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Problem Based Learning in Mathematics what a concept.


This research paper of mine explains how Problem Based Learning can be used as a teaching strategy. Problem Based Learning is a curriculum and instructional approach that develops problem-solving strategies, knowledge bases, and skills by placing students in situations where they are confronted by ill-structured problems which mirror the real world.  This became my favorite teaching strategy due to my extensive industry experiences.  Having worked for many industry leaders and scientist I believe this is an excellent method to educate the younger generation in order to be industry leaders.

 Starting from grade one to college level and even after college, the successes, and failures I had in learning different subjects. Also observing many of co-workers learning abilities and their strength in applying that to the real world (industry), their creative vision in writing new patterns gave me a special interest in PBL.  As a big believer in multiple intelligence theory and in the concept of all kids are created equal but they have to taught differently to succeed, fitted very well with the Problem Based Learning.  Now I firmly believe that this statergy could be used not only in education but also in sports like Basketball and Baseball.

















How it works as a teaching strategy


“How can I get my students to think?” is a question asked by many faculty, regardless of their disciplines. Problem Based  Learning (PBL) is an instructional method that challenges students to “Learn to Learn,” working cooperatively in groups to seek solutions to real word problems.  These problems are used to engage students’ curiosity and initiate learning the subject matter. PBL prepares to students to think critically and analytically, and to find and use appropriate learning resources.(

                                                                   Barbara Dutch


I hear…….and I forget

I see …….and I remember

I do …….and I understand

                                                                             CHINESE SAYING

(Calculus and Analytical Geometry MIZRAHI AND SULLIVAN, Preface to the student) 


Current cognitive theories claim that learning occurs not only by absorbing information but interpreting it. Effective learning depends on the internal processes of the learner who must construct his or her own knowledge. Constructivism proposes that meaning is constructed by individuals through their experiences in particular contexts. The contexts for learning and the activities of the learner affect how something is understood, and therefore what is learned. Through the context of Problem Based Learning it

creates, as well as the activities in which learners in such an environment participate. Problem Based Learning impacts learners’ construction of knowledge.(



What is Problem Based Learning?
Problem based Learning (PBL) is a style of learning in which the problems act as the context and driving force for learning . All learning of new knowledge is done within the context of the problems. PBL differs from problem solving in that in  PBL  the problems are encountered before all the relevant knowledge has been acquired  and solving problems results in acquisition of knowledge and problem solving skills.



Where it first developed?

Problem Based Learning first developed in the field of medical education to answer a perceived need for a curriculum , which encouraged learners to be more active and less competitive, and which was stressful than traditional curriculum.


What are the outcomes of a PBL approach?

It is claimed that a PBL approach produces more motivated students, develops a deeper understanding of the subject, encourages independent and collaborative learning, develops higher order cognitive skills and develops a range of skills which include problem solving, group working, critical analysis and communication.



How is it different in practice?

In PBL, the curriculum is organized around the problems. Consequently, students learn the ‘content’ that is required to solve those problems. So problems have to be carefully matched to desired learning outcomes. In PBL students work in group to solve problems. There are no lectures, instead students engaged in self-directed learning, and the tutor acts as a facilitator, mentor or guide.



How do PBL students compare with traditional students?

Research suggests that PBL students perform as well as or slightly worse than students from traditional courses on conventional examinations of knowledge. However PBL students are superior with respect to their approach to study and learning, long-term retention of knowledge, motivation, use of resources, key skills and subsequent success of postgraduates. (


How does PBL work in practice?

During the first classroom session the students are divided into groups and presented with the problem. They may brainstorm in order to clarify the nature of the problem and identify their learning needs. They may delegate roles within the groups and share existing knowledge. The tutor’s role one of observation, guidance and support. Out side the classroom session , the students engage in independent study in order to fill any gaps in subject knowledge. They come together again in a group or classroom study in order to fill any gaps in subject knowledge. They come together again in group or classroom session to share and critically evaluate resources and information gathered. Using the newly acquired information they work towards a solution to the problem. Again the tutor’s role is one of guidance and support. This cycle of independent study, group interaction and critical analysis may be repeated as many times as dictated by the problem. Eventually the students presents their solution and reflect on process and solution






PBL is a learner-centered educational method

In PBL learners are progressively given more and more responsibility for their own education and become increasingly independent of the teacher for their education. PBL produces independent learners who can continue to learn on their own in life and in their chosen careers. The responsibility of the teacher in PBL is to provide the educational materials and guidance that facilitate learning. (



PBL is based on the real world problems

In PBL learning is based on the messy complex problems encountered in the real world as stimulus for learning and for integrating and organizing learned information in ways that will ensure its recall and application to future problem. The problems in PBL are also designed to challenge learners to develop effective problem-solving and critical thinking skills.



The PBL learning process

In the PBL learning process learners encounter a problem and attempt to solve it with information they already possess allowing them to appreciate what they already know. They also identify what they need to learn to better understand the problem and how to resolve it.

Once they have worked with the problem as far as possible and identified what they need to learn, the learners engage in self-directed study to research the information needed finding and using a variety of information resources (books, journals, reports, online information, and a variety of people with appropriate areas of expertise). In this way learning is personalized to the needs and learning styles of the individual.

The learners then return to the problem and apply what they learned to their work with the problem in order to more fully understand and resolve the problem.

