Based Learning in Mathematics what a concept.
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
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 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.(http://www.udel.edu/pbl)
I do …….and
(Calculus and Analytical Geometry MIZRAHI AND
SULLIVAN, Preface to the student)
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.(http://www.edb.utexas.edu/mmresearch/students97/Hemstreet/pl3.htm)
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.
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.
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
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.
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. (http://dbweb.liv.ac.uk./ltsnpsc/primers/intrpbl4.htm)
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 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
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
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.
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.
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.
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. (http://www.pbli.org/pbl/pbl.htm)
The role of the PBL teacher
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. (http://www.pbli.org/pbl/pbl.htm)
PBL is a motivating way to learn
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. (http://www.pbli.org/pbl/pbl.htm)
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.
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
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
well-flat seminar room with movable furniture. In addition students need to have
ready access to any relevant resources in the library, Internet etc.
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.
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.
A Definition of Intelligence
is a complex topic. An overview of some of this complexity is provided in Hunt
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.
following definition is a composite from various authors. Intelligence is a
combination of the ability to:
This includes all kinds of informal and formal learning via any combination of
experience, education, and training.
This includes recognizing problem situations and
transforming them into more clearly defined problems.
This includes solving problems, accomplishing tasks, fashioning products, and
doing complex projects.
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).
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.
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).
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.
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
noted earlier in this chapter, different researchers have identified different
components of intelligence. Sternberg (1988, 1997) focuses on just three main
intelligence--the ability to do well in informal and formal educational
settings; adapting to and shaping one's environment; street smarts.
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.
intelligence--the ability to process information effectively. This includes
metacognitive, executive, performance, and knowledge-acquisition components that
help to steer cognitive processes.
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.
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.
can be thought of as a combination of cognitive and social
theories, as developed by Piaget and Vygotsky,
The major points of each of these theories are
in the table below.
Mind is in the head;
on “Cognitive “ reorganization
Mind is in social transaction and emerges from acculturation into
Materials; uses primary
,”manipulative,” or other interactive materials
environments reflect real-world complexities.
and Learning responsibility in students Hands to foster ownership.
Choice and Common Interests, builds on common interests and experiences
within a learning group, and gives some choice to that group; learning
meaningful, and both product and process oriented”
Organization/Cognitive Framing; information organized around concepts,
problems, questions, themes, interrelationships ; activities framed within
thinking related terminology
Processing and Reflection; encourages group processing of experiences.
and Personal Motivation;
related to personal ideas and experiences.
Dialogue and Elaboration; uses activities with multiple solutions,
uncertainty, novelty, etc, demanding dialogue, idea sharing, etc.;
for their responses through discussion, questioning, group presentations
knowledge and Misconceptions builds on prior knowledge and addresses
Explanations Support & Demonstrations demonstrates problems steps and
provide hints, prompts, cues, and clarifications where
Promotes individual inquiry with open-ended questions; encourages
multiple ways of understanding A problem;
in audience beyond the instructor
(From Bridges, Edwin M., Problem Based Learning for Administrators, 1992)
Research Efforts in PBL
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.
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
third reason to question the question “Is
PBL better than traditional instruction?” relates to research methodology.
and Hallinger(1991) suggest that it is more appropriate to ask, “How
effective are the various species of PBL in achieving the educational outcomes
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.
& Hallinger. (1991) PBL in Medical and Managerial)
Problem-Based Learning and Current Cognitive Theory
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
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.
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
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.
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.
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.
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.
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.
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.
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
opportunity for and support reflection on both what is learned and on the
Reflection helps students to develop metacognitive awareness. In PBL, reflection
is one of the goals of the teacher's questioning of students' plans, processes,
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).
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
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.
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.
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.
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).
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
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
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).
Teaching for Transfer
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
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.
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.
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.
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
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).
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
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
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
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.
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.
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.
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.
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
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.
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.
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.
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.
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?
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 (http://mcli.dist.maricopa.edu/pbl/info.html)
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
school. As a politician, I might see PBL as
a way for school system to
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)
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