Understanding student pathways in context-rich problems

Abstract

This paper describes the ways that students’ problem-solving behaviors evolve when solving multi-faceted, context-rich problems within a web-based learning environment. During the semester, groups of two or three students worked on five physics problems that required drawing on more than one concept and, hence, could not be readily solved with simple “plug-and-chug” strategies. The problems were presented to students in a data-rich, online problem-based learning environment that tracked which information items were selected by students as they attempted to solve the problem. The students also completed a variety of tasks, like entering an initial qualitative analysis of the problem into an online form. Students were not constrained to complete these tasks in any specific order. As they gained more experience in solving context-rich physics problems, student groups showed some progression towards expert-like behavior as they completed qualitative analysis earlier and were more selective in their perusal of informational resources. However, there was room for more improvement as approximately half of the groups still completed the qualitative analysis task towards the end of the problem-solving process rather than at the beginning of the task when it would have been most useful to their work.

Appendices

Appendices

1.1 Appendix A: Problem Descriptions

• 1. “How much ice will you need?” You are in charge of keeping the drinks cold for a picnic. You have a styrofoam box that is filled with cola, water and you plan to put some 0° ice in it. Your task is to buy enough ice to put in the box at 6 am so that the temperature stays at 0°C until the picnic starts at 4 pm. You don’t want to buy too much ice because that means that you’ll have less money to spend on food and other picnic items.

  How much ice will you need? You have 90 “minutes” to calculate the amount of ice, before your cousin picks you up to drive to buy the ice. Getting information from the resources (on left-hand panel) may cost you some ‘time’. The resources will only cost you “ time” when you first access them and the cost will be always indicated. Your score will depend partially on how much ‘time’ you have left in your account.

• 2. “Optimal Operating Conditions.” You are an engineer designing a nuclear power plant. The core of the reactor is designed to operate at a temperature of T_H and the cooling water is at a temperature of T_C. Your group has found that you may be able to reduce the cost of the plant considerably by using smaller engines to convert the heat from the reactor into work in the form of electrical energy. The design concept you have developed is to use a tank of liquid lithium as heat buffer to be held at temperature T between T_H and T_C and then use one generator to operate between the core and the lithium tank and another to operate between the tank and cooling water.

  In 90 min you are to present your idea to the engineering committee which is to decide whether a full scale engineering study of this design is to be undertaken. You need to develop the case for this design, including what temperature T for the lithium tank produces the greatest efficiency and how does this efficiency compare to the standard design.

• 3. “Making a Perfect Fifth.” Your friend, an artist, has been thinking about an interesting way to display a new wind sculpture she has just created. In order to create an aural as well as visual effect, she would like to use the wires to hang the sculpture as sort of a string instrument. Her basic design involves vertically hanging two pieces of wire from two eye-hooks on the ceiling, then hanging the heavy sculpture from a horizontal bar from some point along the bar. The distance between two eye-hooks on the ceiling is the same as the total length of the horizontal bar.

  The aural effect that she would like to achieve is that when the wind blows across two vertical strings, they play a perfect fifth, i.e. the ratio of the frequencies of the two sounds is 3:2.

  Your friend tells you that she has been successful in hanging the sculpture but not in choosing the point along the bar to hang the sculpture giving the desired sound. Desperate for success, she knows you are taking physics and asks you for help.In 90 min you are due to meet her at the local coffee shop. What is your advice concerning the design of the sculpture. What notes will the two strings play with your design?

• 4. “Designing a Blood-Flow Meter.” You have a summer internship at a company that makes medical instruments. During medical surgeries, there is a need to measure the amount of blood flow through arteries that have been exposed by the surgery, but otherwise have not been cut. That is, blood is still flowing through these arteries.

  You know from your studies of biochemistry that blood contains a reasonable amount of both positive and negative ions. If you place a small magnetic field across the artery, then these moving ions would experience a magnetic force. Your company also manufactures a range of devices that can measure the electrostatic potential between two points.

  In 90 min you are due to meet with your boss. You need to sketch out a device that could provide the blood flow based on the measurement of the electrostatic potential across two points on the artery. Based on the model you develop, what electrostatic potential would you expect to observe? For the device to be practicable it needs to respond relatively quickly, so you should also estimate the order of magnitude of time it takes for the electrostatic potential to develop across two points on the artery.

• 5. “How Will the Utility Company Detect the Theft?” You are helping out during the summer at a relative’s farm. In one corner of the farm are some high-tension power lines. Having aced Phys 222, you know that each power line will be surrounded by a magnetic field that changes with time. You wonder whether you could use this to induce an emf in a coil, and use the induced emf to drive some of the farm equipment. To test this idea you construct multiple loops of wire and connect it to an AC voltmeter.

  In 90 min you are due to show your relative your loop, your measurements and an explanation of how this works. What induced emf will you measure? Your relative will also want to know whether this is really power for free, or how could the utility company detect the theft of this power.

1.2 Appendix B: List of resources available to students for Problem 1

Data

• a) dimensions of box (10 min)

• b) insulating properties of Styrofoam (10 min)

• c) amount of drinks, water (5 min)

• d) heat capacity of water, ice (5 min)

• e) latent heat of fusion of water (5 min)

• f) words describing temperature forecast for the day (10 min)

Physical Principles and Equations

• a) temperature increase and specific heat capacity (5 min)

• b) latent heat of fusion (5 min)

• c) equation of state of materials (5 min)

• d) zeroth law of thermodynamics (5 min)

• e) first law of thermodynamics (5 min)

• f) 2nd law of thermodynamics (5 min)

• g) Heat conduction (5 min)

• h) Heat convection (5 min)

• i) Heat radiation (5 min)

Diagrams

• a) sketch of box, including dimensions (10 min)

• b) graph of temperature forecast for the day (10 min)

Ask experts for advice

• a) How to plan a good picnic (10 min)

• b) How to solve a complex physics problem (10 min)

• c) How to setup a thermodynamic problem (10 min)