After they have finished their problem work the learners assess themselves and each other to develop skills in self-assessment and the constructive assessment of peers. Self-assessment is a skill essential to effective independent learning. (


The role of the PBL teacher

The principle role of the teacher in PBL is that of a facilitator or educational coach (often referred to in jargon of PBL as a "tutor") guiding the learners in the PBL process. As learners become more proficient in the PBL learning process the tutor becomes less active. This is a new skill for many teachers and specific training is required. (


PBL is a motivating way to learn

PBL is a motivating way to learn as learners are involved in active learning, working with real problems and what they have to learn in their study is seen as important and relevant to their own lives. (


Students must have the responsibility for their own learning

As the students in a problem-based learning curriculum work with a problem they should be able to identify what they need to learn and what resources they are going to use to accomplish that learning .In this way student can design their learning to meet individual needs(as they all have differing knowledge and experience) and career aspirations. Allowing students to have the opportunity to assure this responsibility, under faculty guidance, prepares them to become effective and efficient life-long learners-an absolute essential in a profession where new types of problems and new information surfaces with almost logarithmic expansion. The old educational truism states that half of what the students learn school will be wrong or outdated by the time they are in the real world, and no one knows which half that is. This means that the teachers working with the students should not provide the students with what they feel is the information students need in their studies nor give them reading or study assignments. The students must learn how to decide on what they need to learn and to seek out appropriate learning resources, using the faculty consultants.



Collaboration is Essential

Students Collaboration occurs naturally during the group’s discussion with the tutor. However, the students must be encouraged to collaborate during their self-directed study. Collaborative work among students in the group at this time can be the most rewarding and productive part of their learning as the students work together helping each other to gain understanding of what they are learning and its application to the problem. It is the collaboration that allows the students to develop the security and the authority they need to be responsible for their own learning. Collaboration is an essential skill the students must have in their careers, as they will invariably working as members of teams. (


What about assessment?
As this is a very different type of learning activity it may not appropriate to assess students in a traditional way. The assessment should be matched to the desired learning outcomes. Assessment may focus on the solution to the problem or the problem solving process or the skills development aspect. Tutors must decide whether they wish to give each member of a group the same mark or whether they wish to build in an individual element. Students may be involved is assessing each other’s contribution to the activity or may be involved in self-assessment and reflection. Useful assessment tools include logbooks and diaries, written reports, oral presentations, and reflective evaluation.



What are the resource implications?

The major resource implication is time; time develop and trial good problems, to train staff and to tutor the students. PBL takes more staff time than traditional methods because the group size have to be restricted A PBL session with 200 students in lecture theatre doesn’t work! Many institutions may be short of the sort of space that helps PBL

Works well-flat seminar room with movable furniture. In addition students need to have ready access to any relevant resources in the library, Internet etc.



What are the advantages of PBL?
Students should develop the ability to learn and gain a sound understanding of knowledge. They should be able to make sense of the material by integrating new knowledge with prior knowledge and experiences. In order to successfully solve the problems students should develop a range of critical cognitive and transferable skills with the context of their discipline.



And the disadvantages ?
Time and resources implications should not be underestimated.  In addition, the content covered in this way reduced compared to the amount that is covered in lecture-based courses PBL may be a new experience for staffs and students and they may require some support or training. Group work often suffers from non-participation or personality clashes and strategies have to be put in places to deal with group that don’t work Some students may not take the needs for independent study seriously and some time may be required to make to make clear the outcomes and commitment required.




Research and Theories


A Definition of Intelligence

Intelligence is a complex topic. An overview of some of this complexity is provided in Hunt (1995).

Howard Gardner, David Perkins, and Robert Sternberg have all been quite successful in helping spread knowledge about the meaning of "intelligence" and applications of this knowledge to education.




The following definition is a composite from various authors. Intelligence is a combination of the ability to:

1.     Learn. This includes all kinds of informal and formal learning via any combination of experience, education, and training.

2.     Pose problems. This includes recognizing problem situations and

3.     transforming them into more clearly defined problems.

4.     Solve problems. This includes solving problems, accomplishing tasks, fashioning products, and doing complex projects.

This definition of intelligence is a very optimistic one. It says that each of us can become more intelligent. We can become more intelligent through study and practice, through access to appropriate tools, and through learning to make effective use of these tools (Perkins, 1995).

PBL can be used as a vehicle in which students can use and improve their intelligence. More detail on the work of Gardner, Sternberg, and Perkins is given in the next three subsections.




Howard Gardner has proposed a theory of multiple intelligences. He originally identified seven components of intelligence (Gardner, 1983). He argues that these intelligences are relatively distinct from each other and that each person has some level of each of these seven intelligences. More recently, he has added an eighth intelligence to his list (Educational Leadership, 1997).

Many PBL-using teachers have studied the work of Howard Gardner and use some of his ideas in their teaching. For example, in creating a team of students to do a particular project, a teacher may select a team whose collective "highest" talents encompass most of the eight areas of intelligence identified by Gardner. The teacher may encourage a team to divide up specific tasks in line with specific high levels of talents found on a team. Alternatively, a teacher may encourage or require that team members not be allowed to work in their areas of highest ability in order to encourage their development of knowledge and skills in other areas.



