Tech Review #1
Desmos
Desmos, Inc.
Telephone: (415) 484-5342 Website: https://www.desmos.com/
7th - 12th Grade
Mathematics
Desmos, Inc.
Telephone: (415) 484-5342 Website: https://www.desmos.com/
7th - 12th Grade
Mathematics
Description:
Desmos is an online graphing calculator that allows students to explore a variety of graphing topics. Once you launch the calculator, students are able to use pre-created graphs to explore topics such as linear functions, slope, quadratic functions, trigonometric functions, conic sections, transformations, derivatives, and many more. These pre-created graphs allow students to play with the standard form of each given function or concept. Through the slider animations students are able to change certain values to see how it affects the graph itself. For example, when exploring slope-intercept form students can adjust the slope from -10 to +10 and see right on the graph what the change in slope does to the line.
Students can also use the Desmos calculator as a blank graph allowing them to enter their own data, equations, and functions. Student can enter multiple graphs in different colors for comparison. From the graph students can create a table of values or pick specific values from the graph, such as the x-intercept of a linear function. Students are able to use either the keys from the keyboard or the keys from the keyboard that appears on the screen. The screen keyboard can be minimized to allow for a larger view of the graph. Students can also enter a slider animation to see how changing a value of their functions will affect their graphs.
On the website itself there are also saved graphs available to explore. Some are creative art graphs that other people have created to form pictures, while others are used to explain mathematical concepts. These are typically interactive with the slider animation like the pre-created graphs on the calculator. On the website there is also a link to their blog. On their blog are ideas for labs to be used in the classroom using Desmos.
Accuracy of Content:
The accuracy and completeness of Desmos is very high. It is easy to navigate through the menu of pre-created graphs on the calculator. The pre-created graphs were organized in a logical order starting with algebraic concepts and leading up to calculus concepts. I did find that there was not a pre-created graph on systems of linear equations and think it is an important topic to be added. The graphs available on the website are not as well organized. They are split into three categories: Staff Picks: Math Examples, Staff Picks: Creative Art, and Recently Saved Graphs. The graphs are not organized by topic and there does not seem to be a way to search through these graphs other than to scroll through the page. I would suggest that a search be added to the website to allow to easy access to other pre-created graphs. The website is free of bias and is easy to use for all middle and high school students.
Technical Quality:
The website is very easy to access. Once on the website you simply click the launch calculator button and it opens immediately. You can create an account to save your graphs, which only requires a username, e-mail, and password. If an account cannot be created due to a lack of e-mail, graphs can also be printed although it will lose the slider animation aspect.
On the top left hand corner of the calculator is a “open graph” menu where pre-created graphs can be accessed. Graphs can be named and saved on the top menu bar as well. On the top right hand corner of the graph there is a print button, share button, settings button, help button, and language button. The print button allows you to print your graph. The share button allows you share your graph by providing you with a link, allowing you to email the graph, providing a embed code, or by taking a screenshot of the graph. The settings button allows you to choose what type of graph paper (cartesian or polar), determine what labels and grid lines should be visible, and determine the window for your graph. There is also a projector mode button to allow for projector use of the graph. There are also trig settings that allow you to change from radians to degrees. The help button brings you to a menu of four options: sliders, tables, restrictions, and advanced tables. By clicking on one you are given a quick tutorial on the given topic. You can also select the Desmos User Guide or Knowledge Base to search for questions. This is also the place to leave feedback or ask a specific question. The language button allows for you to change the language the graph is presented in. There are currently 21 languages available including English, Spanish, and French. Overall, the website and calculator are very easy to use and navigate.
The presentation of the calculator and the website are very aesthetically pleasing. There are very few graphs and the colors are very basic. The website and the calculator are both done in black, white, grey, and green making it easy to focus on the content. There are not too many graphics that are distracting and the videos are not overwhelming; in fact, they are on a separate page.
Use of Technology:
Desmos makes very good use of the technology for the intended educational use of graphing in the mathematics classroom. The technology does not just allow students to enter a function or equation, but actually allows them to play with the values in the function and see how it affects the graph. The technology also allows students to easily pull up a table of values for each function to see how the change in one value affects the other values in the function. Students will be able to use Desmos as a way to discover the effect these changes have on a function independently without teacher instruction. Through student discovery and exploration using this tool, conceptual understanding will become deeper.
Role of Students:
Students will be empowered when using the pre-created graphs because they will be able to discover new mathematical concepts on their own. Students will also be empowered when creating their own graphs because of the ease and freedom this website provides. One constraint that might occur is the fact that it is all exploration. Desmos does not provide step-by-step instructions on the pre-created graphs to tell students what they should be looking for as they change a given value. At the same time, this could be very empowering for a student who likes to work at his own pace. Students have full control of the website once the calculator is open. Students are able to enter their own functions on a blank graph or play with a pre-created graph. Students can easily create a graph using Desmos, interactive or non-interactive. This can be used to assess students’ understanding of a graphing concept such as the y-intercept on a linear function. This can also be used as either an individual or group activity. Students can create graphs to share with each other or work together to create a graph (although they would need to do it together on one computer). This website will help students value their own thinking and learning process because it will allow them to discover new mathematical concepts on their own and allow them to explain it to others through the creation of graphs.
