Here is a typical problem tackled by students in the newest course in the FOSS middle school program, Force and Motion. How do we prepare students to think through this problem effectively?

It took Clancey 10 minutes to ride his skateboard 2 kilometers down the hill to Richie’s house. They played Claw on the computer for 20 minutes. It took Clancey 20 minutes to walk back home up the hill. Make a data table and two graphs to show Clancey’s movement.

This is a typical problem tackled by students in Investigation 4 of the newest course in the FOSS middle school program, Force and Motion. How do we prepare students to think through this problem effectively?

The course starts with the basic concept on which the whole vast and colorful family of interactions we recognize as motion depends: the concept of position. At any given moment in time, every object must be someplace. That someplace is the object’s position. Change of position defines distance and displacement. Speed and velocity are functions of distance and displacement per unit time. Change of velocity per unit time is acceleration.

These are simple concepts in colloquial conversation. The multiple meanings and loose definitions are perfectly fine for casual use. These same concepts are difficult when considered within the rigorous constraints of physics. Precise definitions and complete, accurate, conventional, and intellectual constructs associated with these concepts are the lingua franca (or common language) of Newtonian physics.

When students have built a solid knowledge base around motion, the curriculum turns to the agent responsible for change of motion, force. Force is abstract and illusive, but its effects can be readily observed. The course concludes with a brief excursion into momentum and impulse.

Back to Clancey... in the Clancey problem, students need to understand and apply several concepts.

- Clancey’s adventure involves three separate motion/time events. These are identified as legs.
- Clancey has an initial position (xi) and a final position (xf) for each leg.
- Change of position yields two pieces of information: Total distance traveled (like on an odometer) and displacement from a starting position. Clancey traveled a specific distance (d) during each leg, which can be calculated using the equation d = xf –xi. Distance is the magnitude of the change of position, so it is always positive. Displacement (∆x) is calculated using the equation ∆x = xf –xi, but the change of position can be positive or negative, depending on direction.
- Distance per unit time is speed. Speed (v) is calculated using the equation v = d/∆t.
- A two-coordinate graph can be an effective way of representing a relationship between two variables, such as time and position or time and distance.

These concepts are developed carefully and thoroughly in Investigations 1–3. Clancey appears in Investigation 4. Students first organize the data given in the problem in a table. The given data look like this.

Leg | t (min.) |
x (km) |
∆t (min.) |
∆x (km) |
d (km) |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | ||

1 | 10 | 2 | |||

2 | 30 | 2 | |||

3 | 50 | 0 |

Next, students fill in the rest of the table with derived (calculated) data, which look like this.

Leg | t (min.) |
x (km) |
∆t (min.) |
∆x (km) |
d (km) |
---|---|---|---|---|---|

0 | 0 | 0 | 0 | ||

1 | 10 | 2 | 10 | 2 | 2 |

2 | 30 | 2 | 20 | 0 | 2 |

3 | 50 | 0 | 20 | -2 | 4 |

This table exposes some important fundamental concepts. Leg 1 is straightforward. In 10 minutes Clancey moved from a position at 0 km to a position at 2 km in the positive direction. The change of time from initial time (ti) to the final time (tf) was 10 minutes, the change of position (∆x) was 2 km, and so was the distance.

Leg 2 is a little more interesting. Here, Clancey played Claw on the computer for 20 minutes. Time marched on, so at the end of the Claw session, 30 minutes had passed. His position, however, did not change; it was still 2 km. By extension, the change of time for Leg 2 was 20 minutes, the change of position was 0 km, and the distance was still 2 km.

Leg 3, the motion home, ended when 50 minutes had passed, and Clancey was back home at 0 km. Again, by extension, the change of time from the start of Leg 3 to its end was 20 minutes, the change of position was 2 km in the negative direction, and the total distance traveled at the end of Leg 3 was 4 km.

Visual representations of the outing can be rendered in two-coordinate graphs, as either a position graph, which shows where Clancey is throughout his trip, or a distance graph, which shows how far Clancey has traveled throughout his trip.

Similar attention to detail and precision is found in introductions to acceleration, force, gravity, and momentum.

The theoretical concepts and the logical/mathematical thinking come to life when students conduct experiments. Investigating functions of time and position requires instrumentation that allows students to acquire time and position data. To this end, the FOSS development staff teamed with Marshall Montgomery, Matthew Gilliland, andGrant Gardner to develop a simple breakthrough in the acquisition of these data, the FOSS electronic Dotcar™.

The FOSS electronic Dotcar is a freerolling car fitted with a phototransistor that monitors changes in reflective quality ofa black-and-white-striped drum attached to the car’s axle. After making an untethered run, data stored in the microprocessor on the car are downloaded to a classroom computer for display. Position data in tenths of a centimeter are displayed every tenth of a second throughout the run. These data can then be transformed into average velocity, instantaneous velocity, acceleration, and a host of other useful results.

The Force and Motion Course was developed for sixth and seventh graders, but it will find a home in many eighthand ninth-grade classes as well. The math in the course will be challenging for sixth graders from acceleration onward. Science teachers might want to team with the math teacher when possible. But the course can be equally challenging for ninth graders if every opportunity for inquiry into basic physics is pursued.

Students engage in a variety of different encounters with the concepts introduced in this course. Students are physically active, experiencing change of position by moving from one place to another. They calculate their own speed over a measured distance with stopwatches. They run two separate tracks, hitting numbered marks on consecutive seconds—one representing a constant velocity of 0.5 meters per second, and the other representing a constant acceleration of 0.5 meters per second per second. And they push and pull on all sorts of things to develop a sense of force/mass interactions. Students have extensive direct, firsthand kinesthetic experience with fundamental concepts in Newtonian physics.

Students conduct experiments with mechanical and electronic Dotcars to gather immediate and accurate time and distance data for analysis. They fly planes, time rolling cars, compare acceleration of cars of different masses, and lift loads under different friction conditions to advance their understanding of fundamental Newtonian concepts.

Students work with several interactive multimedia programs to exercise and extend the basic concepts. The Photo Finish simulation, involving calculating head starts for racers that run at different speeds, is of high interest to students. The Force Bench is a simulated laboratory environment where students can manipulate variables to investigate fundamental principles that underlie all force and motion interactions. The bench can be operated in a frictionless environment, bringing clarity to the F = ma equation.

And finally, there are lots of opportunities for problem solving, like the Clancey outing, using concepts and understandings introduced in the activities. These often have a significant mathematical component, either in the areas of calculation, proportionality, graphing, or simple algebra.

Delta began shipping the Force and Motion Course in January. Contact your regional FOSS representative to test drive a Dotcar and give your students a chance to experience force and motion the FOSS way.