Tips and Strategies to Make Functions Accessible

Students with visual impairments may face challenges when working on the Mathematics standards in the Common Core State Standards (CCSS).  As a response to this, Perkins School for the Blind convened a panel of experts to identify specific standards that would be a potential challenge to students who are blind or visually impaired, and then proposed ideas for materials, foundational skills, tips and strategies, and lesson ideas to help to address these challenges.

 

This post is part of a series about different parts of the Mathematical standards.

 

Topics:

What is a student likely to be working on in this area: 

• A function is a set of inputs and a set of permissible outputs where one output is directly related to one input.  It is often compared to a machine where one thing goes in is directly related to what comes out.  Students may start by learning a function table in early grades but will use this knowledge through high school.  

What are the particular challenges for a student who has a visual impairment?

• This skill leads to the understanding of linear relationships. Practice with tactile drawing of input tables and graphs (single and four quadrant) is essential.

Foundational Skills: 

• Nemeth: superscript indicator, baseline indicator, fraction indicators, radical, index of radical, termination indicator, and parentheses
• Understand how to graph points, independent vs. dependent variable 
• Know how to set up a table of values 
• Know how to read tables and graphs
• Understand a Vertical Line Test
• Calculate slope/rate of change of a line graphically
• Understand the layout of an equation and how to read tables and graphs
• Distinguish between linear and nonlinear functions
• understand independent vs. dependent variable, the idea that functions can be modeled in a variety of ways, and how to read tables and graphs
• Calculate and interpret constant rate of change/slope from a graph 
• Calculate and interpret initial value (y-intercept) from a graph
• Represent linear relationships graphically
• Understand resources available to draw a graph and what works best for that student so he/she can draw the model easiest based on his/her fine motor skills and knowledge of what would make a graph rise or fall
• Distinguish rate of change within an interval of a function 
• Interpret directionality and steepness of the graph of a function 
• Sketch a graph given algebraic context or a scenario (slope and initial value) 
• Create a plausible story given a graph
• Use the concept of function to solve problems
• Understand how to read tables and graphs
• Understand what types of numbers would be used in different situations
• Understand how a fraction can represent a rate of change
• Understand how to use a symbolic representation to make a table of values and graph points
• Understand how to manipulate equations into equivalent forms and solving equations
• Understand the properties of exponents and percent
• Understand the relationships between functions algebraically, graphically, verbally, or in tables

Materials

• Tactile graphics for any graphs of a system of linear equations
• Graph Paper (tactile or bold-line) and tactile dots
• Graphic Aid for Mathematics
• Orion TI-36X Talking Scientific Calculator, notetaker calculator, or iPad scientific calculator
• Orion TI-84 Plus Talking Graphing Calculator or iPad graphing calculator
• Perkins Brailler
• APH Draftsman Tactile Drawing Board
• Quick draw paper
• Sketch Pad
• Computer with JAWS or VoiceOver 
• Spreadsheet software

Tips and Strategies

• When using graphic calculators, use tactile graphics of linear and non-linear functions. 
• Use the Orion TI-84+ Talking Graphing Calculator to quickly explore non-linear functions.
• When using tactile graphics, make sure they are depicting various functions. 
• Use the APH Graphic Aid for Mathematics, the APH Draftsman, or other drawing tools to sketch a function associated with a scenario.

Lesson Ideas

• Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
• Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
• Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
• Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
• Determine the values or rule of a function using a graph or a table.
• Make the graph or table relevant to real world problems
• The student will need to be explicitly taught how to read the graph or table
• Describe how a graph represents a relationship between two quantities.
• Use meaningful examples
• Given a function table containing at least 2 complete ordered pairs, identify a missing number that completes another ordered pair (limited to linear functions).
• Have students make a table consisting of the number of items in the independent variable column and the total cost of x items in the dependent variable column
• Determine the values or rule of a function using a graph or a table.
• Make the graph or table relevant to real world problems
• The student will need to be explicitly taught how to read the graph or table
• Choose problems that relate to a student’s interests.
• Number of animals mapped to number of legs, etc.
• Use the concept of function to solve problems.
• Construct graphs that represent linear functions with different rates of change and interpret which is faster/slower, higher/lower, etc.
• Identify spots on a graph that are at zero, at a high point, at a low point, growing, or falling.