Role of Teacher:
To begin using this website in the classroom, the teacher would need to provide each student with the website address and allow the students time to create an account. The teacher may want to first introduce the calculator by having the students complete an activity at the same time as the teacher using the projector. The teacher would need to walk around the classroom in order to monitor student use of the website as there is no way to monitor student use from the website itself. The student accounts are not tied into the teacher account in any way. There is a blog on the website which provides some labs for classroom use. This is a great resource for teachers who are looking for ways to implement Desmos into their classrooms.
Classroom Usage:
I believe the best way to start using Desmos in the classroom is to begin with a basic pre-created graph that is done through teacher instruction using the projector. Students should also be on the website following along with the teacher. It is also a good idea to allow students to have time to play with the blank calculator and try each of the tools, such as the slider. Desmos could be used individually, as pairs, as groups, or full class (most likely on the projector), although it would be most successful with individual or pairs since it can only be completed on one computer.
This fits very closely into many middle school and high school mathematics classes since there are many examples of different functions that are introduced in Algebra I through Calculus available on the calculator and website. For example, the calculator has a pre-created graph called Visualizing Slope. It presents a line with slope triangles to represent the slope up the entire line. Students are able to adjust the slope of the line and the slope triangles adjust as well showing the steepness of the given line. This could be used as an introduction to slope with an Algebra I class. On the website there was a saved graph called Circle Demo which allows students to play with the radius and center of a circle. As these values are adjusted, the graph of the circle is moved on the plane. This could be used as a way to introduce the equation for circles in a geometry class.
Critical Summary:
Overall I think Desmos is a great tool for a middle school or high school mathematics classroom. The website and calculator have many strengths: it is easy to use, it is easy to navigate, it provides great pre-created graphs, and can be used for a variety of graphing activities. I really enjoy the fact that the graphs can be made interactive to allow for student discovery. It is available in multiple languages and is, therefore, accessible for many different students. One highlight is that students are able to share their graphs in multiple ways. This is a great way to use the tool for assessment because students can simply email their graph to the teacher. The one downfall I found to the website was the lack of the ability to search the saved graphs available on the website.
Overall Rating:
I would give Desmos a 9 out of 10 rating. The website is easy to use and is very organized. The calculator allows students to discover new mathematical concepts related to graphs and functions independently. It also allows students to create and share their own graphs, both interactive and non-interactive. I would high recommend Desmos as a tool to use in a middle school or high school mathematics classroom.
Desmos is an online graphing calculator that allows students to explore a variety of graphing topics. Once you launch the calculator, students are able to use pre-created graphs to explore topics such as linear functions, slope, quadratic functions, trigonometric functions, conic sections, transformations, derivatives, and many more. These pre-created graphs allow students to play with the standard form of each given function or concept. Through the slider animations students are able to change certain values to see how it affects the graph itself. For example, when exploring slope-intercept form students can adjust the slope from -10 to +10 and see right on the graph what the change in slope does to the line.
Students can also use the Desmos calculator as a blank graph allowing them to enter their own data, equations, and functions. Student can enter multiple graphs in different colors for comparison. From the graph students can create a table of values or pick specific values from the graph, such as the x-intercept of a linear function. Students are able to use either the keys from the keyboard or the keys from the keyboard that appears on the screen. The screen keyboard can be minimized to allow for a larger view of the graph. Students can also enter a slider animation to see how changing a value of their functions will affect their graphs.
On the website itself there are also saved graphs available to explore. Some are creative art graphs that other people have created to form pictures, while others are used to explain mathematical concepts. These are typically interactive with the slider animation like the pre-created graphs on the calculator. On the website there is also a link to their blog. On their blog are ideas for labs to be used in the classroom using Desmos.
Accuracy of Content:
The accuracy and completeness of Desmos is very high. It is easy to navigate through the menu of pre-created graphs on the calculator. The pre-created graphs were organized in a logical order starting with algebraic concepts and leading up to calculus concepts. I did find that there was not a pre-created graph on systems of linear equations and think it is an important topic to be added. The graphs available on the website are not as well organized. They are split into three categories: Staff Picks: Math Examples, Staff Picks: Creative Art, and Recently Saved Graphs. The graphs are not organized by topic and there does not seem to be a way to search through these graphs other than to scroll through the page. I would suggest that a search be added to the website to allow to easy access to other pre-created graphs. The website is free of bias and is easy to use for all middle and high school students.
Technical Quality:
The website is very easy to access. Once on the website you simply click the launch calculator button and it opens immediately. You can create an account to save your graphs, which only requires a username, e-mail, and password. If an account cannot be created due to a lack of e-mail, graphs can also be printed although it will lose the slider animation aspect.