Robert Sternberg

Many teachers have provided testimonial evidence that PBL encourages participation on the part of their students who do not have a high level of "school smarts." They report that some of their students who were not doing well in school have become actively engaged and experienced a high level of success in working on projects. These observations are consistent with and supportive of the research of Robert Sternberg.

As noted earlier in this chapter, different researchers have identified different components of intelligence. Sternberg (1988, 1997) focuses on just three main components:

5.     Practical intelligence--the ability to do well in informal and formal educational settings; adapting to and shaping one's environment; street smarts.

6.     Experiential intelligence--the ability to deal with novel situations; the ability to effectively automate ways of dealing with novel situations so they are easily handled in the future; the ability to think in novel ways.

7.     Componential intelligence--the ability to process information effectively. This includes metacognitive, executive, performance, and knowledge-acquisition components that help to steer cognitive processes.

Sternberg provides examples of people who are quite talented in one of these areas but not so talented in the other two. In that sense, his approach to the field of intelligence is somewhat like Howard Gardner's. However, you can see that Sternberg does not focus on specific components of intelligence that are aligned with various academic disciplines. He is far more concerned with helping people develop components of intelligence that will help them to perform well in whatever they chose to do.

Sternberg strongly believes that intelligence can be increased by study and practice. Quite a bit of his research focuses on such endeavors. Some of Sternberg's work focuses specifically on "street smarts" versus "school smarts." He notes that some people are particularly talented in one of these two areas, and not in the other. This observation is consistent with the work of Lev Vygotsky (Fosnot, 1996) who argues that the type of learning that goes on outside of school is distinctly different than the type of learning that goes on in school. While some students are talented in both informal and formal education, others are much more successful in one rather than the other. A teacher who is skillful in developing PBL can help students to design projects that are consistent with their learning abilities and interests.



PBL can be thought of as a combination of cognitive and social

constructivist theories, as developed by Piaget and Vygotsky,

respectively. The major points of each of these theories are

outlined in the table below.


Cognitive Constructivism


Social Constructivism


The Mind is in the head;

Focus on “Cognitive “ reorganization

The Mind is in social transaction and emerges from acculturation into  a

Community of practice.

Raw Materials; uses primary

Data ,”manipulative,” or other interactive materials

Authentic Problems;

Learning environments reflect real-world complexities.

Student Autonomy;

Thinking and Learning responsibility in students Hands to foster ownership.

Team Choice and Common Interests, builds on common interests and experiences within a learning group, and gives some choice to that group; learning activities are

“relevant, meaningful, and both product and process oriented”

Conceptual Organization/Cognitive Framing; information organized around concepts, problems, questions, themes, interrelationships ; activities framed within thinking related terminology

Group Processing and Reflection; encourages group processing of experiences.

Meaningfulness and Personal Motivation;

Learning related to personal ideas and experiences.

Social Dialogue and Elaboration; uses activities with multiple solutions, uncertainty, novelty, etc, demanding dialogue, idea sharing, etc.; encourages student

Elaboration/justification for their responses through discussion, questioning, group presentations

Prior knowledge and Misconceptions builds on prior knowledge and addresses misconceptions

Teacher Explanations Support & Demonstrations demonstrates problems steps and provide hints, prompts, cues, and clarifications where


Questioning Promotes individual inquiry with open-ended questions; encourages question-asking behavior

Multiple View points;

Fosters multiple ways of understanding A problem;

Builds in audience beyond the instructor







(From Bridges, Edwin M., Problem Based Learning for Administrators, 1992)


Ongoing Research Efforts in PBL

One request heard frequently at the Illinois Mathematics and Science Academy’s Center for Problem Based Learning is “Do you have any research sowing that Problem-Based Learning is better than traditional instructions?” I cringe a little bit every time I hear it.


 Why? PBL is one curriculum and instructional strategy among many. While it is a powerful strategy, PBL like any other strategy, is not necessarily better in all cases for all students  Second, many ask the question without having a clear definition of PBL or traditional instruction. How can we make decisions about potential value and effectiveness without a clear set of parameters for PBL  traditional instruction?

A third reason to question the question “Is PBL better than traditional instruction?”  relates to research methodology.

Bridges and Hallinger(1991) suggest that it is more appropriate to ask, “How effective are the various species of PBL in achieving the educational outcomes you select?”

With a clear definition of what is meant to PBL and rich a rich description of what it looks like in various education settings, we can make informed decisions about what is “better” for students.

(Bridges & Hallinger. (1991) PBL in Medical and Managerial)


Problem-Based Learning and Current Cognitive Theory

PBL first developed in the field of medical education to answer a perceived need for a curriculum which encouraged learners to be more active and less competitive, and which was less stressful than the traditional curriculum (Aspy et al., 1993). While practical concerns might have served as the impetus for the development of PBL, subsequent literature has examined it from a theoretical viewpoint, to find that PBL embodies many of the principles of current cognitive theory.



Current cognitive theories claim that learning occurs not by absorbing information but by interpreting it. Effective learning depends on the internal processes of the learner, who must construct his or her own knowledge (Resnick, p. 2). Constructivism proposes that meaning is constructed by individuals through their experiences in particular contexts. The context for learning and the activities of the learner affect how something is understood, and therefore, what is learned (Honebein et al., 1993). Through the context of problem-solving it creates, as well as the activities in which learners in such an environment participate, PBL impacts learners' construction of knowledge.

