I choose a 8th grade mathematics standard from Common Core.
- Common Core Standards [8.G.B.6] - Explain a proof of the Pythagorean Theorem and its converse.
1) GeoGebra
GeoGebra is a software that combines features from graphing, geometry, spreadsheet, probability, statistics, and 3D graphs (for calculus) into a single platform. In 8th grade mathematics, a geometry feature from GeoGebra is used to explore standards related to geometry, like the above standard from Common Core. GeoGebra is a free software, and it's designed for students at all levels of education. To access GeoGebra, an individual can visit its website or download an app. GeoGebra is compatible with all computer devices (e.g., computers with Windows OS and macOS), and it's also compatible with all mobile devices (e.g., devices with Android OS and iOS). I used Common Sense Education for the review site for the following reasons: 1) an expert who reviewed this application have been employed in education for 20 years or more, 2) this review is unbiased, as it's not influenced by developers or funders of GeoGebra, and 3) this website is nonprofit, which means the reviewers do not get paid for leaving reviews.
2) Desmos
Desmos is a software that's primarily known for graphing features, as it allows the user to graph equations and manipulate them by using sliders associated with the entered equations. Desmos also provides a variety of features such as a scientific calculator, four-function calculator, geometry, matrix calculator, and 3D graph. Although Desmos and GeoGebra have very similar features, there's one major difference: Desmos Classroom Activity. Desmos Classroom Activities are interactive digital lessons built by the Desmos Team or educators that engage that's designed to engage students in understanding mathematical concepts easily through visuals, manipulation, and live feedback from teachers. To use Desmos Classroom Activities, a teacher must create an account. There are numerous Desmos Classroom Activities that a teacher can use to teach proof of the Pythagorean Theorem and its converse. Desmos is a free software, and it's designed for students in middle school and beyond. To access Desmos, an individual can visit its website or download an app. Desmos is compatible with all computer devices (e.g., computers with Windows OS and macOS), and it's also compatible with all mobile devices (e.g., devices with Android OS and iOS). A review from Common Sense Education was selected fro the following reasons: 1) an expert who reviewed this application is a teacher with at least eight years of experience, 2) the review is unbiased, as it's not influenced by developers or funders of Desmos, and 3) this website is nonprofit, which means the reviewers do not get paid for leaving reviews.
3) Numbers
Number is a spreadsheet software that allows users to perform calculations (using the Formula feature), analyze data, and create visualization from the data. I believe this is a great supplementary tool that teachers and students can use to record their findings, along with the use of GeoGebra or Desmos when investigating the converse of Pythagorean Theorem. For example, a teacher can set up a template (e.g., length of a, length of b, length of c, value of a^2 + b^2, and value of c^2). As students record their findings, they will eventually realize that c^2 > a^2 + b^2 is an obtuse triangle and c^2 < a^2 + b^2 is an acute triangle. Numbers is a free software, and it's designed for students in middle school and beyond. Number is compatible with all Apple devices (e.g., iPhone, iPad, MacBook, and Mac). People who have Windows OS or Android OS can use this by going to the iCloud website, but they will need to create an Apple account. A review from Common Sense Education was selected for the following reasons: 1) an expert who reviewed this application has experience in education field, 2) the review is unbiased, as it's not influenced by developers or funders of Numbers, and 3) this website is nonprofit, which means the reviewers do not get paid for leaving reviews.
I believe...
Desmos is the best app out of the three apps I selected for this assignment for multiple reasons. First, Desmos supports various types of learners through interactive visual and manipulation features. For example, visual learners can explore the slope-intercept form in real time, and kinesthetic learners can learn the effects on the line when manipulating the slope of the slope-intercept form in real time. Second, Desmos is free and user-friendly. In my opinion, I believe Desmos has a user interface that's very intuitive, which saves its users from having to learn how to find and use tools in Desmos. Third, Desmos is very versatile, as it offers a variety of features such as a scientific calculator, four-function calculator, geometry, matrix calculator, and 3D graph. This variety of features allows all students in middle school and beyond understand and delve into mathematics concepts easily. Lastly, Desmos provides Classroom Activities, designed by Desmos Team or educators, that covers plenty of mathematical concepts. These activities allow teachers to conduct an engaging lesson that could benefit students in multiple ways. For example, Classroom Activities allows teachers to monitor students' progress in real time, and this allows teachers to provide real-time feedback to students. To put it simply, Desmos takes mathematics beyond the textbook; it brings mathematics to life. That's why I believe Desmos is the best app.
You chose some good apps and provided a great comparison and explanation of the three. I agree that Desmos is a game-changer for engagement and real-time formative feedback, although I disagree that it is user friendly for everyone. It may just be me but I fear my students would get overwhelmed with this app. I also chose GeoGebra for my app review, mainly because of your mentioning it in your previous Blog Post. I went down the rabbit hole of discovery playing with it and have plans to use it, especially in my geometry unit. On another subject, I know its more of a whole curriculum than other apps and it costs but BrainPop! seems really cool to me. I have already requested to use it through my Principal and maybe I get the go ahead before school starts. Overall, your reviews and blogs have been very useful to me especially since you have more experience teaching Math than me.
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