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Velocity, acceleration, and students in motion
With CBLs, physics students can become the body in motion in their own experiments with acceleration and velocity.
By Nancy J. Easterly
For the eighteen years I have taught physics to juniors and seniors in high school, one of the most difficult concepts for my students to understand is the difference between velocity and acceleration. Students arrive in my class with preconceived ideas from incorrect observations about the world around them. Their observations are the same made by Aristotle over 2,000 years ago. For this reason, I try not to teach that they observed incorrectly, just that there are factors that they failed to take into account. They come to class thinking that you must be moving if you have acceleration. They do not realize that acceleration is the change in the speed and/or the direction of the object. They don't realize that an object can be temporarily stopped, yet also be accelerated. They don't realize that it is an unbalanced force that causes the acceleration.
    To attempt to change their thinking, I have thrown a ball in the classroom, painted visual pictures of the students driving down the highway, played videodisk demonstrations, discussed amusement park rides, had the students describe moving situations to me, yet the students tend to make the same conceptual understanding mistakes over and over again.
A second problem I have encountered is the inability of the students to see the connection between the concepts taught in their math class to physics and vice versa. Both classes cover graphing, equations, and properties of curves, but from different points of view. Math examines and manipulates the equations, fitting curves (or graphs) to a formula; physics relates each part of the equation to a physical quantity and uses graphs to identify trends in data to then write the equation describing the situation.
    To try to overcome both of these problems, last year the physics and precalculus teachers combined efforts and wrote a grant proposal to purchase a class set of calculator-based laboratory units (CBL's) with additional probes and an overhead projection unit. These instruments are fully portable and attach to a Texas Instruments-82/83/85 graphing calculator. The data can be downloaded to computers in the physics computer lab, and, in the future, to the computers in the precalculus classrooms. We are working now on ways to use the software collaboratively to actively reinforce each other's course.

Our collaborative effort began with excitement. One of the first laboratory activities I asked my students to do was to observe the characteristics of eight different graph families commonly used in both physics and precalculus. Using the computer, the students easily generated these graphs, making changes to the constant of proportionality, the y-intercept, or the amplitude and frequency, depending on the type of graph. Students began to see relationships between the manipulation and the shape of the graphs. Comments rang through the room as the students enthusiastically shared their discoveries: "Look, increasing the constant of proportionality makes the line steeper." "A negative constant means the line goes the other way." "Now I understand that changing the y-intercept means the starting point of the graph is changed." And, most important, perhaps, "This all makes sense!"
Teacher demonstrates CBL motion sensors
Marilyn demonstrates the CBL with motion sensors at a teacher workshop.
Though the technology helped the class understand certain concepts, it also precipitated the first misunderstanding created by students using similar technology in two different classrooms. Marilyn, a slightly disgruntled precalculus teacher, walked into the physics office during lunch.
    "We need to talk. I gave a quiz today and the majority of the students enrolled in both physics and precalculus missed a graphing question, while those enrolled only in precalculus got the question right. What are you guys teaching?"
    Earlier in the week, her students had performed an experiment obtaining the cooling curve for water as an example of a decay curve. The experiment was a great success--the students were excited to discover that this type of graph had real world relevance. The data obtained from the temperature probe and CBL was good and fit the characteristics of the curve perfectly. When the students left her room, she thought that they had mastered this concept.
    Unfortunately, the overall shape of the decay curve that the math classes obtained is similar to the shape of the hyperbola that was illustrated in my physics classes. By not making precise observations between the differences of these two curves during the physics graphing lab, the students made a quick evaluation based on the general shape without considering all of the characteristics. Teachers of both classes are now aware of this visual misconception. A new emphasis will be placed on observational skills as well as pointing out the similarities and differences between these two graphs by the teachers of both subjects. Technology not only created a problem, but helped the instructors solve the problem. If it had not been for the ability of the math teacher to recognize that only physics students were incorrectly identifying the curves, this misunderstanding would have been missed by the teachers of both subjects.

Once that issue was settled, I continued to use our technology to try to help the students better understand motion.
    "Look, there are toys in the physics lab. Hey, man, cool!" Toys to help teach physics? You bet! Playing with toy cars relieves the threatening feeling of the hard-core physics and mathematics, allowing the student to begin to see the relationships we have discussed in class. It also helps them realize that physics is everywhere. This physics computer laboratory activity involves hooking battery-operated cars to a smart pulley (computer-based probeware) to analyze the characteristics of constant velocity. The students print out graphs of displacement vs time, velocity vs time, and acceleration vs time. Slopes and areas are calculated and compared to the values read from the data tables. The students also study accelerated motion in the same way and compare the graphs between the two situations. The students really enjoy this lab, because they are beginning to see the relevance of physics to their lives.

