This site provides users with interactive applet for exploring the intuitive notion of the chain rule.
In the applet we see an x-wheel, a u-wheel, and a y-wheel. You can change the speed of the x-wheel, and you can connect the wheels with belts and change their radii. You can use this model to explore the chain rule and try to get an intuitive understanding of where the formula comes from.
It asks the user several interactive questions and it also allows the user to cross the belt to explore the inverse relationship on the overall product.
It explains the chain rule with examples.
Type of Material:
Simulation
Recommended Uses:
Lecture Notes, assignments, or Handouts for Calculus I. Calculus I lab session activity.
Technical Requirements:
Any browser
Identify Major Learning Goals:
To provide students with an interactive applet to explore chain rule intuitively. In addition, students can practice their understanding of this material by checking the provided three examples.
Major Learning Goals are:
The user can interactively learn the intuitive notion of the chain rule.
The user can visualize the chain rule and its modus operandi by connecting the wheels with belts and by changing their radii.
It asks the users several interactive questions, related to the concept of the chain rule.
The concept of the chain rule is explained with examples.
Target Student Population:
High School, College Lower Division. Students of Calculus I course.
Prerequisite Knowledge or Skills:
College Algebra and Pre-Calculus
Content Quality
Rating:
Strengths:
This site provides an interactive applet about the chain rule using a wheel model to help users understand the chain rule intuitively. Users can change the speed of x-wheels, and they can connect the wheels with belts as well as they can change their raddi using the available options on the left-hand side of this applet. This site offers a great help for students of Calculus I who want to understand and practice the chain rule. This site can be included as a part of lecture or as an extra online tutorial for students. This site can serve a practice interactive example at the Calculus I lab session.
The user can interactively learn the intuitive notion of the chain rule.
The user can visualize the chain rule and its modus operandi by connecting the wheels with belts and by changing their radii.
It asks the users several interactive questions, related to the concept of the chain rule.
The concept of the chain rule is explained with examples.
Concerns:
None
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
Both instructor and student can use this site in the Calculus I class in lectures or assignments related chain rule.
You can use this model to explore the chain rule and try to get an intuitive understanding of where the formula comes from.
It asks the user several interactive questions and it also allows the user to cross the belt to explore the inverse relationship on the overall product.
It explains the chain rule with examples.
Concerns:
The number of rotation of x-wheel, u-wheel and y-wheel are shown at the bottom x=0, u=0 and y=0, which actually indicates the number of rotation of the wheel and has no relation with the wheel radius.
If the user enables the cross belt option, du/dx or dy/du or dy/dx turns negative. And if all the wheels are cross belt, the final product dy/dx turns positive. This can be confusing to the user unless it is explained by the instructor with examples.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
This applet is easy of use applet and very interactive. Students and instructors can access this applet easily, and they can choose one of the available options on the left-hand side of this applet. All they need is to follow all given instructions because these instructions provide step-by-step guidelines to understand chain rule intuitively. Students can practice chain rule using the three examples that have been provided under the applet.
Concerns:
None
Creative Commons:
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