Problems: A Key Factor in PBL

Barbara Duch,
Center for Teaching Effectiveness

Example Problems:
-- Physics: Level 1, Level 2, Level 3
-- Biology: Level 1, Level 2, Level 3

How does problem-based learning differ from other forms of active, group, or student-centered learning? The primary distinction is the focus on introducing concepts to students by challenging them to solve a real world problem. In contrast to the more traditional approach of assigning an application problem at the end of a conceptual unit, PBL uses problems to motivate, focus, and initiate student learning.

Therefore, a critical factor in the success of PBL is the problem itself. What are the characteristics of good problems? Where can you find problems or cases in your discipline to use in your courses?

Characteristics of good problems

Many faculty who have adapted PBL in their courses, and students who have taken those courses agree on several factors that are essential for good problems (or cases).
  1. An effective problem must first engage students' interest, and motivate them to probe for deeper understanding of the concepts being introduced. It should relate the subject to the real world, so that students have a stake in solving the problem.
  2. Good problems require students to make decisions or judgements based on facts, information, logic and/or rationalization. Students should be required to justify all decisions and reasoning based on the principles being learned. Problems should require students to define what assumptions are needed (and why), what information is relevant, and/or what steps or procedures are required in order to solve them.
  3. Cooperation from all members of the student group should be necessary in order to effectively work through a good problem. The length and complexity of the problem or case must be controlled so that students realize that a "divide and conquer" effort will not be an effective problem-solving strategy. For example, a problem that consists of a series of straight-forward "end of chapter" questions will be divided by the group and assigned to individuals and then reassembled for the assignment submission. In this case, students end up learning less not more.
  4. The initial questions in the problem should have one or more of the following characteristics so that all students in the groups are initially drawn into a discussion of the topic: This strategy keeps the students functioning as a group, drawing on each other's knowledge and ideas, rather than encouraging them to work individually at the outset of the problem.
  5. The content objectives of the course should be incorporated into the problems, connecting previous knowledge to new concepts, and connecting new knowledge to concepts in other courses and/or disciplines.

Higher order thinking skills

In addition to these characteristics, good problems should challenge students to achieve higher-level critical thinking. Too often, students view learning as remembering facts, terms and definitions in order to answer questions on tests. Many students seem to lack the ability or motivation to go beyond factual material to a deeper understanding of course material. In Bloom's Taxonomy of Educational Objectives (1956), cognitive levels along with parallel student activities are arranged from simple to complex (see table below). PBL problems should strive to induce students to learn at the higher Bloom levels, where they analyze, synthesize and evaluate rather than simply define and explain.

Bloom's Cognitive Level Student Activity
Evaluation Making a judgment based on a pre-established set of criteria
Synthesis Producing something new or original from component parts
Analysis Breaking material down into its component parts to see interrelationships / hierarchy of ideas
Application Using a concept or principle to solve a problem
Comprehension Explaining/interpreting the meaning of material
Knowledge Remembering facts, terms, concepts, definitions, principles

Reference: Bloom, B. (1956) Taxonomy of Educational Objectives, New York: McKay.

Where to find good problems

So now that we know what makes a good problem for use in PBL -- where can you find them in your discipline? Unfortunately, in most of our undergraduate content areas, there are no books, manuals or notebooks of PBL problems. Most of us who use PBL in our classes have had to write our own. Some faculty use video-clips, stories, novels, articles in the popular press, and research papers as a basis for a problem. Frequently, faculty find a typical textbook problem, and rewrite it as an open-ended, real world problem. Some examples from physics and biology are shown, although the ideas behind the adaptations will work in any discipline.

A Level 1 problem is a typical end-of-chapter problem, at Bloom's Knowledge or Comprehension cogitive level. The problem is generally confined to the topic(s) addressed in the chapter, and all the information needed to solve the problem is given.

A Level 2 problem adds a story-telling aspect to the end-of-chapter problem. This adds some motivation for students to solve the problem, and it requires students to go beyond simple "plug-and-chug" in order to solve it. There may even be some decision-making involved, placing the questioning at Bloom's Comprehension or Application level. All the information needed to solve it is given in the problem or the chapter.