On the top left hand corner of the calculator is a “open graph” menu where pre-created graphs can be accessed. Graphs can be named and saved on the top menu bar as well. On the top right hand corner of the graph there is a print button, share button, settings button, help button, and language button. The print button allows you to print your graph. The share button allows you share your graph by providing you with a link, allowing you to email the graph, providing a embed code, or by taking a screenshot of the graph. The settings button allows you to choose what type of graph paper (cartesian or polar), determine what labels and grid lines should be visible, and determine the window for your graph. There is also a projector mode button to allow for projector use of the graph. There are also trig settings that allow you to change from radians to degrees. The help button brings you to a menu of four options: sliders, tables, restrictions, and advanced tables. By clicking on one you are given a quick tutorial on the given topic. You can also select the Desmos User Guide or Knowledge Base to search for questions. This is also the place to leave feedback or ask a specific question. The language button allows for you to change the language the graph is presented in. There are currently 21 languages available including English, Spanish, and French. Overall, the website and calculator are very easy to use and navigate.
The presentation of the calculator and the website are very aesthetically pleasing. There are very few graphs and the colors are very basic. The website and the calculator are both done in black, white, grey, and green making it easy to focus on the content. There are not too many graphics that are distracting and the videos are not overwhelming; in fact, they are on a separate page.
Use of Technology:
Desmos makes very good use of the technology for the intended educational use of graphing in the mathematics classroom. The technology does not just allow students to enter a function or equation, but actually allows them to play with the values in the function and see how it affects the graph. The technology also allows students to easily pull up a table of values for each function to see how the change in one value affects the other values in the function. Students will be able to use Desmos as a way to discover the effect these changes have on a function independently without teacher instruction. Through student discovery and exploration using this tool, conceptual understanding will become deeper.
Role of Students:
Students will be empowered when using the pre-created graphs because they will be able to discover new mathematical concepts on their own. Students will also be empowered when creating their own graphs because of the ease and freedom this website provides. One constraint that might occur is the fact that it is all exploration. Desmos does not provide step-by-step instructions on the pre-created graphs to tell students what they should be looking for as they change a given value. At the same time, this could be very empowering for a student who likes to work at his own pace. Students have full control of the website once the calculator is open. Students are able to enter their own functions on a blank graph or play with a pre-created graph. Students can easily create a graph using Desmos, interactive or non-interactive. This can be used to assess students’ understanding of a graphing concept such as the y-intercept on a linear function. This can also be used as either an individual or group activity. Students can create graphs to share with each other or work together to create a graph (although they would need to do it together on one computer). This website will help students value their own thinking and learning process because it will allow them to discover new mathematical concepts on their own and allow them to explain it to others through the creation of graphs.
Role of Teacher:
To begin using this website in the classroom, the teacher would need to provide each student with the website address and allow the students time to create an account. The teacher may want to first introduce the calculator by having the students complete an activity at the same time as the teacher using the projector. The teacher would need to walk around the classroom in order to monitor student use of the website as there is no way to monitor student use from the website itself. The student accounts are not tied into the teacher account in any way. There is a blog on the website which provides some labs for classroom use. This is a great resource for teachers who are looking for ways to implement Desmos into their classrooms.
Classroom Usage:
I believe the best way to start using Desmos in the classroom is to begin with a basic pre-created graph that is done through teacher instruction using the projector. Students should also be on the website following along with the teacher. It is also a good idea to allow students to have time to play with the blank calculator and try each of the tools, such as the slider. Desmos could be used individually, as pairs, as groups, or full class (most likely on the projector), although it would be most successful with individual or pairs since it can only be completed on one computer.
This fits very closely into many middle school and high school mathematics classes since there are many examples of different functions that are introduced in Algebra I through Calculus available on the calculator and website. For example, the calculator has a pre-created graph called Visualizing Slope. It presents a line with slope triangles to represent the slope up the entire line. Students are able to adjust the slope of the line and the slope triangles adjust as well showing the steepness of the given line. This could be used as an introduction to slope with an Algebra I class. On the website there was a saved graph called Circle Demo which allows students to play with the radius and center of a circle. As these values are adjusted, the graph of the circle is moved on the plane. This could be used as a way to introduce the equation for circles in a geometry class.
Critical Summary:
Overall I think Desmos is a great tool for a middle school or high school mathematics classroom. The website and calculator have many strengths: it is easy to use, it is easy to navigate, it provides great pre-created graphs, and can be used for a variety of graphing activities. I really enjoy the fact that the graphs can be made interactive to allow for student discovery. It is available in multiple languages and is, therefore, accessible for many different students. One highlight is that students are able to share their graphs in multiple ways. This is a great way to use the tool for assessment because students can simply email their graph to the teacher. The one downfall I found to the website was the lack of the ability to search the saved graphs available on the website.
Overall Rating:
I would give Desmos a 9 out of 10 rating. The website is easy to use and is very organized. The calculator allows students to discover new mathematical concepts related to graphs and functions independently. It also allows students to create and share their own graphs, both interactive and non-interactive. I would high recommend Desmos as a tool to use in a middle school or high school mathematics classroom.