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Peer Review

Fundamental Theorem of Calculus: An Investigation

by James Rutledge


Overall Numeric Rating:

4.75 stars
Content Quality: 4.75 stars
Effectiveness: 4.75 stars
Ease of Use: 5 stars
Reviewed: Dec 19, 2012 by Mathematics
Overview: This site contains a ready-to-use Calculus module consisting of a “write-pair-share activity” that initially involves a model based on direct variation. The activity involves analyzing a function that describes eating speed in a hypothetical dinner table experience. Completing this project leads a user to a practical understanding of the Fundamental Theorem of Calculus. This activity is based upon a prequel entitled Calculus of the Dinner Table: Mathematical Modeling found at in which students construct the original mathematical model.
Type of Material: Assignment, drill and practice
Recommended Uses: Can be used in either a small class or a large lecture setting. Students participating in the activity will be divided in small groups.
Technical Requirements: Works an every browser. However, if students use the Mathematics Visualization Toolkit, they will need the latest version of Java and/or Flash.
Identify Major Learning Goals: The major learning goals of this module are to enable students: (a) exercise their mathematical modeling skills; (b) develop a deeper understanding of the Fundamental Theorem of Calculus; (c) apply calculus concepts to pseudo-real-life experiences;(d) recognize the role and importance of with an anti-derivative.
Target Student Population: Calculus I or Calculus II students.
Prerequisite Knowledge or Skills: Calculus I.

Evaluation and Observation

Content Quality

Rating: 4.75 stars
Strengths: This module contains a project that is meant to be done by small student teams. The project is based on use a mathematical model created in the prequel to this activity entitled Calculus of the Dinner Table: Mathematical Modeling (see the description for the exact reference). In the current module students use the First Fundamental Theorem of Calculus to perform the required activity. The main idea and the goal of the project is to develop a deeper understanding of the Fundamental Theorem of Calculus and the concept of the anti-derivative. Special attention is paid to the meaning of the constant of integration and its connection to initial conditions of the problem. The link between the area under the curve of the original function and the linear difference between the pertinent values of the anti-derivative function also becomes highlighted when the activity is completed.
Concerns: Even though students should have sufficient knowledge to understand the concept of anti-derivative, some information regarding perquisite knowledge should be provided to help stimulate the students understanding.

Potential Effectiveness as a Teaching Tool

Rating: 4.75 stars
Strengths: The site clearly explains the intended use of the project, provides a suggested format and time frame, and even recommends the size of the class and a student group to work on the project. It is a ready to use learning module that any instructor can start using immediately just by following the instructions provided. The site also contains teaching notes and tips and recommends assessment. All this makes the module pedagogically sound.
Concerns: One concern could be the limited information as to what specifically is the prerequisite knowledge needed for learners to be successful at this activity.

Ease of Use for Both Students and Faculty

Rating: 5 stars
Strengths: Any instructor can start using this module immediately. It is well thought out and organized. The instructions very easy to follow. There is also a link to a graphing tool (MVT) which is conveniently provided in the module. Several instances of interactivity can be manifested. Students are interacting with each other, the instructor is interacting with the students by summarizing the findings and clearly the students are interacting with the instructor by presenting their work.
Concerns: A direct hyperlink to the prequel of this project would very helpful. Other interactive software could perhaps be used in addition to the Mathematics Visualization Toolkit.