"Our classrooms are becoming paperless." This statement is flying around classrooms but what does it mean for students with visual impairments and blindness? How can we help our students who are VIB make this digital transition, especially when it comes to math concepts? Traditionally, math is provided in a tactual format for K-12 students who are braille readers; yet, college and STEM career materials are typically digital only. How do we prepare our students for this digital transition - transitioning from paper materials to digital materials? Once students understands the basic concept using tactile materials, how can we teach these academic students to apply these same foundational concepts to accessing digital math materials?
Let's start by taking a closer look at how to traditionally teach the foundational math skill 'grids' and how to transition grid concepts from tactile materials to digital materials.
- Number Line: is a straight line marked with numbers that is often used to answer addition and subtraction questions.
- Grid: is evenly divided and equally spaced squares on a figure or flat surface.
- Math Grid: is another name for the coordinate plane consisting of a space of small squares, sometimes with an x-axis and y-axis.
- Coordinate Grid: A coordinate grid has two perpendicular lines or axes, labeled like number lines. The horizontal axis is called the x-axis. The vertical axis is called the y-axis. The point where the x-axis and the y-axis intersect is called the origin. The numbers on a coordinate grid are used to locate points. Each point can be identified by an ordered pair of numbers; that is, a number on the x-axis called an x-coordinate, and a number on the y-axis called a y-coordinate. Ordered pairs are written in parentheses (x-coordinate, y-coordinate).
Ordered pairs are typically introduced in 3rd or 4th grade and graphing equations in 4th or 5th grade.
Traditional Educational Tactile Grid Resources
- Grid paper: APH Bold Line Tactile Graph Sheets Item Number 1-04080-00
- APH Grid Graphic Aid for Mathematics (Framed rubber mat embossed with 34 X 30 grid of ½ inch squares. Included are three flat spring wires, 14 push pins and rubber bands. Item Number: 1-00460-01
- APH Advanced Desk Top Stick-On Number Lines Item Number 1-03482-00; (Also available are consumable number lines both large print and braille/tactile.)
Additional Tactile Grid Resources
- Battleship board game is a classic tactile game that entails a grid, battleships and pegs which are used to indicate where a player has tried to find/sink a battleship. Players call out the row and column number trying to find their opponents hidden battleship.
- Lego grid: Teachers can create quick tactile representations of grids using a Lego base and Lego blocks. Instead of using letters like in the crossword game, have the students locate specific Lego characters/blocks and identify the coordinates. Have the students place a character in a specific location.
- Tactile–Braille Crossword Puzzle Using a wooden board and braille letter pieces create words in up-and down or side-to-side format. The kit includes a wooden board which has 10 rows and 13 columns and 99 plastic braille letter tiles. This crossword puzzle is designed to be used as a word game. However, the game board is actually a grid which can be used to teach grid concepts. Be sure to use row and column numbers when discussing points on the grid. Tactually labeling the rows and columns might be beneficial for many students.
- Crossword puzzles are frequently a fun way for students to learn vocabulary words, spelling words, and other language arts activities. When the class is given a printed or digital crossword puzzle, teach your student to answer the crossword puzzle initially using the paper grids, where you can quickly mark out blank spaces tactually. Be sure to label the row and column numbers. If necessary, use a tactile marker (such as a tiny sticky-backed foam dot) to indicated the beginning of a word.
- Traditional crossword puzzle: Most crossword puzzles use even numbers and odd numbers to indicate rows or columns. A braille student should have only one word starting per row or line. Example: If the rows are odd numbers, and a word starts in Row 3, then the associated definition of the word will be labeled 3. The student will know that the first letter of his answer will start in the first open space in row 3. The second letter will be to the right of the first letter, still in row 3. If the answer is an even number 2, the student will find the first open space in column 2 and second letter of the answer will be added below the first letter.
- For young students, use APH's Feel 'n Peel Stickers (braille letters Item Number 1-08846-00) or use teacher-created braille letters so that students can "stick" the letter in the correct space rather than trying to align and braille the letter within the crossword puzzle.
- Modified crossword puzzle: Modify your student’s crossword puzzle by using ‘row,column’ (two numbers, such as ‘3,4’ to indicate 3rd row, 4th column) instead of even and odd numbers.
Additional crossword games
- Ask your student to place a specific letter in a specific location. Example: Place the letter D in 2,3.
- Spell out words. Example: Place the letter D in 2,3. Place the letter O in 2,4. Place the letter G in 2,5. What does it spell?
- Spell words by finding letters that are randomly on the board. Example: Place 10 letters scattered across the board. Give the student the coordinates and have the student find the letter. Place the letters in order to spell the mystery word.
- The teacher places a letter in a specific location. The student is asked to name the coordinates.
- Specifically teach that rows move across (right or left) in a straight line while columns move up and down. Row coordinates are listed first followed by column coordinates.