Savery and Duffy (1994) examined constructivist theory, and distilled eight instructional principles that could guide the practice of teaching and the design of learning environments. They then examined PBL, which they found almost ideally captures these design principles:


Anchor all learning to a larger task or problem. The learner must have a purpose in learning, and must see the importance of the specific learning activities in terms of its relationship to the larger task at hand. PBL uses realistic problems, and expects the learner to identify his or her specific learning needs, so the importance of those learning activities is obvious.


Support the learner in developing ownership for the overall problem or task. The goals of the learner will largely determine what is learned, so it is important that learners buy into the task at hand. PBL units are designed to present a problem that learners readily adopt as their own.


Design an authentic task. An authentic learning environment is one in which the thinking required of the learner is consistent with the cognitive demands in the real environment from which the task is drawn. As discussed earlier, authenticity is a key characteristic of PBL environments. Learners are expected to approach problems the way experts would.


Design the task and the learning environment to reflect the complexity of the environment learners should be able to function in at the end of learning. Instead of simplifying the environment for the learner, the environment should remain complex, and the learner should be given supports to manage complexity. PBL environments are complex, though it is up to the design of the individual program to provide support for this complexity.


Give the learner ownership of the process used to develop a solution. Even in environments where students have ownership of the learning goal, the teacher often dictates the process they use. By having to develop their own process to solve the problem, students are engaged in authentic thinking. PBL units should be designed so as not to prescribe one best process to solution.


Design the learning environment to support and challenge the learner's thinking. While the learner should have ownership of the goal and process of learning, he or she needs support to select the suitable goals and structure productive processes. The teacher must assume the roles of consultant and coach, questioning the student at the leading edge of his or her thinking. While students define the problem in a PBL unit and determine the process they will use to arrive at a solution, they are given support to define the problem well, and reflect on the effectiveness of their process. The teacher usually assumes the role of a metacognitive coach.


Encourage testing ideas against alternative views and alternative contexts. Constructivism says that understanding is socially negotiated, meaning that only by testing one's understanding against the views of others can growth occur. While not considered essential to PBL, usually cooperative teaming is used to promote the generation of ideas and refinement of strategic thinking during a PBL unit.


Provide opportunity for and support reflection on both what is learned and on the learning activity. Reflection helps students to develop metacognitive awareness. In PBL, reflection is one of the goals of the teacher's questioning of students' plans, processes, and opinions.




Situated Cognition

An assumption common in education today is that knowledge exists independently of the contexts in which it is acquired, and that once a person learns something, he or she knows it and can apply it to any relevant situation. Failure to use this knowledge when it is pertinent is understood to be a problem of the individual's failure to recognize its relevance (Resnick,1989).

This assumption that knowledge can be separated from the context in which it is learned and used has come under criticism in the past decade. Brown, Collins et al. argue that cognition is fundamentally situated. By this they mean that the activity in which knowledge is developed is an integral part of what is learned, and that by divorcing knowledge from the context in which it is used, schools take away the meaning and purpose of learning that exists in real-life situations. By ignoring the situated nature of cognition, traditional education defeats its own purpose of promoting students' development of useable, robust knowledge.

The decontextualized problems that students typically work on in school fail to mirror the effective problem-solving done by people in their everyday lives or by expert practitioners within their domain. To illustrate this, Brown, Collins, et al. (1989) compared the activities of "just plain folks" (JPFs), students, and practitioners. As Table 3 shows, the activities of JPFs and practitioners bare close similarities, whereas the activities of students differ greatly. As will be discussed in greater detail in the next section, transfer is more likely to occur when there are similarities between the context in which something is learned and the context in which it is used. Obviously, the problem-solving activities typically found in schools represent a different context than would be found in other aspects of students' lives, so transfer of problem-solving skills from school to out of school activities would be limited.


Situated cognition, then, offers an explanation for why traditional schooling fails to prepare students for either the problem-solving they will have to do in their everyday lives, or the problem-solving they would eventually need to do if they were to become practitioners within one of the domains typically addressed in school (mathematics, biology, archaeology, for example). PBL environments, on the other hand, resemble the activities of JPFs and practitioners, which suggests that learning in such an environment is more likely to transfer to other problems encountered in real life.

Efforts to use problem-based learning in K-12 environments have tried to involve students in a meaningful context for learning in two ways. First, students are immersed in the problem situation, which is rich in details. An example of this type of environment comes from the work done by the Cognition and Technology Group at Vanderbilt. They refer to these problem situations as "anchors" because they situate or anchor instruction in a realistic, rich context, which they call a macrocontext (CTGV, 1992). Anchors are in story format, and contain all of the information students will need to solve the complex problem that each anchor sets up. Thus, all learning is situated within the context created by the anchor.

A second way to situate learning for students is to assign the students a specific role within the context of the problem situation. By placing the students in the roles of the people who are actually confronted by such problems, students are challenged to develop the knowledge base and strategies that are normally required to solve the problem. Sometimes the roles that students assume are those of "just plain folks," as in The Adventures of Jasper Woodbury series, while at other times, they take on the roles of professionals (Gallagher & Stepien, 1996).

Stepien et al. (1993) assert that when students are placed in specific roles within a problem situation they become "stakeholders," who bring to the problem their own perspective, biases, and values. This helps to shape the type of experience the student has and the type of thinking in which he or she is likely to engage.