Computer, monitor, and keyboard.
Using toy cars lessens the intimidation of hard-core physics.
Until last year we had no way to allow the students to experience what we are discussing in class. With the acquisition of the CBL equipment, the students are able to participate directly in experiments that mirror our class discussions. The new technology gives us the opportunity to involve the students in an activity that allows them to experience the motion while trying to match a motion graph. Graph-matching is a true test of understanding motion.
    To begin this activity, a student stands in front of a motion sensor, connected to the CBL and graphing calculator. A displacement-time graph is displayed on the calculator screen. At the signal, the student standing in front of the motion detector begins to move, trying to match the graph. The feedback to the participant and observers is immediate. The motion detector does not wait for the students to think about what they are doing. If the student hesitates, the match is incorrect. Others in the group are allowed to coach or help.
    The precalculus classes experimented on the very first day of school in August. Since no introductions were provided, the students completed the exercise by trial-and-error. The classes roared and cheered and ahhed as various students met with success and failure. Some students wanted to try again to do better. Everyone was a chairside coach. One result of this activity was total classroom involvement as students watch their friends. This event also piqued the interest of most students. It was an unqualified success.

I was eager to have my students repeat this activity, because I knew that having knowledge of velocity and acceleration would help the students match the graphs quickly and more accurately. Since the students had had so much fun in their math class with this activity, I was surprised when I met resistance. Students who had been involved with the precalculus activity earlier in the year started to fuss.
    "We've seen this before, why do we have to do this again? Do we h-a-a-ve to do this?" With the carrot of free time upon completion, and by pitting some of the more competitive students against each other, the students were quickly persuaded to repeat the activity.
    The competition in some groups was intense.
    "Look, James, you didn't even start out moving in the right direction . . . the line is going up instead of down! Get out of the way, I can do better."

    Some groups planned, others didn't. After observing the graph to be duplicated, one group of planners decided, "Okay, now you have to walk slowly toward the detector, stop for about 3 seconds and then go back faster to the starting point. Have you got it? Now, try!"
    The risk takers' conversation sounded more like: "Ready, get set, GO . . . Oh no, you went the wrong way, . . . faster . . . no slower . . . stop, now move farther away. Let's try again! slowly, now stop, wait, now move. One more time and I think we'll have it. Good job! I think it's a keeper."
    The students, who had tried this experiment earlier using trial and error in the precalculus class, were amazed at how much easier this activity was since they now knew the secrets of motion. All students in the lab successfully completed the activity. Much to my surprise (after all the whining), many also worked feverishly to answer the related questions before leaving the classroom for the day. From the activity and tone in the room, it was obvious a great deal of understanding had been achieved.


Two students standing in front of room.
Two students using the CBL to understand motion.
Being the object in motion allowed the students to experience fully what has been discussed in class. The lab activity took place in their frame of reference in real time. They had to actively think while the CBL was demanding their actions, resulting in a deeper understanding of motion. Most students recognized the value of this activity. Here are a few of their comments:
"Being part of the experiment instead of an observer allowed me to experience constant and accelerated motion."
"I now know how the precalculus formulae relate to real situations."
"I can't even walk down the hall, drive my car, or go anywhere without seeing the physics and mathematics involved."
"You made what I thought was going to be another dull, dry science class exciting."

I am so encouraged by the many different successes from using this technology, that I am already planning for next year. There is great potential for taking this equipment outside the classroom to examine other real world situations. The teachers involved are currently discussing a field trip to a local playground later in the year to let the students examine and determine the different types of motion that occur on swings, merry-go-rounds, slides, and rocking horses. As we become more confident with the operation of the equipment, we hope to use these devices to gather data at a commercial amusement park. So, if you drive by a playground with a bunch of big kids playing during school hours, stop and see if there's not a laptop computer where data from CBL's and graphing calculators is being stored to later examine in the classroom. Stop and ask some questions--you might be surprised by the enthusiasm of students explaining physics and precalculus to you!
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Link to Teacher testimony and to comments and suggestions for Nancy Easterly is a teacher in Houston, Texas. Read more about this author.

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