written by
Ronald K. Thornton and David R. Sokoloff

This tutorial for conceptual physics asks students to predict the appearance of distance and velocity graphs for different types of walking motion, then verify their predictions with a motion sensor. If all members of the cooperative group predict correctly, the group moves to the next problem. If not, the group's task is to analyze the error to see what went wrong, then write statements about how to modify incorrect ideas to avoid the same mistake in the future.

This tutorial was developed by the University of Maryland Physics Education Research Group (UMPERG). It is based on Tools for Scientific Thinking, a microcomputer-based laboratory curriculum for student development of concepts and intuition in the laboratory.

Editor's Note:See Related Materials for a link to the full index of Sense-Making Tutorials and for an editor-recommended simulation-based lab on graphing motion.

6-8: 4F/M3a. An unbalanced force acting on an object changes its speed or direction of motion, or both.

9-12: 4F/H8. Any object maintains a constant speed and direction of motion unless an unbalanced outside force acts on it.

9. The Mathematical World

9B. Symbolic Relationships

6-8: 9B/M2. Rates of change can be computed from differences in magnitudes and vice versa.

6-8: 9B/M3. Graphs can show a variety of possible relationships between two variables. As one variable increases uniformly, the other may do one of the following: increase or decrease steadily, increase or decrease faster and faster, get closer and closer to some limiting value, reach some intermediate maximum or minimum, alternately increase and decrease, increase or decrease in steps, or do something different from any of these.

9-12: 9B/H4. Tables, graphs, and symbols are alternative ways of representing data and relationships that can be translated from one to another.

Common Core State Standards for Mathematics Alignments

Functions (8)

Use functions to model relationships between quantities. (8)

8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

High School — Algebra (9-12)

Creating Equations^{?} (9-12)

A-CED.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions, and simple rational and exponential functions.

High School — Functions (9-12)

Interpreting Functions (9-12)

F-IF.4 For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities, and sketch graphs showing key features given a verbal description of the relationship.^{?}

High School — Statistics and Probability^{?} (9-12)

Making Inferences and Justifying Conclusions (9-12)

S-IC.2 Decide if a specified model is consistent with results from a given data-generating process, e.g., using simulation.

Common Core State Writing Standards for Literacy in History/Social Studies, Science, and Technical Subjects 6—12

Text Types and Purposes (6-12)

1. Write arguments focused on discipline-specific content. (WHST.11-12.1)

This resource is part of a Physics Front Topical Unit.

Topic: Kinematics: The Physics of Motion Unit Title: Graphing

Unique approach based on a prediction model of learning. Students predict the appearance of distance and velocity graphs for different types of walking motion, then verify their predictions with a motion sensor. If all members of the group predict correctly, they move to the next problem. If not, the group's task is to analyze the error to see what went wrong, then write statements to modify incorrect ideas. Lesson was designed using evidence from physics education research (PER).

<a href="https://www.compadre.org/precollege/items/detail.cfm?ID=11965">Thornton, Ronald, and David Sokoloff. Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs. 2003.</a>

R. Thornton and D. Sokoloff, Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs (2003), <http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf>.

Thornton, R., & Sokoloff, D. (2003). Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs. Retrieved December 11, 2023, from http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf

Thornton, Ronald, and David Sokoloff. Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs. 2003. http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf (accessed 11 December 2023).

Thornton, Ronald, and David Sokoloff. Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs. 2003. 11 Dec. 2023 <http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf>.

@misc{
Author = "Ronald Thornton and David Sokoloff",
Title = {Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs},
Volume = {2023},
Number = {11 December 2023},
Year = {2003}
}

%A Ronald Thornton %A David Sokoloff %T Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs %D 2003 %U http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf %O application/pdf

%0 Electronic Source %A Thornton, Ronald %A Sokoloff, David %D 2003 %T Tutorials in Physics Sense-Making: Catching Mistakes: The Case of Motion Graphs %V 2023 %N 11 December 2023 %9 application/pdf %U http://www.physics.umd.edu/perg/OSTutorials/01_Position_and_Velocity/Tutorial_01_X_and_V.pdf

Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

This digital graphing activity accepts user inputs in creating "prediction graphs", then provides real-time animations of the process being analyzed. Learners annotate graphs to explain changes in motion.