Assuming a stake in the situation forces the students to recognize the roles perception and responsibility play in problem definition and resolution..... Assigning a stake forces students to define the problem within a set of parameters that separates realistic problem solving from that too often used in classrooms, problem solving without a specific perspective or responsibility for the problem solver (p. 343).

Cognition, then, is situated in a PBL environment both by the nature of the complex, realistic situation in which a problem is anchored, and by the effect that taking on a specific role has on the shaping of the learner's thinking.




PBL developed in response to a perceived need for students to build a knowledge/skill base that they could then use in practical situations. In other words, the goal of PBL is to enable students to transfer what they learn in class to other problems and situations they encounter.

Transfer has been a topic of investigation for educational researchers for over a century, yet the research literature on transfer has been replete with reports of failure (Marini & Genereux, 1995). Resnick (1989) described transfer as "the holy grail of educators" (p. 8); an ultimate goal that has thus far proved elusive.

One reason that transfer has proven to be such an elusive goal is the historic focus on general transfer, that is, the application of abstract knowledge learned in one situation (the classroom) to a broad variety of other tasks in other settings (home, work). Studies dating as far back as 1924 have shown a lack of support for the notion of general transfer, which has led researchers in the past decade to moderate their expectations (Singley, 1995) and focus instead on questions like those in the following section (Marini & Genereux, 1995).


Issues in Teaching for Transfer

Should efforts to promote transfer focus on tasks, learners, or context? The basic elements involved in transfer are the learner, the training and transfer tasks, and the training and transfer contexts. Research done early in the century focused on the tasks involved in learning, and saw transfer as the result of "identical elements" between the training and transfer tasks. Later researchers focused on the role of the learner's internal processing, and how it can be improved to enhance transfer.

More recently, many researchers have come to view context as the most important element of transfer. Brown, Collins, et al. (1989) argue that knowledge is tied to the sociocultural context in which is was acquired, and therefore it does not transfer easily to different contexts. According to this theory, transfer can only be expected if the transfer context mirrors that of the training context.

Marini & Genereux (1995) caution that task, learner, and context are all play key roles in transfer, and that a holistic approach is advisable.

What extent of transfer can we reasonably expect to achieve? As researchers have begun to view general transfer as an unrealistic goal, a wide variety of categories that describe degrees of transfer have been theorized. A common distinction is between near transfer and far transfer. Near transfer occurs when the conditions of the transfer task and context are similar to those used during training. For example, if a child learns how to tie the shoelaces of a pair of athletic shoes, then ties the laces of a pair of dress shoes, near transfer has taken place. Far transfer refers to those situations in which the task and context during training is very different from that in which the new knowledge is spontaneously use. If a child learns to identify adjectives in school, then spontaneously begins to include more vivid adjectives in her private diary, far transfer has occurred. Near and far transfer can be seen as a continuum (Detterman, 1993). While some researchers argue that only very near transfer (within the training task subarea of a domain) is possible, other researchers have found that a moderate level of transfer can reasonably be expected.


What should we teach to optimize transfer? One focus of research designed to answer this question has been strategic knowledge. Strategic knowledge includes procedural steps, strategies for identifying and meeting subgoals, and metacognitive strategies for directing, monitoring, and evaluating one's own learning. An emphasis on teaching strategic knowledge has often been accompanied by the argument that if very general strategies that are applicable to a wide range of tasks, such as metacognitive strategies or generic problem-solving procedures, can be identified and taught, then general transfer of learning can be achieved. Larkin (1989) suggests that the generic problem-solving strategies that are designed to promote general transfer form such a small part of the knowledge required to solve problems in a new domain that the benefit of teaching them is negligible. She instead proposes teaching more specific types of strategic knowledge, such as the following.

Strategies attached to general features. There are some strategies that are applicable to sets of related domains that, when combined with domain-specific knowledge, can be useful in problem-solving. An example that Larkin offers of a strategy that can be used across several domains in the physical sciences is that of decomposition, which is the process of breaking apart a complex object into simpler components, performing computation on these components, and comparing the results. For such strategies to transfer effectively, both knowledge of their relevance and domain-specific knowledge are necessary. Identifying and teaching strategies that are useful in related domains may produce successful efforts to promote transfer.

Strategies to identify subgoals. Substantial problems usually must be broken down into subgoals, and students must understand the connections between these subgoals and the main goal. Knowledge about how to set subgoals appears to be similar throughout related groups of domains (Larkin, 1989).

Metacognitive skills. These skills involve an individual's ability to monitor and manage his or her own internal processing of a learning task. Examples of metacognitive skills include managing one's mood, time, and negative self-talk, and monitoring one's own understanding. These skills are not domain-specific, so they have the potential to be transferred across a wide range of domains.

Problem-Based Learning and Transfer

Problem-based learning appears to be an educational strategy that would be conducive to transfer. First, PBL environments are designed to be as authentic as possible. That means that both the instructional context and tasks are designed to mirror real life contexts and tasks. To the extent that the contexts and tasks are similar in the training and transfer environments, the type of transfer expected is near, and therefore easier to achieve. Also, as explained earlier, PBL encourages the development and use of strategic knowledge by presenting students with complex, ill-structured problems. Students must engage in strategic thinking in order to define the problem and identify subproblems  which they must work to solve. Students are challenged to develop their skills to monitor and manage their own thinking through the use of metacognitive coaching during PBL.

