Modeling Oscillating Systems: Physics Component Teaching Strategies |

Most of the lessons in this module reflect the teaching strategies engaged in by the authors. Specifically, the authors are interested in conceptual learning and techniques which produce conceptual change. Students who are successful in a traditional physics class still may possess naïve physics conceptions. This module incorporates several teaching strategies and types of assessment which have been used by various programs to improve and assess student conceptual learning.

The initial exploration activity illustrates the different approach taken in this module.Each team of students is encouraged to explore a different system and then the students share the results of their investigation with the class.This technique is known as white-boarding in some projects, but students could use a variety of media to share.The key feature of this strategy is the peer interaction component.Students are encouraged to discuss their results with each other.The teacher acts as moderator and guide, focusing the discussion when necessary but not serving as a direct source of information.

During the laboratory investigations, the teacher should provide minimal direction. Rather, the investigations should be student driven. Given the basic tasks to be performed and assuming the students have sufficient experimental procedure prior to this point, they should be able to design and conduct these simple experiments without a step-by-step set of directions.

The authors believe that students learn best from models they build themselves rather than using pre-built models.Prior to this unit the students will have built several models to illustrate simple kinematics concepts as well as a basic force model and some applications of force models.By the time they reach this unit, they should be quite adept at identifying the new elements needed in the model and the output desired.

Another strategy used by one of the authors is to have the students develop a rubric. Given the task of determining the factors which influence the period of a pendulum and then presenting their findings to the class, the students developed a rubric that the class and teacher could use. The rubric was used to evaluate both the rigor of their investigation and the quality of their presentation. As they performed the experiment and prepared their presentations with the rubric in front of them, the students were better able to meet the requirements of the task.

Another strategy that teachers might use during this module to evaluate student conceptual understanding is based on Mazur’s Peer Instruction model. While Mazur primarily uses the method in lecture to address 3 or 4 concepts, one author has used a similar approach to check student understanding. After the initial discussions about oscillatory motion and Hooke’s Law, on subsequent class days, the instructor may place a multiple-choice question designed to test conceptual understanding on the overhead. Students hold up cards with their choice of the correct answer and the instructor quickly assesses the percentage of the class which has the right answer. If that number is above 80%, the instructor verifies the correct answer and has a student explain the reasoning to the class so the other 20% know why they are wrong. If the number is below %40 the instructor explains the correct answer and illustrates the concept with further examples. Between 40 and 80%, the students engage in peer instruction, discussing with their seat- mates the problem and the correct choice. After a suitable time, the instructor asks the students to hold up their cards again with their revised choice of an answer. This is followed by a short class discussion and then the students are asked a related question. In the author’s opinion, this technique was a major contributing factor to student success on end-of-course exams.

As mentioned above and in other places within this module a major concern is the preconceptions which students bring to the classroom and whether or not a particular lesson or unit is successful in guiding students to a content appropriate way of thinking about the concepts. The design of this module and the teaching strategies listed above reflect the authors’ current understanding of potentially successful strategies for revealing student preconceptions and addressing them. Here is a list of some of the student preconceptions which may be addressed by this module. Teachers should keep these conceptual understandings in mind when they design assessments. At the beginning of each section, the source of the list is identified. Full references can be found in the references and resources section.

**Project Galileo - NSF 1998 Faculty Enhancement
Conference**

Teaching Introductory Physics, Conservation Laws First

Documented Student Difficulties

- KINEMATICS
- Recognizing the difference between average and instantaneous velocity.
- Understanding the physical significance of the sign of a body’s velocity.
- Making, using and interpreting graphs with time as the variable plotted on the x-axis.
- Connecting the motion of a real object to "model" motion (e.g. motion of a point within a coordinate system): a person is a moving object with extensions and moving parts in different directions. So in order to describe a person’s motion, simplifying assumptions must be made; either focus on a best practical point on the person or an average point. Thus a person’s motion is most usefully represented by the motion of a well chosen point, for example your navel.
- Kinematical quantities can change depending upon when and how often we do the measurements.

- FORCE
- Students expect that forces are associated with movement (so no movement means no forces) and are "active" (passive forces, such as the normal force, are not recognized).
- All motion, including constant-velocity motion, is sustained by a "force of motion"; speed is proportional to force.
- Forces are properties of objects, rather than manifestations of interactions between objects; for example, weight is a property of an object, rather than reflecting the force of gravity between the Earth and the object.
- Only living things can exert forces on other things.
- All forces are mediated through contact; forces cannot be exerted between two things if they are not in contact.

**C3P Student Preconceptions**

- KINEMATICS
- Acceleration and velocity are always in the same direction.
- Velocity is a force.
- If velocity is zero, then acceleration must be zero too.

- NEWTON'S LAWS
- There is no connection between Newton's Laws and kinematics.
- The product of mass and acceleration, ma, is a force.
- Only animate things (people, animals) exert forces; passive ones (tables, floors) do not exert forces.
- A force applied by, say a hand, still acts on an object after the object leaves the hand.

- HARMONIC MOTION
- The period of oscillation depends on the amplitude.
- The restoring force is constant at all points in the oscillation.
- The heavier a pendulum bob, the shorter its period.
- All pendulum motion is perfect simple harmonic motion, for any initial angle.
- Harmonic oscillators go forever.
- A pendulum accelerates through lowest point of its swing.
- Amplitude of oscillations is measured peak-to-peak.
- The acceleration is zero at the end points of the motion of a pendulum.

FORCES AND MOTION

- A rigid solid cannot be compressed or stretched.
- Only animate objects can exert a force. Thus, if an object is at rest on a table, no forces are acting upon it.
- Force is a property of an object. An object has force and when it runs out of force it stops moving.
- The motion of an object is always in the direction of the net force applied to the object.
- Velocity is another word for speed. An object's speed and velocity are always the same.
- Acceleration is confused with speed.
- Acceleration always means that an object is speeding up.
- Acceleration is always in a straight line.
- Acceleration always occurs in the same direction as an object is moving.
- If an object has a speed of zero (even instantaneously), it has no acceleration.

Pendulums

- Mass ("weight") is the primary factor determining the period of a pendulum.
- Some students will believe the pendulum with the light bob moves faster while others will believe the heavier one will move faster.
- In fact, the speed depends on both the effective length and the angle of deflection.
- The string length alone is the important contributor that determines the period of the pendulum.
- What the pendulum is made of determines the period of the pendulum.
- The period of the pendulum is the same as how long it swings before it stops.
- The shape of the pendulum determines its speed.
- Some students cannot distinguish the effects of gravity, air resistance, and friction from factors that affect the period of the pendulum.