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Briefing Document: "Graphs of Quadratic Functions of the form +/- (x -a)(x-b) : Self Assessment HTML5 JavaScript Simulation Model"

1. Overview

This document focuses on a specific interactive resource: a self-assessment HTML5 JavaScript simulation model designed to help users understand graphs of quadratic functions in the form +/- (x - a)(x - b). It's hosted by Open Educational Resources / Open Source Physics @ Singapore and is part of a larger collection of educational simulations. The primary purpose of this resource is to provide a hands-on learning experience for students studying mathematics, particularly functions and graphs, equations, and inequalities. The simulation allows for manipulation and exploration of quadratic functions.

2. Key Themes and Ideas

• Interactive Learning: The core idea is to leverage interactive simulation for learning. The resource isn't just static text; it's a dynamic tool that users can engage with to see the effects of changing parameters on the graph of a quadratic function.
• Focus on a Specific Quadratic Form: The simulation is tightly focused on the form +/- (x-a)(x-b), which directly relates to the roots (x-intercepts) of the quadratic. This allows users to directly see how changing 'a' and 'b' shifts the parabola horizontally, and how the +/- affects concavity.
• Self-Assessment: The resource is designed for self-assessment, suggesting that users can check their own understanding through their interactions with the simulation.
• HTML5 and JavaScript: The technology used (HTML5 and JavaScript) indicates that the simulation is intended to be accessible via web browsers, without requiring additional plugins. This makes it highly accessible on a variety of devices.
• Open Educational Resource: The resource is clearly an Open Educational Resource (OER), which means it's designed to be freely available for educational purposes, promoting equitable access to learning materials. It's licensed under a Creative Commons Attribution-Share Alike 4.0 Singapore License.
• Part of a Larger Ecosystem: This specific tool is part of a much larger collection of simulations hosted by Open Educational Resources / Open Source Physics @ Singapore. The large list of links and resources on the page indicates that this is a hub for various learning tools spanning multiple scientific and mathematical disciplines, as well as different educational levels.

3. Important Facts & Details

• Location: The resource can be found embedded within the provided webpage, at the provided URL.
• Technology: The simulation is developed in HTML5 and JavaScript.
• Licensing: It uses a Creative Commons Attribution-Share Alike 4.0 Singapore License, but commercial use of the underlying EasyJavaScriptSimulations Library requires a separate license and contact with its developers.
• Author: The author's name isn't explicitly given but can be inferred from the links included to other simulations and workshops where authors and presenters are named.
• Target Audience: The resource targets mathematics learners studying functions and graphs.
• Related Resources: The sheer volume of links to related materials on the page point to a vast library of simulations, workshops and research projects that relate to the use of interactive simulations for teaching science and math concepts. This is not just a single resource but part of a larger project. The related links suggest that similar tools may have been used in other educational settings. For instance, some entries suggest the use of simulations for use in Teacher Training workshops (TRASI, etc) as well as use in classrooms, and in other events.
• The simulation was created using Easy JavaScript Simulations (EJS) tool: which is a Java program for constructing interactive simulations.

4. Notable Quotes/Information:

While the source doesn't contain any long quotes from itself, the entire page serves as a context for the nature of the resource itself. The license details are important to note:

"Contents are licensed Creative Commons Attribution-Share Alike 4.0 Singapore License . Separately, for commercial use of EasyJavaScriptSimulations Library, please read https://www.um.es/fem/EjsWiki/Main/EJSLicense and contact fem@um.es directly."

This statement indicates the open nature of the materials but also clarifies the stipulations of using the underlying library commercially.

5. Implications and Recommendations:

• Instructional Use: The simulation is well-suited for classroom use, homework assignments, or independent study. It can help students visualize the relationship between the factors of a quadratic equation and the resulting graph, and check their own understanding.
• Further Exploration: The wealth of related resources on the site suggests there are numerous other simulations that can be incorporated into a broader educational curriculum covering multiple STEM fields.
• Teacher Training: The mention of multiple workshops suggests that teacher training and development are a strong focus of the OER / OSP Singapore program.