Research also supports the ability of PBL to promote transfer of learning. Williams (1992) reports on research from the medical field that shows that students who participated in a PBL curriculum had less difficulty in clinical rotation than students in a conventional track, suggesting that PBL resulted in transfer of skills from the learning environment to the work environment. The researchers at CTGV found that anchored instruction resulted in superior near transfer of planning strategies, comprehension of the relevance of subgoals to a main goal, and problem-solving skills on mathematical word problems than traditional instructional environments (CTGV, 1992).

Research on transfer can also advise the design of PBL units. Because the effectiveness of instruction in general problem-solving strategies has not been shown to promote transfer, it should be avoided, but support for the development of strategies that are specific to the domain or to a group of related domains is still needed. Second, since near transfer is more achievable than far transfer, students need to experience the acquisition and use of knowledge in situations and domains as similar to real life as possible. This would indicate that knowledge which is useful in a variety of situations needs to be taught in more than one situation, and students must become aware of its assorted uses in order to transfer it successfully.


Hypermedia Supports for PBL

PBL may have the potential to promote the acquisition of robust knowledge that learners can transfer from the context of the classroom to situations they encounter in other aspects of their lives. Yet problem-based learning has a serious drawback: it is difficult to design and manage the complexity of such environments.

Domains are complicated sets of interconnected facts, processes, and issues. They are rich in their own problems that are well worth solving, and any practitioner or teacher in a particular domain is probably capable of generating numerous rich, complex problems. However, this generation of worthwhile problems in insufficient to the task of setting up a successful problem-based learning environment. Developers, be they teachers or instructional designers, must chart out the knowledge students will "run into" (Stepien et al., 1993) in the course of working on a problem, and compare this to the stated goals of a course. They must then make sure that a wide variety of materials that deal with the learning issues needed to solve the problem are available and suitable to the needs of diverse learners. Once students are engaged in problem-solving, teachers must provide a variety of supports, managing group interactions to ensure that all groups are productive, encouraging the cognitive development of all students, and serving as a metacognitive coach to help students develop skills to monitor their own thinking. The difficulty of such tasks makes PBL unfeasible for most classroom teachers.

The professional design and development of materials to support PBL seems justified. These materials can be developed in collaboration with content experts, and can be carefully designed to consider the learning within the domain that students must do in order to solve the problem. Through testing of the materials, designers can make certain that all necessary resources are included, and that these resources are provided in a variety of forms to meet the needs of diverse learners.

Additionally, professionally developed PBL units can have built in instructional supports that make the use of them more feasible for classroom teachers. Problem-based learning environments are complex; as discussed earlier, this complexity is a strength, which should be maintained in their design. However, its complexity can make a PBL environment overwhelming for learners, and most efforts at using PBL have included various forms of support for the learners.

In this section, the types of supports generally needed to facilitate learning in a PBL environment are discussed, the methods that teachers have used to provide each are reviewed, and the possibilities that hypermedia holds to provide these supports are offered.

Types of Support Needed

A rich, realistic context in which a problem is situated. To encourage transfer, students need to learn in contexts that are as similar to real life as possible. In medical programs, students take on the roles of doctors, and are presented, as a doctor is, with patient information. They can then order tests, conduct interviews, and consult with other doctors to get more information. Each problem, in the form of a patient, is accompanied by a Master Action List and a Patient Encounter Book, which provide the information the students request. These resources are rich and detailed; they offer the students no hints about which questions to ask or which issues are relevant, because they provide a wide variety of details, many of which are irrelevant to the given problem. Students must also search medical textbooks, but the problems do not indicate which books or resources are the most useful (Williams, 1992).

Anchored instructional environments created by the Cognition and Technology Group at Vanderbilt are also rich contexts that present problems that "just plain folks" might be called upon to solve in their everyday lives. The materials developed by this group contain features that help make the complexity of the environment manageable. They use a story format, which is a context well-understood by even young children. Stories are presented using video laser disk, which provides dynamic images that helps all students, even poor readers, form a mental model of the problem. The video contains all the information necessary to solve the problem, which means that learners need not experience the frustration of searching for information that is not available in a textbook or school library (CTGV, 1992; Williams, 1992). The laser disk format means that the video is readily searchable.

Rich, complex environments can also be created using hypermedia, and supports for complexity similar to those built into anchored instructional materials can be included. Hypermedia can situate a complex problem in a story format, and make additional information about the problem readily available.

Additionally, hypermedia can provide a database of information that students will need to solve the problem. This database can follow the example set in medical schools, where more information than is necessary is included, and the organization of the information provides no hints about what is important or relevant to the problem.

Support for learners' development of strategic knowledge. The results of numerous research efforts indicate improving the quality of problem-solving that students do requires an effort aimed specifically at that objective (Nickerson, 1994). A criticism that Williams (1992) levels at the model of PBL used in medical schools is that it fails to support students in the development of strategies to handle the problems they are given. She recommends a modification to current practice so that students have the opportunity to see how experts perform in problem situations. She believes that this modification would help students learn effective problem-solving strategies more quickly, cut down on the development of ineffective strategies that could hamper future learning, and limit the floundering that sometimes frustrates novices to problem-based learning.

