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Peer Review

Exponential Growth: A Detailed Look

by James Rutledge


Overall Numeric Rating:

4.75 stars
Content Quality: 4.75 stars
Effectiveness: 4.5 stars
Ease of Use: 4.75 stars
Reviewed: Jan 22, 2013 by Mathematics
Overview: This site contains a pedagogical module consisting of a ConcepTest and a write-pair-share activity involving Florida's population growth. The activity is designed to develop a better conceptual understanding of exponential growth in general and recognize its progressive nature.
Type of Material: The learning activity can be used as an assessment, assignment, or a developmental tool.
Recommended Uses: Homework or in class group work.
Technical Requirements: Works an every browser.
Identify Major Learning Goals: Investigate through data and develop better understanding of exponential growth. Learners will gain further insight into the dynamics of exponential growth by working with population data.
Target Student Population: College Algebra and Liberal Arts Mathematics students.
Prerequisite Knowledge or Skills: Basic understanding of exponential function.

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 activity asks students to decide whether a ten-year growth rate can be divided by 10 to produce the corresponding annual growth rate for each of the ten years. The results show that, while students may have learned that exponential growth is a multiplicative process, their conceptual understanding concerning exponential growth may not be sufficient. The project is based on a graph of Florida's population growth from 1960-2000 along with data that include ten-year growth rates for each decade. The site also has a link to an online tool for investigating U.S. demographic. Students are given a Concept Test and then are asked to discuss the test results and underlying reasoning in a write-pair-share activity. In conclusion, the instructor asks students to share their results and presents the correct answer along with an explanation of how exponential growth progresses through the ten-year period. As a result of the project students are brought to a realization that exponential growth at a given rate produces increasingly larger results as time goes on. The design of the activity promotes active learning. Students are actively learning independently as well as collaboratively with their peers. In addition, students will make that real – life connection with exponential growth.
Concerns: Prerequisite knowledge is unclear. The activity suggests that it is appropriate for college algebra or liberal arts math students. However, the level of learning is still unclear. Based upon personal experience, learners will need to have some knowledge about functions as well as operations on exponents.

Potential Effectiveness as a Teaching Tool

Rating: 4.5 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. The instructor's concluding explanation ensures that students recognize the progressive nature of exponential growth and develop their understanding of the exponential growth process. The teaching materials and notes are concise, to the point and easy to follow.
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: 4.75 stars
Strengths: Any instructor can start using this module immediately. It is well thought out and organized. The instructions very easy to follow. The author did a great job in ensuring the ease of use. 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: Other interactive software could perhaps be used to tally students’ decisions and present them to the class, especially in the case of an online environment where their “neighbors” might not be necessarily sitting next to them.