November 11, 2016

This learning cycle features 19 videotaped experiments, organized sequentially for introducing fundamentals of motion in introductory physics courses. Each video includes learning goal, prior information needed to understand the material, and elicitation questions. Topics include constant velocity, constant acceleration, falling objects, projectiles, and the physics of juggling. The instructional method is based on cognitive apprenticeship, in which students focus on the process of science by observing, finding patterns, modeling, predicting, testing, and revising. The materials were designed to mirror the activities of scientists when they construct and apply knowledge. See Related Materials for links to the full collection by the same authors and for free access to an article explaining the theoretical basis for this instructional method.

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Reason abstractly and quantitatively.

Analyze functions using different representations

Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.?

Graph linear and quadratic functions and show intercepts, maxima, and minima.

Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Build a function that models a relationship between two quantities

Write a function that describes a relationship between two quantities ?

Determine an explicit expression, a recursive process, or steps for calculation from a context.

Build new functions from existing functions

Identify the effect on the graph of replacing f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology. Include recognizing even and odd functions from their graphs and algebraic expressions for them.

Construct and compare linear, quadratic, and exponential models and solve problems

Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.