Supporting the development of strategic knowledge does not mean providing direct instruction on a strategy followed by assigning students to apply the strategy to the problem at hand. A strength of PBL is its ability to create situations where students recognize a need for particular knowledge, and therefore see its usefulness. The most effective time to teach problem-solving strategies is when students need them in order to solve a problem.

Extensive research has been done on general strategies for solving problems in a variety of domains, but, as previously discussed, these general strategies have arguably limited benefits. Rather, the strategies that are taught need to be specific to the domain, or in the case of PBL, to the problem at hand. Therefore, the purpose of the section below is not to discuss the merits of particular strategies, as the choice of these strategies needs to be determined in the context of a specific problem, but rather to identify the points within the problem-solving process where students might benefit from support for the development of strategic thinking.

Problem-finding. While PBL presents students with problem situations, it typically does not clearly state a particular problem for students to solve. Students must first determine if there is a problem, then must define and refine it until they reach a clear problem statement. For example, in medical programs, students are confronted with a story in which a patient describes a complaint, but must then determine if the complaint is actually the result of a true medical problem.

Students who have engaged in PBL have shown a significant increase in their problem-finding ability (Gallagher et al.. 1992). This may be the source of two cognitive benefits involved in PBL. First, problem-finding is authentic; in everyday life people must define the problem in a troublesome situation before they can work on solving it. For this reason, problem-finding may encourage transfer. Second, problem-finding has been shown to correlate with creative productivity (Okuda, Runco, & Berger, 1991). Improved problem-finding skills might encourage the enhancement of creativity.

Identification of learning issues. One of the concerns about PBL that arose in medical programs was that students sometimes failed to identify all of the learning objectives which the faculty who had designed the problems thought they should encounter (Williams, 1992). Duek and Wilkerson (1995) found that students who worked in tutorless groups identified significantly fewer of the learning objectives determined by faculty than students in groups that had tutors. This would indicate a general need for support in the identification of the relevant topics that students must study in order to solve the problem.

Representations. Representations are versions of the external world that people hold within them to think about and work on. When attempting to solve a problem, the representation that a person has of that problem will influence the way he or she approaches it and the solutions considered. The ability to create effective representations of a problem has often been cited as an important difference between the thinking of experts and novices (Nickerson, 1994). While some representations such as contingency tables, graphs, and flow charts are useful in a wide variety of domains, most domains possess representations that are only useful inside that domain. Training students in the effective use of general and domain-specific representations could improve their ability to solve the problems with which they are confronted during PBL.

Development of an action plan. General problem-solving instruction may have little impact on students in terms of transfer, but strategies that are specific to a domain or related group of domains may transfer more effectively (Larkin). Helping students to understand how experts within a domain approach such problems, and the specific strategies they employ may support their development of effect strategic thinking.

The responsibility for supporting students in the development of strategic knowledge can be left to teachers, but as Singley (1995) points out, each of these steps is difficult and prone to error. While the teacher could be responsible for part of the support students need to develop strategic knowledge, hypermedia can also be used to support this task.

Direct instruction in the use of strategies during problem-based learning is one option for providing support for the development of strategic knowledge. However, a superior alternative might be found in the literature on cognitive apprenticeship. Cognitive apprenticeship is an approach to instruction that is particularly suited to situated learning, and the literature on the two have developed together. It can be defined as an approach whereby the learner, or apprentice, becomes aware of and internalizes the cognitive processes of experts within a domain. The learner does this within the context of an authentic environment, and is exposed to these processes as they become relevant. One of the teaching methods used in cognitive apprenticeship is modeling (Collins et al., 1989). This involves giving the learner an opportunity to observe the internal cognitive processes of an expert as he or she problem-solves. Usually this is done by having the expert do "think alouds" as they deal with a problem or by sharing stories of the thinking processes he or she has used to solve problems in the past. This helps students to develop conceptual models of the processes that are required to accomplish the task. The effectiveness of modeling is strongly supported by research (Honebein et al., 1993).

Hypermedia systems have been shown to be effective in delivering instruction based on cognitive apprenticeship methods (Casey, 1996). A hypermedia program can be designed to offer modeling of pertinent strategies as students are engaged in problem-solving by providing expert opinions at appropriate points throughout the program. These "experts" could share relevant stories or explain a useful strategy. They could engage students further by asking students to answer questions that apply these ideas or strategies.

Serve as metacognitive coach. Teachers are typically expected to serve as metacognitive coaches in a PBL environment ( Stepien et al., 1993; Williams, 1992). They stimulate the self-monitoring process by asking questions such as "Is there something more you need to know at this point?" or "Why is that an important question?" The purpose of this coaching is to model and encourage students to eventually internalize the habit of questioning. In their role as coaches, teachers can also get students to realize and articulate when a strategy is useful, and when it is not. This type of metacognitive knowledge has been shown to promote transfer of strategic thinking (Singley, 1995).

Teachers determine the type of coaching to offer on the basis of their observations. Coaches offer hints, scaffolds, feedback, reminders, models, and new tasks designed to bring students' performance closer to the performance of experts (Brown, Collins, et al., 1989). But, as Wilson and Cole (1991) point out, coaching probably involves the most instructional work of any of the cognitive apprenticeship strategies, and given typical class sizes, teachers are not likely to be able to provide all the coaching that is appropriate.

