Graph Predictions for Position, Velocity and Acceleration

• Learn to make and interpret position, velocity and acceleration graphs.
• Begin understanding the relationship between them.
• Be prepared for maximum benefit from guided discovery lab or Interactive Lecture demonstration on the topic.

Educational level & setting: High school or introductory college introductory Physics studying 1-D kinematics. These Just-in-Time-Teaching pre-class questions are designed to be used before the class in which students will investigate position, velocity and acceleration graphs using a guided discovery laboratory (e.g. RealTime Physics Module 1 labs 1 & 2) or interactive lecture demonstration.
Time required: 5-10 minutes in class,
System requirements: Students need to be able to submit JiTT questions over the web via a learning management system (LMS) that supports SCORM packages, WebAssign, or a locally managed system for collecting JiTT responses.

There are four sets of questions to be posted for students to complete before class. They deal with:

• Position graphs while moving at a constant velocity
• Velocity graphs while moving at a constant velocity
• Velocity graphs while changing velocity at a constant rate
• Acceleration graphs while changing velocity at a constant rate

Expand the appropriate link below to on how to obtain the exercise depending on your format.
These should be made available to students several days in advance of the class or laboratory that students will carry out a guided discovery laboratory or participate in an Interactive Lecture Demonstration dealing with the respective types of graphs. In some classes, two sets will be appropriate for a given class and both may be assigned. One or two days before the first activity is due, the instructor should demonstrate in class how to draw graphs on one example by clicking to place points.

After students have submitted responses, get a list of the textual responses/feedback from your system.

• HTML JiTT page: Collect the values of the (hidden) form elements named "ans_n_feedback"??? where n is an integer (unless you modified input names).
• WebAssign: Go to the score page for that assignment and select "Download" and then check the box "Responses." You will get a spread sheet with usernames, assignment scores, and assignment responses. For each of the graphs on the assignment, there will be three columns: one with a '1' or a '0', one which is a string of numbers separated by commas and semicolons, and one that contains short text statements. Copy the last one for each question.
• LMS: Different systems allow access to student data through different pages, so you will have to figure out how yours is configured. Internally the values are stored with a key "cmi.interactions.n.student_response" which may be useful in finding them. Caution: some systems allow see responses only student by student, so collecting the entire set of class responses can be a time-consuming task.

Once you have downloaded the set of student responses for one question, paste those values into the first column on the data sheet of the Excel template provided, replacing the data with "AAA," etc. Go to the chart sheet and refresh data (red exclamation mark), and copy the graph to whatever document you will use in the beginning of class, and repeat for each question. (If copying to MS Word, use "Paste Special"??? to paste a picture instead of an Excel Chart object). Also select relatively articulate open-ended explanations that represent the different popular choices on each of the questions.

At the beginning of the class or laboratory, show students the chart and briefly discuss with students, trying to get then to think about the reasoning behind all the main choices, so that when they do the activity, they will realize what the graph the see means.

Excel template for creating graphs from student responses (Excel 11kB Jul16 07)

When you present this in class, try not to "give away" the answer by clearly favoring the "correct" prediction--you really want to try to get the students pondering and discussing it, not be confident that they already know the right one due to clues from the teacher. Instead, use student responses to describe the different options, and perhaps point out consequences. For example, on the constant velocity predictions, the most popular "wrong" answer will probably be a upward sloping graph, which is what the position graph would look like. You might want to point out that that implies that is really no difference between a velocity graph and a position, and then go on without indicating that is not the case--just leave the students who chose that response a little uneasy so that they will be ready to pay close attention to the upcoming laboratory or ILD activity.

There are several levels of assessing this activity when used in conjunction with a guided discovery laboratory or a ILD. The direct assessment for this activity will be the prediction graphs on the ILD or guided discovery lab. For the student, seeing the result of the experiment will be a strong formative assessment, which will be reflected in the final graphs/observations in the ILD or laboratory.

Examples of discovery laboratories to use following this activity can be found in the first two laboratories of: Sokoloff, D.R., R.K. Thorton, and P.W. Laws, RealTime Physics: Active Learning Laboratories Vol. 1. 1999, New York: John Wiley & Sons.

Interactive Lecture Demonstrations on this topic can be found in Sokoloff, D.R. and R.K. Thorton, Interactive Lecture Demonstrations, Active Learning in Introductory Physics. 2006, New York: John Wiley & Sons.