A Level 3 problem is a good PBL problem, at Bloom's Analysis, Synthesis or Evaluation levels. It is related to the real world, drawing the student into the problem. Not all the information needed is given in the problem, or chapter, or perhaps even in the texbook. Students will need to do some research, discover new material, arrive at judgements and decisions based on the information learned. The problem may have more than one acceptable answer, based on the assumptions students make.


Examples:

Physics: Level 1

A simplified electrical circuit for a home is shown below. Calculate the currents through the fuse, lightbulb, electric crock and toaster.

[Circuit schematic]

Reference: Van Heuvelan, A. (1986) Physics: A General Introduction, Harper Collins.

Physics: Level 2

Jim and Jenny just moved into a rental house. Early Sunday morning, Jim decides to surprize Jenny and cook breakfast for her. He starts cooking bacon in the electric frying pan (1000-watt) while he perks the coffee (600-watt). Jim decides to make some toast (700-watt) while he waits for the bacon and coffee to finish cooking. Just before he starts the toaster, Jim notices that the kitchen circuit is protected by a 20 amp fuse. He looks around and can't find any spare fuses. Should Jim start the toast now, or wait until the coffee and bacon are done? (Assume that the appliances are in a parallel circuit.) Will it matter if Jim has the overhead light (100-watt) on or not?

Physics: Level 3

OVERLOAD
(page 1)

Sharon and Stanley are building their dreamhouse. They have already designed the layout of all the rooms, with the help of Stan's father who is an architect. You are good friends with Sharon and Stan and since you've just studied circuits in your physics class, you are interested in the wiring plans for the new home. Sharon tells you that the house will have 4 bedrooms, a family room, living room, dining room, 2 bathrooms, a utility/wash room, and a combination kitchen/breakfast area. Stan tells you that he doesn't know how many circuits his house needs in order to be safe. In fact, Stan isn't even sure he knows what a circuit is, or how a circuit breaker works. Does he need some 240 V lines as well as 120 V ? What voltage are the electrical lines coming into the house? How are the ratings on the circuit breakers determined? How are houses wired?

Using your knowledge of physics, answer Stan's questions. If you don't know the answer, where can you find the information you need? What questions should you ask Sharon and Stan in order to determine their wiring needs?

(When finished with these questions, ask your instructor for page 2.)

(page 2)

Sharon tells you that they will have many appliances in the kitchen. A microwave, refrigerator, blender, toaster oven, toaster, can opener, electric fry pan, electric wok, mixer, clock radio, clock, crock pot, and dishwasher. Stan says that his computer and printer, and Sharon's ironing and sewing "stuff" will be in the same bedroom. Stan uses an electric razor, while Sharon uses a blow dryer and curling iron in the main bath.

They also inform you that in the morning, Stan cooks breakfast while Sharon does her hair in the bathroom. And in the evening, while Sharon cooks dinner, Stan works on his computer or watches TV in the living room. Sharon likes to sew or iron while Stan does the budget on the computer.

They show you a sketch of the floor plans for the house. The dimensions of the rooms are as follows: kitchen: 12'x15', living room: 15'x25', spare bedroom: 10'x12'.

Is there a minimum number of outlets that must be wired for each room? How are overhead light switches wired into the circuit?

Sketch the wiring diagram for the kitchen. Do you need more than one circuit breaker for the kitchen? Design the wiring so that no circuit breaker opens while Sharon is using several of her appliances cooking dinner. Be sure to give several examples of multiple appliance use.

When you have answered these questions and sketched the wiring diagram, check with your instructor before doing the final activity.

Construct a wiring plan for the kitchen, main bathroom, spare bedroom, and living room in the new house with the minimum number of circuits which will still suit Stan's and Sharon's mode of living. Your design should insure that no circuit breakers will trip during the busy mornings or evenings. Be sure to include the normal items in rooms (lights, stereo, VCR, etc.) as you plan your wiring diagram.

Written by Barbara J. Duch
May, 1995; Revised January 1996


Biology: Level 1

How is the energy flow through ecosystems related to the processes of photosynthesis and respiration, discussed in Chapters 7 and 8?