6. Conclusion

The "Graphs of Quadratic Functions of the form +/- (x -a)(x-b) : Self Assessment HTML5 JavaScript Simulation Model" is a targeted and accessible interactive tool for learning about a key aspect of quadratic functions. Its focus, combined with its open nature and context within a large ecosystem of similar resources, makes it a valuable asset for math educators and learners. The focus on visual understanding through dynamic manipulation should be very helpful for students. The breadth of the site and associated initiatives reveals a large effort devoted to using interactive simulations to teach scientific and mathematical concepts at various levels.

Quadratic Functions Study Guide

Quiz

Instructions: Answer the following questions in 2-3 sentences each.

1. What is the general form of a quadratic function being explored in the provided simulation model?
2. What are the parameters 'a' and 'b' related to in the quadratic function of the form +/- (x -a)(x-b)?
3. How does the +/- sign in front of the quadratic expression affect the shape of the graph?
4. What is one way this interactive model could help students better understand quadratic functions?
5. How does the simulation model use JavaScript?
6. What is one example of a related resource provided in the list?
7. What is the significance of the term "Open Educational Resources" in the context of this simulation?
8. What does the term "HTML5" mean in the context of the simulation model?
9. What does the listed Creative Commons license indicate about the use of the materials?
10. Why might a teacher find this simulation a useful tool in their math class?

Quiz Answer Key

1. The general form is +/- (x -a)(x-b). This form highlights the x-intercepts (roots) of the quadratic function.
2. The parameters 'a' and 'b' correspond to the x-intercepts (or roots) of the parabola where the graph crosses the x-axis.
3. A positive sign will create a parabola that opens upwards, while a negative sign will create a parabola that opens downwards.
4. The interactive model allows students to visualize how changing the values of 'a' and 'b', or the +/- sign, affects the graph's shape and position.
5. The simulation model uses JavaScript to create the interactive elements, allowing users to manipulate parameters and see the immediate impact on the graph.
6. One example is "AC or DC Appliances JavaScript Simulation Applet HTML5", listed under the "Forgot your username" section.
7. It means that the resource is freely available for educational use, encouraging sharing and adaptation.
8. HTML5 refers to the latest version of the standard web markup language that is used to provide richer interactive web content, enabling the simulation to run in a web browser without needing additional software.
9. It indicates that the material can be shared, adapted, and used for educational purposes as long as proper attribution is given and any adaptations are shared similarly.
10. Teachers may find it useful because it is an interactive, visual tool that helps make the abstract concept of quadratic functions more concrete and engaging for students.

Essay Questions

Instructions: Choose one of the following questions and develop a well-structured essay that demonstrates your understanding of the provided materials.

1. Discuss the pedagogical value of interactive simulations like the one described in the context of teaching mathematical concepts. How might such a tool promote deeper understanding than traditional teaching methods?
2. Analyze the importance of open educational resources for expanding access to quality learning materials, and offer examples from the provided list.
3. Explain how the different elements of a quadratic equation, such as the ‘a’, ‘b’, and the +/- sign, interact to create the graph of the equation. Use specific examples to support your analysis.
4. Explore the broader range of educational resources provided within the linked site, such as simulations and workshops, and explain the benefits to the educational community.
5. Compare the specific quadratic function simulation to at least two other resources on the site to explain how simulations can be used as both a teaching tool and a research tool.

Glossary of Key Terms

Quadratic Function: A polynomial function of the second degree, generally written as f(x) = ax² + bx + c. In this context, it’s presented as +/- (x -a)(x-b).

Parabola: The U-shaped curve that is the graph of a quadratic function.

X-intercepts (Roots): The points where the graph of a function crosses the x-axis. For a quadratic function in the form +/- (x -a)(x-b), the x-intercepts are at x=a and x=b.