Hypermedia can be used to support metacognitive coaching. Through a series of questions and answers, the hypermedia program can "check upon" the student's thinking, and provide helpful suggestions, reminders, or additional information that may extend the student's thinking. While this support may not be as sensitive to particular student needs as a teacher can be, it may compensate for this shortcoming in part by providing all students with an individualized opportunity to consider their own thinking. Encourage articulation and reflection. Cognitive apprenticeship advocates two other teaching strategies which can support learning in a PBL environment. Articulation refers to "any method of getting students to articulate their knowledge, reasoning, or problem-solving processes in a domain," while reflection "enables students to compare their own problem-solving processes with those of an expert, another student, and ultimately, an internal cognitive model of expertise" (Collins et al., 1989, p. 482).

A feature of PBL environments created by IMSA includes the use of problem logs (Stepien et al., 1993), which each student is assigned to keep. These logs provide a journal type record of the development of the problem. Students are free to record whatever insights come to them, but are also given specific assignments that help the teacher to keep track of their thinking. Examples of problem log assignments are "Create a statement of the problem,"and "How did this activity change your thinking?" Because students are required to complete entries in their logs (as part of the course grade), they are forced to examine their thinking and articulate it. Through discussion, students can also be encouraged to reflect on their ideas and adjust them to accommodate new information and insights.

Hypermedia can assist this process by assigning individualized questions for students to answer in their problem logs based on their interactions with the program, then offering several expert (and sometimes conflicting) opinions for comparison. This process can be made interactive by asking students to respond "I agree," or I disagree" to statements made by these experts. By reflecting on these multiple perspectives on an issue, students can both compare and evaluate their own thinking.

Facilitate group interactions. Cooperative learning is itself a strategy to promote the externalization of the thinking process needed to problem-solve, but to be effective in that task, it must be supported. During cooperative learning, teachers work to facilitate the involvement of all students in a group on the assumption that active involvement benefits the individual, and that the contributions of all benefit the group (Stepien et al., 1993).

Research also indicates that the effectiveness of cooperative learning in terms of both achievement and attitude is related to the amount and type of verbal interaction between students within cooperative groups. Groups where students give and receive explanations, discuss strategy, and verbalize the decision-making process have been shown to demonstrate greater problem-solving ability than groups that do not (Sherman & Klein, 1995). Hypermedia has been shown to be able to encourage the involvement of all students and mediate the types of interactions that occur during cooperative group work. Sherman & Klein used a hypermedia program with embedded cues to facilitate group interactions. These cues prompted students to summarize, explain, or listen to their partners. Students in the cued version performed better on the posttest and demonstrated significantly more summarizing and helping behaviors than students in the noncued version. By directing groups to engage in certain verbal activities, hypermedia may be able to facilitate strategic thinking and problem-solving during PBL.

Research Questions

Problem-based learning is a challenging instructional method. Learners, especially young ones with limited experience in problem-solving, need a variety of supports to successfully solve the complex problems in which they engage during PBL, and to optimize their learning of strategic knowledge. While teachers are typically expected to provide this support, hypermedia may be able to share some of this responsibility. The study proposed in this paper will attempt to determine if hypermedia can provide some of the support students need during PBL as effectively as a teacher, and if the use of PBL results in the transfer of strategic knowledge to other problems. In particular, this study will attempt to answer the following questions:

1. Can hypermedia based cognitive modeling assist students in problem finding and the identification of learning needs in a PBL environment as efficiently as a classroom teacher?

2. Are students as likely to use domain-specific strategies when they receive hypermedia based cognitive modeling as when these same strategies are presented by the teacher?

3. Can hypermedia support the active participation of all members of a PBL environment?

4. Can hypermedia facilitate the near transfer of strategic thinking presented in a PBL environment?

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Results  (Maricopia center for learning &instruction)


Students involved in problem-based learning acquire knowledge and become proficient in problem solving, self-directed learning, and team participation. Studies show that PBL prepares students as well as traditional methods. PBL students do well as traditional methods. PBL students do as well as their counterparts from traditional classrooms on national exams, but are in fact better practitioners of their professions (


                 As a teacher, I might see PBL as a way for students to control their learning to an even greater degree and as a way for me to step back form control of the learning environment   As an educator, I might see PBL as a way to teach problem-solving, so students may be successful after they

Leave school. As a politician, I might see PBL as a way for school system to

Train tomorrow’s leaders in the foundations of problem-solving  And as a parent, I might see PBL as a way for my child to learn not only problem-solving but logic. (Center for Problem-Based Learning (1995). Introductory document Aurora IL IMSA)


My opinion


PBL may be the most revolutionary concept in teaching history, it is certainly the most interesting teaching method that  I as a student and as a teacher have ever seen.


                  With PBL, I learned that one must never assume that any problem is unsolvable. While I see PBL as a wonderful idea for teaching, and most importantly for learning itself. I wonder why it hasn’t been used to its fullest. I look forward to the day when learning does not take place in the classroom, but in places where students of every race, gender, age, and creed attempt to solve the problems that faces our global community.


                                     In my opinion Problem Solving should introduced to students at very early stage in their life through Problem Based Learning which will help them to achieve a lot in their life. It is very similar to a child learn to  walk  and talk in his or her early years. This is part of their cognitive skills. However learning problem solving though Problem Based Learning will be metacognitive skill for them to use the ability in real word problems