Project Math Access

Teaching Mathematical Concepts

Basic Number Facts and Operations

Collaborative and Inclusive Strategies

The Personal Perspective of Abraham Nemeth

It is critical to teach students about the availability and appropriate use of tools of measurement. Ideally, students should be exposed to a broad range of tools, including those which are not specifically produced for use by blind persons but can be modified, if necessary, in a cost effective, “low-tech” manner. Mainstream, unadapted tools should be used whenever possible, since they will ultimately be the least expensive and easiest to obtain; but certainly students should be aware of all that is available so they can make informed choices in the future.

Instruction should include background information regarding purpose of the tool, where or how to purchase it, and approximate cost. Specific instruction on proper use of the tool should be followed by multiple opportunities to use it in a functional application, either in the direct solution of mathematics problems or in activities of daily living.

Following is a list of examples of tools which are either manufactured specifically for use by visually impaired people, or modified through easy, non-technical means.

- Braille rulers (variety of sizes and materials)
- Braille measuring tape,
- click ruler (3’, audible click every 1/16”)
- Micrometer Caliber (6”, accurate to 100 mm)
- Tape measure with notches at each inch, staples at each foot

- Battery operated level indicator
- Long handled metal spoon, handle bent at 90 degrees to form dipper
- Standard syringe with notches cut into handle and stop at end of plunger (farm supply store)
- Standard plastic measuring containers with overflow holes punched out at certain levels

- Braille scales, for weighing up to 2 pounds
- Talking scales, for weighing up to 10 pounds
- Balance scale with trays and tactile needle, for weighing liquids and small objects

- Braille thermometer, for liquids
- Talking thermometer, for liquids, air, and body

- Braille clocks and watches
- Talking clocks and watches

- Cut several cardboard rectangles of different sizes (e.g., measuring 1” by 2”, 1” by 3”, 1” by 5”, 2” by 3”, etc.). Have the student measure the sides of each rectangle with a raised line or braille ruler. After explaining perimeter, have the student add the lengths of the sides and write down the perimeter of the rectangle. Next, give the student a box of 1” squares (wooden or plastic parquetry squares, or cardboard squares the teacher has cut). The student places 1” squares on top of the rectangle, determining how many squares are needed to completely cover the cardboard. After explaining that he or she has discovered the area of the rectangle (review the difference between perimeter and area), the student can be taught to multiply the length of the long side by the length of the short side to determine area. Answers can be compared with answers obtained using the 1 inch cardboard squares.
- The student can also place his or her rectangles along a line, according to size (area). He or she will see that rectangles of different sizes can have the same area (i.e., a 3” by 4” rectangle has the same area as one which is 6” by 2”).
- Have the student draw a diagonal line with a crayon (or use a Wikki Stix to create a diagonal line) on some of the rectangles, and cut them into 2 right triangles. Have him or her measure the area, teaching that since each triangle is half of a rectangle, its area can be determined by dividing the area of the rectangle in half.

All of these instruments and activities will afford blind students the opportunity to interact with the physical environment with an emphasis on the study of mathematics.