Computers and Elementary School Mathematics

Computers as Tutors

The computer works as a tutor when it teaches concepts or skills. In most cases, the computer presents information and asks questions. The learner responds; the computer evaluates the response and decides what to present next. This type of teaching is known as Computer-Assisted Instruction (CAI). The types of CAI are tutorials, drill and practice, simulations, and instructional games.

Tutorials present new subject matter. Usually the program explains the material, presents information in small segments, and asks for specific responses, so that the learner will be involved in learning each step of a procedure, such as multiplying two-digit numbers. After this walk-through, the learner is given more leeway in responding. If the learner types a wrong response, the computer usually repeats the information required to give a correct response. Some tutorials have pictures that illustrate the ideas being taught. However, many tutorials for elementary school mathematics do not emphasize meaning, but merely present the steps in a procedure, so that students will learn to respond in a prescribed way.

Drill and practice programs are designed to help students remember material. The computer asks a question, and the learner responds. When responses are correct, the learner is usually reinforced with comments such as "Super" or a smiling face on the screen. If the response is incorrect, the computer will usually tell the learner to "try again."

Repetition is built into drill and practice programs and thus can be boring. Some are in a game format, which increases interest in the drill and practice. The program may be designed to give a record of the student's work to the student and :he teacher. To enable children to grasp the meaning of the material they are endeavoring to remember, Clements (1989) recommends that drill and practice programs be used only after understanding has been developed.

Simulations enable learners to step into the real world. Simulation programs are designed to allow students to carry out activities as they would in real life, They stress exploration, decision making, and problem solving. An example is the Whatsit Corporation (Sunburst) that enables groups of learners to set up and manage a business that markets one product for six months.

Instructional Games are not drill and practice activities but, rather, motivating activities with an element of competition. The programs are designed to teach concepts or strategies. An example is How the West Was One + Three x Four (Sunburst). This game involves a race between a stagecoach and a locomotive along a number trail. Each player is given three randomly generated numbers to use to plan a move that will advance him or her and will interfere with the progress of the opponent. