Chapter 2 The description of motion* in one dimension.

Chapter 2 The description of motion* in one dimension. What sort of motion is referred to? Describe the motion of the cart?, cart’s front right wheel?

Chapter 2 The description of motion* in one dimension. *translational motion of objects (as the motion of a specified point) or the motion of any point

Introduction: Our approach Preliminaries –definitional –historical –cognitive Representations of motion –visual –mathematical Exploring uncertainty Modeling motion Wrap-up

Preliminaries What is and isn’t translational motion? Galileo’s revolutionary description of motion (without a center of the universe) Begin with a look at what we will know –the summary review in the Study Guide A closer look at knowing (more later) –Received knowledge –Subjective knowledge –Procedural knowledge –Constructed knowledge

Representation of motion - 1 Visual representations of motion –different positions at different times (always with respect to a frame of reference) [next] –strobe view ranking tasks –motion diagrams –motion graphs (conceptual, not a picture) Visual language can provide a starting point for understanding &q=lexus+commercialhttp://video.google.com/videoplay?docid= &q=lexus+commercial

Representation of motion - 1 Visual representations of motion –different positions at different times (always with respect to a frame of reference) [see][see] –strobe view ranking tasks ranking tasks –motion diagrams? –motion graphs? (conceptual, not a picture) Visual language can provide a starting point for understanding &q=lexus+commercialhttp://video.google.com/videoplay?docid= &q=lexus+commercial

Representation of motion - 2 Mathematical representations provide clarity and precision about position, velocity, acceleration in one dimension. –vectors in general –vector quantities in one dimension –instantaneous and average values –slope function = derivative –questions (brain storm/prioritize/ask) Real motion –prediction and observation ILDs

Representation of motion - 3 Constant velocity motion –examples, graphs, equations Constant acceleration motion –examples, graphs, equations Exercises –(+,-,0 ) x, v, a –shapes of motion graphs –same data? Looking at the mathematical functions –

Representation of motion - 4 Problem solving and representing motion –problem solving quotequote Class activity: Time to second bounce –begin, then continue in following days Same data run? (exercise) Changing acceleration motion –auto performance example Exercise Insight into car commercial (If time) Exploring Uncertainty (Group Lab)

Modeling motion (numerical integration) Modeling language (Stella) Working backwards from “rate of change” –numerical integration –like skipped part of chapter

Wrap-up (Along with finishing Class Activity) What questions do we have? –questions (brain storm/prioritize/ask) Looking at our ways of knowing kinematics –questions (brain storm/prioritize/ask) Motion we could now describe?

the end

Note on problem-solving “Representation entails more than a direct or literal translation of a problematic situation into a mathematical model such as a formula or a diagram. When engaging in representing, problem solvers imagine a visual story – one that is not always or necessarily implied by the problem formulation. They impose that story on the problem, and, acting on this representation, they derive from it the sought solution (Arcavi 2003).” from Mathematics Teacher vol. 101, no.5. backback