- Always introduce the layout of the grid – how many rows and columns? Students need to be encouraged to explore the layout first, naming the number of rows and columns. When using digital grids, the screen reader should always introduce the grid layout first. (Typically the alt text for the grid image should provide the grid layout as soon as the grid appears. If you - the teacher - is creating a digital grid, be sure to include the grid layout in the written description of the grid or in the alt text if the grid is an image.)
- When creating a grid, be sure to eliminate the unused rows or columns. Example: If using a paper grid that is 4x5, cut off the additional rows and columns. For physical boards, cover the areas that are not being used as this will help students develop the concept of size. Students will learn that a 4x5 board is much smaller than a 10x12 board.
- If the grid is 4x5, the student should immediately recognize the coordinates of the four corners. 1,1 (top left), 4,1 (bottom left), 1,5 (top right), 4,5 (bottom right).
- Identify the goal of the activity and then be sure to teach/emphasize that goal throughout the activity. The goal might be to teach the grid layout and the relationships within that grid layout, such as the coordinates of the four corners.
- When teaching students about grid concepts, start young with very simple, concrete activities that are age-appropriate. Kindergarten students should be introduced to a number line before a grid. When introducing a grid, young students might find a character in a specific place on a Lego board and say the corresponding row and column numbers. Then the student might place a character on the Lego board and state the numbers and/or the teacher can call out the numbers and the student places the character in that spot. The next step might be for students to use a very simple crossword puzzle with five sight words. Students should not be introduced to grids when they are in algebra and expected to graph equations!
- Be sure to discuss with students that a coordinate grid often begins labeling the y-axis from the bottom up and coordinates are in ‘x,y’ order. Meanwhile, tables and other grids often begin labeling from the top down and screen readers announce the row, then the column.
- Students should be comfortable with both reading written grid layout and coordinates and with listening to grid layout with coordinates; students should be able to develop a mental map of the grid. Remember, the goal is to provide a firm foundation of grids through concrete tactile activities AND to transition the student to listening to and understanding grid information!
- Tie the grid into functional O&M routes and activities; tactile maps can be used initially. Example: The neighborhood is 3 blocks by 4 blocks. The school is in the top left corner. The gas station is in the top right corner. How many streets do you need to cross?
- Grid concepts are similar to table concepts. Students who understand grids should be able to transfer these skills to table concepts. Tables are basically laid out like grids but include row headers and column headers.
Digital Games That Include Grid Concepts
- Blindfold Bowling: iOS App – This is a free iOS app that teaches/reinforces spatial concepts and mental mapping. Instead of a square/rectangular grid like the typical grids, this game uses a triangular shape grid. (Bowling pins are in a triangle shape and are numbered.) For more information about Blindfold Bowling including tactile activities for teaching the spatial layout, see the post, Blindfold Bowling: iOS Spatial Concepts App.
- Blindfold Connect App – This is a free iOS app that is similar to the popular Connect Four game. This game reinforces/teaches spatial concepts/mental mapping. Blindfold Connect uses a grid layout (typically 7x6 grid). Swipe right or left to move through the columns. Double tap to drop your red checker into the column. The goal is to get a line of red checkers in one column before your computer opponent creates a line of black checkers.
- Blindfold 3D Tic Tac Toe by Blindfold Games - This is a free iOS app similiar to the classic Tic Tac Toe game - except this app is 3D. Now available!
- Coding Games – There are several wonderful coding concept games available for young students; however, these games are typically not accessible with screen readers. There are numerous Paths to Technology posts about coding. Swift Playgrounds, the free Apple coding game, is accessible; however, Swift Playgrounds is a little more advanced and is not intended to be used to teach basic grid concepts.
Many of these coding games include a “path” and players provide the commands to move left, right, up or down through squares on this path. These games often have a grid-like layout. Creating tactile grids with a starting point and destination and that include paths, walls, obstacles, will help develop a mental concept of these coding games. Students have to determine how many squares to move in each direction. Legos is a great resource to quickly recreate these type of coding games so that students can learn the basic coding concepts.
- CodeQuest created by a student team at the University of North Carolina, is a free, fully accessible iOS coding concept app designed for young students. Available soon!
- Sonokids apps - several apps that will include memory/spatial concepts, grids, tables, and more!
O&M Hint: Students are already applying spatial skills, mental mapping and other 'math' skills daily as they travel daily O&M routes. Be sure to connect O&M lessons with these math/grid lessons!
Look ahead! What higher math skills will your students need in high school, college, and in STEM fields? Think about the graphing skills that your students will need for Algebra – lay the foundation now with grid concepts, mental mapping, and spatial concepts. Are you building solid foundation skills now so that your student will successfully be able to use tools like a talking scientific graphing calculators? These calculators and calculator apps use spoken information paired with sonification (sounds that provide information about the graphics). The Desmos app, is an accessible scientific graphing calculator which is now backed by Pearson, approved by the College Board, and integrated into Smarter Balance tests. (See the Paths to Technology post, Desmos a free, accessible graphing calculator app.) Are your students embracing these types of digital math tools? Will your students be ready to successfully complete online math assessments? In the comment section below, please share your ideas, activities and needs as you help your students with these digital transitions!
Digital Transitions #1: