore, teachers should be encouraging and inclusive, and allow student engagement in classroom planning processes when possible.

Expertise

Expertise will be defined here as, deliberate and effortful practice that has resulted in a consistent and superior performance by an individual in the context of a specific domain . There is a general consensus that expertise cannot be attributed solely to innate ability, rather it is an acquisition of skill and knowledge over time through deliberate practice Given that it is not necessary to have been born with the gift of expertise, it would follow, that any individual could potentially become an expert in a chosen domain. However it is a slightly more complex interaction of factors that determine which individuals achieve expertise such as; environment, genetics, practice and constraints This section will briefly explain the process of becoming an expert and why not everyone becomes one.

Attributes of an Expert

What does it look like to be an expert and does once an expert mean always an expert? We will now discuss some common attributes that research has identified amongst experts and specific contexts in which expertise exists. These attributes listed in Table 3 reflect cognitive and behavioural tendencies that are common to experts. The cognitive advantages that experts have above novices are largely related to their specific experience and the accessibility of prior knowledge . It seems that experts have acquired automated thought, which is allows for more speedy access to knowledge related to solving problems as hand. This means that is does not require as much conscious thought to process problems similar to previously encountered ones. Experts are also superior to novices in 'creating a plan of action' because of the way in which knowledge is organized within their memory, that is easily accessed when needed. While it would seem that experts are simply more intelligent than novices in general, it is vital to remember that expert ability is constrained to a specific domain or domain specific knowledge therefore an expert in calculus will not display the same elevated performance when playing the trumpet. An expert that learns a new skill, within a new domain will begin at a novice level. Domain specific knowledge can be contrasted with general knowledge, which is best described as broad knowledge that may be useful in a variety of tasks .

Attributes of an expert
• Ability to process larger amounts of information • Faster and more efficient strategies than novices • Able to ‘hold more information in short-term and long-term memory’ • Better metacognition strategies • ‘Spend more time analyzing a problem’ and problem representation 'at a deeper level’

'Table 3. Attributes of an Expert'

Becoming an Expert

Environmental Influence

A valid question arises around the role of genetics and young children that have achieved expertise in a specific domain such as musical abilities. Was the child born with an innate ability to become an expert in a specific domain? Current research deems expertise to be an acquired skill rather than an inherited ability and the role of social surroundings is that it must support the achievement of expertise . This is best explained as a process that begins with an interest in a specific area. It is important to keep in mind that parents often offer many options to their child and the child may choose one or even several as favourites. For example, a child may try several sports, activities such as dance and gymnastics or even more than one musical instrument but may choose one as their favourite. The child may demonstrate a slight natural ability, which is the innate component, however, the ability will then need to be nurtured by parents and eventually the individual may become an expert within the specific domain. Upon recognizing an interest or ability parents then shape the growth by increasing the availability of the activity . If the child appears enjoy and perform well in gymnastic activity, it is likely that more time will be invested in gymnastic classes in comparison to a sport that the child did not prefer or excel in. Researchers have agreed that to become an expert typically takes 10 years of deliberate practice, a topic that will be discussed in further detail next . Therefore it is a fledgling ability, interest and an intentional commitment to 10 years of an environment that encourages growth in a specific domain to achieve expertise.

