This is a collection of over 50 interactive calculus activities. These dynamic figures were created using GeoGebra for use on the LibreTexts platform. These figures are available to remix into any calculus custom textbook.
Type of Material:
Dynamic Figures. Learning objects are content items, practice items, and assessment items. These resources are self-contained, digital resources that can be used for learning, education or training. Learning objects can be organized to easily form collections of themed content, including traditionally designed courses.
Recommended Uses:
It can be used in the class lectures, group assessment, student presentations, and homework.
Technical Requirements:
Wave Browser, Internet Explorer, Microsoft Edge, or Google Chrome.
Identify Major Learning Goals:
The students will be able to visualize the calculus objectives and definitions by using the dynamic figures.
Target Student Population:
College undergraduate students. Stem students who are in calculus. Mathematics, engineering, and Physics Majors.
Prerequisite Knowledge or Skills:
I- The objectives of Calculus.
II- Understanding graphs of functions.
III- Comparing between different graphs.
IV- Following directions to make changes on graphs.
V- Making conclusions from the dynamic figures
Content Quality
Rating:
Strengths:
This is a collection of over 50 calculus visualization that can be embedded in any calculus textbook on the LibreTexts platform. Student will be able to learn calculus concepts in a much more interactive way than the static textbook. Here are some examples: Damped Spring Motion, Limits: Average and Instantaneous Rate of Change. The dynamic visualizes some main calculus objectives and definitions by using them and selecting to show results. Giving the formulas in some of them very helpful to see and apply. Continuity at a Point will show the limits from the left and the right with different δ. Intuitive Notion of the limit – One Sided Limits: This is a nice visualization of the limit from each side. It allows for the function to be changed for different type of limit explorations.
Concerns:
The Fundamental Theorem of Calculus II – Practical (Selecting different functions does not change the graph). The dynamics are not labelled and do not contain the functions. Therefore, the students will not be able to visualize and connect it the objectives. No summaries for the concepts and the graphs. The collection cannot be used without materials and the textbook. In addition, the dynamics do not give the students an option to practice. Limits: Continuity at a Point (for the different exercises you will not get the definite answer when selecting check, such as the following questions. Does the limit exist at x = 2? Is the function defined at x = 2? Is the function continuous at x = 2? Optimization: Function and Rectangle II: It shows the graph and the rectangle, but does not show the area of the rectangle, so it will not demonstrate the value of x that optimizes the area. Related Rates: Falling Ladder: It shows the line well, but does not show the values of x, h, nor is there an animation that shows dx/dt and dh/dt.
Potential Effectiveness as a Teaching Tool
Rating:
Strengths:
This collection will address the students who learn kinesthetically. As part of the textbook, students will be more engaged and more likely to continue using it. The dynamics and the graphs are very strong tool to visualize the learning objectives. It is built on prior concept that the students will lean in class and need them to be side to side with this module to understand the concepts.
Related Rates: Driving Car ( the graph of the distance is a prior concepts, the student will understand it if he remember the graph an properties)
Optimization: Getting Power to Island: this will provide a better visualization than just a static picture and will allow the students to see the relationship between the parameters and the optimization value.
Concerns:
Optimization: Triangle Circumscribing a Circle (Does not demonstrate the relationship between the concepts). Does not identify the prerequisite Knowledge. It is not a very effective tool to teach since the equations are not given. You cannot test the student’s knowledge. Therefore, is not easy to write an assessment that will really evaluate the student’s knowledge. The Module can not stand along without an attached Textbook. The module does not give the students practice opportunity. Related Rates: Driving Car (Will be helpful if given the formula and the objective, so the student will demonstrate the relationships between the concepts). It will need a long time to learn the concepts since the students need to find the corresponding objectives/ formulas and functions.
Ease of Use for Both Students and Faculty
Rating:
Strengths:
Many of the activities are simple enough to use by just clicking and dragging a point and watching the results. They are easy to use and easy to follow the directions. They are easy to see the changes in the graph by following the directions. If the textbook includes instructions, then the activity will be easy to use.
Concerns:
Most of the activities have no instructions provided. Without guidance from the instructor, many students will not be able to apply the activity to the concept that they are supposed to be learning. Some are not engaging for the students to understand the why, let the student apply their knowledge, and learn the calculations concepts behind them. Here the student only can be an observer.
Creative Commons:
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