HTML5: The latest version of the standard markup language used for creating web content, allowing for more interactive and multimedia rich content than previous versions of HTML.

JavaScript: A programming language commonly used to create interactive effects within web browsers, enabling simulations like the one described in this resource.

Open Educational Resources (OER): Freely available teaching, learning, and research materials that can be used for educational purposes without cost or copyright restrictions.

Interactive Simulation: A dynamic computer model that allows users to manipulate variables and observe the resulting changes to a system.

Pedagogical Value: The educational or instructional importance of a resource or tool, referring to its effectiveness in supporting learning.

Creative Commons License: A type of public copyright license that enables the free distribution of an otherwise copyrighted work. The provided license means you can share, adapt, and use the materials with attribution.

Sample Learning Goals

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For Teachers

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Research

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Video

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 Version:

1. https://www.geogebra.org/material/show/id/Mvjv27dQ#download-popup
   

Other Resources

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FAQ: Graphs of Quadratic Functions

1. What is the primary focus of the simulation model described in this resource? This resource focuses on providing a self-assessment simulation model for graphs of quadratic functions specifically in the form of +/- (x - a)(x - b). The goal is to allow users to interactively explore how changing the values of 'a' and 'b' (and the sign) affects the shape and position of the parabola on the coordinate plane.
2. How is the simulation model delivered and accessed? The simulation model is delivered as an HTML5 JavaScript application, accessible via a provided iframe embed code. This allows the model to be easily embedded into webpages for online learning. This embed is provided as a line of HTML code such as , demonstrating its use for online educational platforms.
3. What are some associated learning goals, if any? While specific learning goals are not detailed directly in this excerpt, it can be inferred from the title and context that key learning goals would include understanding the relationship between the factored form of a quadratic equation (x-a)(x-b) and its corresponding parabolic graph, specifically understanding the role of 'a' and 'b' as roots/x-intercepts and the role of the +/- at the front of the equation in whether the parabola faces up or down. The model probably aims to help users visualize how changes in these parameters alter the graph's features, like vertex, axis of symmetry, and direction.
4. What is Easy JavaScript Simulations (EJS) and how does it relate to this resource? The resource indicates the use of "Easy JavaScript Simulations" (EJS) or its newer iteration "EJSS". EJS is a tool for creating interactive simulations, often used for educational purposes. This resource utilizes an EJS-based model to allow for interactive exploration of quadratic graphs. There are multiple references to EJS throughout the source, noting it is open source physics software.
5. Besides math models, what other types of educational simulations are available through this project? This project offers a very wide range of educational simulations, including physics models such as those related to mechanics, electricity, magnetism, waves, and optics, often using the Tracker software. There are also references to simulations for chemistry, primary school math, and even interactive games focused on environmental topics. This breadth suggests a commitment to interactive learning across many fields.
6. Are there resources for educators within this platform? Yes, the platform explicitly states, "For Teachers" which hints at having tailored resources. The provided text also references many workshops, conferences and training sessions for educators to learn how to use the various simulations. The presence of numerous workshops and events targeted at teachers, plus various models that can be adapted for specific teaching purposes suggests that this platform is very aware of and supportive of educational professional development for teachers.
7. Is this platform localized in anyway or does it have a specific area of use? The platform is based out of Singapore as the name of the organization is "Open Educational Resources / Open Source Physics @ Singapore". This platform also has translations in multiple languages which indicates the need for the use of its models in many international contexts. The platform is not purely localized because it has numerous resources that are not region specific.
8. What is the licensing and usage policy for this resource and its content? The content is licensed under the Creative Commons Attribution-Share Alike 4.0 Singapore License. This means that the material is free to use, adapt, and share as long as attribution is given to the original authors and any derivative works are also shared under a similar license. The provided link is for the commercial use of EJS which shows that EJS is open source and free for educational use but that a payment is required for commercial uses.