Deliberate Practice

When it comes to becoming an expert, practice in itself does not always make ‘perfect’. Simple repetition of a task is inadequate and will be differentiated from deliberate practice, which is both effortful and intentional . We will define deliberate practice as repeated and consistent practice of a specific ability or skill with both feedback and the intent to achieve expertise . It is not a matter of quantity or quality, deliberate practice must contain both elements in addition to ‘immediate, informative feedback’. Without clear constructive feedback to propel improvements, a novice is unable to progress at full potential. Studies have found that over time, consistent deliberate practice surpasses any initial talent . In other words an individual without an innate musical ability but devotes time to deliberate practice of the skill, will surpass the individual who has a natural ear for rhythm but practices inconsistently or without feedback for improvement. Another key component of deliberate practice is accommodation to the pre-existing knowledge base. What this means is that time is not spent redundantly re-teaching skills that have already been mastered, rather the individuals knowledge base is accommodated for by instruction that builds upon pre-existing skills. In addition to constructive feedback, praise and encouragement from teachers or parents help reinforce the importance of deliberate practice. This type of reinforcement is especially important as the learner progresses past the initial phases of interest and ‘playful engagement’ in an activity . As previously discussed, often times an expert begins their journey to mastery with an interest or inclination to participate in a specific activity. For example a young child may enjoy kicking a soccer ball and may even posses higher skill levels than those of their same aged peers and will likely practice playing with the soccer ball often. However to become an expert or professional soccer player, that child must engage in years of deliberate practice. It is during the transition from playing simply for enjoyment to deliberate practice that Bruning et al. emphasises the importance of motivation. The commitment to consistent deliberate practice is so vital that it can become a roadblock or constraint to an individual successfully becoming an expert .

Challenges of Expertise

Constraints

Ericsson, Krame and Tesch-Römer (1993), describes three major constraints that may interfere in the process of deliberate practice. These constraints are a matter of, motivation, resources and effort. As previously mentioned motivation becomes a factor because deliberate practice is not always enjoyable but this challenge must be overcome by the individual’s desire to improve in skill. This constraint could prove to be particularly difficult for young children, leaving it in the hands of parents or teachers to find ways to make the mundane interesting. Parents may wish to participate in practice with their child at this level if possible, providing praise for accomplishment. For example, while a parent may not be able to play the instrument their child is learning, they are able to express interest in hearing the child play the instrument. Alternatively, parents may wish to reward time spent practicing with activities that are more desirable to their child. The resource constraint presents a factor that is often times not controllable. Resources come in the form of finances, teachers or instructors, and time . In order for a novice to progress to the level of expertise they will need the guidance of master mentor . Typically at this level parents are no longer able to guide their child, unless they themselves are an expert in the specific domain, and therefore require the paid services of a tutor or teacher. If a family is unable to carry the financial burden of further instruction, this may become a constraint for the individual progressing to mastery levels of achievement because as we have already learned, deliberate practice involving relevant feedback is necessary to progress . Finally, the effort constraint includes both physical and mental limitations and interacts with the efficiency of deliberate practice. Ericsson et al., (1993) suggests that sessions should be limited to less that an hour to ensure efficient learning , while Bruning et al. (2011) suggests that practice sessions are still efficient for up to three hours, but two hours is optimal.

Obstacles

Bruning et al.,(2011) insightfully highlight three potential obstacles experts should have an awareness of; the cost of becoming an expert, a blindness to alternatives and the expert blind spot . Obstacles differ from constraints in that the latter influence an individual's access to becoming an expert, whereas the former interferes with functioning outside of the domain of expertise. These differences can be observed in Table 3.1 As mentioned previously, to achieve expertise, an individual must devote large quantities of time and resources to a process. The accumulation of cost takes resources and time from other potential domains of focus , such as education, relationships and any other areas of interest. The second obstacle concerns a tendency to only see what the expert wants to see, potentially resulting in incorrect conclusions and blindness to alternative methods . This also has the potential to impair critical thought in that an inability to see alternative solutions is counter the open-mindedness involved in critical thought . Finally, the expert blind spot refers to the tendency of experts to be unable to see problem solving the way a novice will see it . However this obstacle does come with a caveat, that is it is possible that experts may not actually be ‘blind’ to the beginner methods of problem solving, rather they themselves are simply just more efficient. To counter these obstacles it would seem that an awareness is most important, followed by steps to counter them. This awareness becomes particularly important in the context of the classroom where teachers are the experts and students are the novice learners.

