Now that your student has had practice with tactile number lines, it is time to have fun with this exciting and fully accessible number line app, Cosmic Numbers. Can you help Astronaut Tommy as he navigates through space filled with numbers?
The first post in this Number Line series addresses basic number line concepts. The second post addresses addition and subtraction using a number line. This post, Part 3, will focus on the fully accessible number line app, Cosmic Numbers. The fourth post focuses on applying number lines.
Cosmic Numbers Background
There are numerous number line apps available that reinforce number sense and number lines. However, due to the visual nature of number lines, none of these mainstream apps are accessible for students who rely on a screen reader. App developers, textbook publishers and assessment groups struggle with making visual math concepts accessible in a digital format. The computer science department at the University of North Carolina is passionate about finding ways to make educational resources accessible for students who are visually impaired. (See Hidden Resources: Collaborative AT Projects with Universities post.) In the spring of 2019, a student team in the Serious Games course took on the project to make an accessible number line app; one team member continued to work on the app in another course in the fall of 2019. Cosmic Numbers is the exciting result of this project! This app is intended to be a 'proof-of-concept' app for app developers, textbook publishers, and assessment groups; the app is currently not available in the app store. Cosmic Numbers is fully functional with four levels. Let's take a look at the app!
A big thank you to Jessica McDowell - TVI extraordinaire - and her student Logan for their creativity and input about number line concepts and skills taught in general education classrooms! Their expertise guided and nurtured Cosmic Numbers. Careful attention was given to how number lines are represented in general education classrooms and the skills needed to access these number lines. These same concepts were embedded into Cosmic Numbers.
Cosmic Numbers Goals
There are four games/levels in Cosmic Numbers - each game is carefully designed to teach a specific number-line/number sense skill:
- Identify a point on a number line
- Create a point on a number line
- Understand that numbers increase in value as you move to the right/decrease in value as you move to the left (Smaller/Bigger concept)
- Compare two points/numbers on a number line (Greater Than, Equals, Less Than concept)
Tech Skills for Digital Number Lines
Spatial concepts/mental mapping using the drag gesture
- Understanding the layout of a number line
- Drag in a straight line (left to right across the screen and up/down between tick marks and numbers)
- Drag-and-Drop gesture
- Using a Picker Item (spinning menu with variables; swipe up or down gesture)
Cosmic Numbers Level 1
The goal in Level 1 is to determine the number that Astronaut Tommy landed on. At the top of the screen is the Back button and the directions. Above the number line are tick marks (vertical lines above and perpendicular to the number line, above each number.) Directly below the number line are the numbers, 0 - 5. Astronaut Tommy is located on the tick mark (above the number). Along the bottom of the screen starting on the left edge are the answer buttons 0 - 5. in the bottom right corner is the Submit button.
To find Astronaut Tommy, start with your finger on the Back button in the top left and drag your finger straight down the screen, stopping when you hear the word "Tick". If you find the number 0, drag slightly up to find the 'Tick". Now drag your finger in a straight line to the right - you are looking for the next "Tick". Keep dragging along the "Ticks" until you find Astronaut Tommy. When you locate Astronaut Tommy, drag your finger slightly down to hear the number. The first time or two, students might want to confirm the number by dragging slightly up to find Tommy again, and then dragging back down to the number. As students become more efficient, they may count the "Ticks" and estimate the number. They can also use the spatial location of the number to anticipate the correct number. (Example: If Tommy is found on the far right of the screen, he must be on the number 5.)
Note: If dragging right in a straight line is challenging, place a Wikki Stick in a straight line across the page or have the student place his right index finger off the screen by the Home button and drag his left index finger to his right finger. Another option to support dragging in a straight line is for the student to drag his thumb along the physical bottom edge of the iPad while dragging his index finger across the number line.
Once Astronaut Tommy's number has been identified, drag your finger to the bottom left corner to find the 0 button. Drag to the right to find the desired number/answer button. Split tap (or double tap) to select the desired button. Then drag to the bottom right corner to the Submit button and split tap or double tap.
Note: If you drag across the numbers, you will NOT find Astronaut Tommy! Astronaut Tommy is on the number line/tick mark, not the number. This is the same as a traditional visual number line.
If a wrong answer is chosen, you will be given a hint that the correct answer is greater than/less than your answer.