Write the summary equation for photosynthesis. Why is photosynthesis an oxidation- reduction reaction?

How were fossil fuels formed? What effect is the burning of fossil fuels and the clearing of forests having on the carbon cycle? What is the possible consequence to the earth's climate?

Reference: End of chapter "Making Connections" and study questions from McFadden and Keeton, Biology: An Exploration of Life. Norton, 1995.

Biology: Level 2

Tropical rain forests cover only about 3% of Earth's surface, but they are estimated to be responsible for more than 20% of global photosynthesis. It seems reasonable to expect that the lush growth of jungle foliage would produce large amounts of oxygen and reduce global warming by consuming carbon dioxide. But in fact, many experts now believe that rain forests make little or no net contribution to global oxygen production or reduction of global warming. Using your knowledge of photosynthesis and cellular respiration, explain what the basis of this belief might be. What happens to the food produced by a rain forest tree when it is eaten by animals or the tree dies?

Reference: End of chapter "Science, Technology, and Society" question from Campbell, Biology. Benjamin Cummings, 1993.

Biology: Level 3

THE GERITOL SOLUTION

(page 1)

John H. Martin, the director of the Moss Landing Marine Laboratories, thinks the potential problem of global warming could be addressed by dumping iron into the ocean waters off Antarctica. He and his coworkers have demonstrated that the amount of chlorophyll found in ocean water samples collected (in 30 L botttles) from the Gulf of Alaska can be increased up to nine-fold by the addition of iron.

When they repeated this fertilization experiment with samples collected from a few hundred miles off the Antarctic coast, he and his colleagues found that for every unit of iron added to antarctic sea water, the organic carbon content increased by a factor of 10,000.

What is the basis of Martin's premise that seeding the ocean with iron would help combat potential greenhouse warming?

What organisms found in sea water account for the increase in chlorophyll content and increase in biological productivity Martin and his research group observed?

(page 2)

Martin thinks that analyses of 7,000-foot deep Antarctic ice cores provide support for his premise. He makes particular note of CO2 and iron concentrations found 18,000 and 160,000 years ago, about the time of earth's ice-ages. This information is given in the plots shown on the graph below.

[Graph of CO2 and Iron conc.]

(Note that scientists think that the iron found in the ice core came from dust that settled out of the atmosphere, and that the CO2 came from air trapped in bubbles in the ice. The current level of CO2 in atmospheric air is about 350 ppm.) Do you agree with Martin that the information provided by ice core analysis supports his hypothesis? Why or why not?

(page 3)

You are particularly interested in Martin's ideas, since you've just agreed to serve on a study section of a panel of the National Science Foundation (whose task is to review grant proposals and assess their funding priority). One of the proposals you must review is one by a team of scientists who'd like to test John Martin's ocean seeding hypothesis on a 60 square kilometer plot just south of the Galapagos Islands.

You're aware that the idea that biological productivity of ocean waters can be increased by seeding is not a new one. For example, other studies have shown that when nitrates or phosphates are added to the relatively iron-rich, but nutrient-poor water (by comparison with Antarctic) found in most open oceans, a phytoplankton bloom results. You are puzzled by why the grant applicant (and Martin) think that seeding the nutrient-rich Antarctic waters with iron is a better approach than seeding the relatively iron-rich Atlantic waters with nitrates or phosphates. The applicant has not adequately explained the rationale behind this approach. In addition, you're not sure if the applicant's calculation of the amount of iron that would be needed is a realistic one.

Your primary concern, however, is that the applicant hasn't adequately addressed the possible ecological impact of such a large-scale endeavor. You can't decide if this is the most lame-brained scheme of the century, or a brilliantly creative solution to a serious problem for the planet's future.

Will you recommend funding this project? Why or why not?

Reference: This problem was based on an article by Robert Kunzig in the April, 1991 issue of Discover magazine entitled, "Earth on Ice."

Written by Deborah E. Allen
August, 1993; Revised August, 1995; January, 1996


"http://www.udel.edu/pbl/cte/spr96-phys.html"
Last updated Feb. 20, 1997.
Copyright Barbara Duch, Univ. of Delaware, 1996.