Constraints	Obstacles
• Interfere with achieving expertise	• Interfere with functioning outside of expertise
• Motivation, resources, effort	• Costs, inability to alternative views, expert blind spot

Table 3.1 Constraints vs. Obstacles

Instructional Implications

There is evidence that learning decreases when the task is associated with high stakes. In the classroom receiving a poor grade on an assignment creates stress for many students. This highlights the importance of deliberate practice before an exam or task to allow for optimal learning. While the ultimate goal of education is likely not to create ‘experts’ in the literal sense as defined, it is the responsibility of educators to provide opportunity for learners to reach their fullest potential. This can be done by providing novel ways to practice skills, allowing for breaks and giving immediate feedback. Not surprisingly research has found an advantage in using one-to-one teacher-student instruction, but this falls under the category of resource constraint and is not possible in most schools. However, with this is mind, educators must be diligent in their efforts to give individualized feedback. Educators may also want to keep in mind the obstacle of the expert blind spot when introducing and providing support for problem solving activities. The ease in which educators are able to find solutions reflects their own experience and efforts should be made to understand the perspective of the inexperienced learner.

Concluding Thoughts

Problem solving, critical thought and expertise are part of everyday life, both in and outside of the classroom. Each of these topics are complex and must be broken down into the subcomponents that make the whole. There are a variety of types of problems, which require a different approach to successfully solve each type. Expertise is a process that current research has found to be a dynamic interaction between genetics and environmental factors including deliberate practice. The cognitive skills that are involved in problem solving, critical thought and potentially expertise can be improved with practice. Expertise pertains to a specific domain or area of knowledge that an individual has dedicated time and effort to learning and mastering. While becoming an expert comes with many advantages, it is vital to remain aware of the pitfalls that can prevent individuals from seeing the 'bigger picture' or having an open mind, a key component to critical thought. Furthermore, it is not enough to simply possess the skills for critical thought, rather individuals must know how and when to use the skills. It is especially important for educators of any capacity to become informed of different pathways to solve problems and encourage critical thought to satisfy the variety of learners and situations they will encounter in the classroom.

Glossary

• Automated Thought: Thought processes not requiring conscious thought, automatic thought
• Algorithm: A procedure that can be applied to a particular problem that if executed properly, guarantees the correct answer.
• Deliberate Practice: Effortful, consistent practice of a skill with the intention of achieving expertise, involves constructive feedback from an expert in the area of practice.
• Direct Instruction: A guided learning approach that directly teaches cognitive skills and involves knowledge being explicitly passed from teacher to student.
• Disposition [for critical thinking]: The ability to consciously choose a skill, including an inclination for engaging in intellectual behaviours, a sensitivity to opportunities where such behaviours may be engaged, and a general ability for engaging in critical thought.
• Divergent Thinking: Thinking characterized by the generation and testing of multiple and diverse solutions .
• Domain Specific Knowledge: Knowledge in a specific area or field.
• Epistemological Beliefs: Belief regarding the nature and acquiring of knowledge.
• Expert Blind Spot: The tendency for experts to be unable to understand a problem the way a novice would.
• Functional Fixedness: A bias that restricts a person to using an object only in the way it is typically used in everyday life.
• General Knowledge: Broad knowledge or information that is not related in depth to a specific area or domain.
• Ill-defined Problems: Problems that do not have a clear goal, solution path, or an expected answer.
• Inquiry-based Instruction: A form of minimally guided learning that allows students to construct their own understanding of the materials.
• Metacognition: Knowledge people have about their own thoughts.
• Problem-based learning (PBL): A student-centered approach in which students learn about a particular subject through the experience of solving an open-ended problem or question.

• Problem Representation: Allows problem solvers better visualize the problem at hand and thus aids them in arriving at a solution.

• Problem Solving: Cognitive processing' used to accomplish a goal when no solution is apparent to the solver.

• Well-defined Problems: Problems that do not have a clear goal, solution path, or an expected answer.