The video below demonstrates Level 1 of the Cosmic Numbers app (Select Astronaut Tommy's number).
Cosmic Numbers Level 2
In Level 2, the player will drag Astronaut Tommy to the desired "Tick" (number given) and click submit. Astronaut Tommy is located in the top left corner. Below him is the Back button and the the directions. Below that is the number line ranging 0 - 5. In the bottom right corner is the Submit button.
After an update, VoiceOver now announces the directions as soon as the page opens - listen carefully for the given number. Drag your finger to the top left corner to find Astronaut Tommy. Double tap-and-hold activates the drag-and-drop gesture (listen for the "bloop-bloop" earcon (sound) that indicates drag-and-drop has been activated). Drag down the left side of the screen, stopping on either the "Tick" or "0". Drag your finger to the right either counting the "Ticks" or listening to the numbers being announced. When on the desired "Tick", lift your finger. This will drop Astronaut Tommy and you will hear a satisfying "splat" sound. Drag to the bottom right corner and split tap on the Submit button.
Note: Astronaut Tommy must be dropped on the "Tick" or number line and not on the number!
The video below demonstrates Level 2 of the Cosmic Numbers app (drag Astronaut Tommy to the desired number).
Cosmic Numbers Level 3
In Level 3, Astronaut Tommy is on a tick mark above a specific number. Below the number line is the Smaller Button (on the left) and the Bigger button (on the right). Locate Astronaut Tommy by dragging your finger across the "Ticks"; drag down slightly to find the corresponding number. Mentally compare that number with the given number from the directions. If necessary, find the given number on the number line. If Astronaut Tommy's number is to the left of given number, then Astronaut Tommy is smaller than the given number. If Astronaut Tommy's number is to the right of the given number, then Astronaut Tommy is bigger than the given number. Once the bigger/smaller has been determined, drag down on the left side (under the number 1) to select the Smaller button or drag down on the right side (below number 4) to select the Bigger button. Then, drag to the bottom right corner and select the Submit button.
The video below demonstrates Level 3 of Cosmic Numbers (comparing numbers: smaller or bigger).
Cosmic Numbers Level 4
In Level 4, the student compares the given number with Astronaut Tommy's number. This level provides the given number in the directions and Astronaut Tommy is found on a tick mark above a number. Below the number line is the icon of Astronaut Tommy on the left, a Picker item in the middle and then the given number on the right - forming a math equation. A Picker Item is a scrollable list of distinct variables. The Picker Item in Cosmic Numbers has three variables, Greater Than, Equals and Less Than. With VoiceOver running, the student will swipe up to move to the next variable in the Picker Item. When the Picker Item is on the desired answer, select the Submit button.
Note: Picker Items are an essential tech skill that is frequently incorporated into digital textbooks and assessments. Students with visual impairments need to have opportunities to become efficient with Picker Items through game play!
The video below demonstrates Cosmic Numbers Level 4 (greater than, equals, less than).
Cosmic Numbers was updated since the videos in this post were created. The update included:
- VoiceOver focus automatically starts on the direction/title/question at the top of each page (not the back button).
- When a button is selected, VoiceOver now announces "Selected". Students can check to see what was selected before submitting the answer.
- App can be oriented with the Home button on the right as well as the left side.
- The "underline" below each word/number on the buttons were removed.
Cosmic Numbers is gamification at its finest! Students with visual impairments are learning and practicing number sense and number line skills while becoming proficient with a variety of critical tech skills as they play this game. Besides the obvious math skills, students are also learning to apply tech skills to digital math concepts such as dragging across the screen in a straight line, building mental maps about numbers such as the 5 is located on the right side of the screen, learning terms such as bigger/smaller, greater than, equals and less than and so much more. Finally, a fun math concept game that can be used by by all students in a general education classroom!
UNC Computer Science Comsic Numbers Teams
A big thanks to these passionate and dedicated professors and students for developing this fully accessible number line app, Cosmic Numbers!
COMP 585 (Serious Games Course) team members, spring 2019; Dr. Diane Pozefsky
- Malak Harb
- Karin Li
- Tian Liu
- Rob Rodgers
COMP 495 (Mentored Research Course) team member, fall 2019; Dr. Gary Bishop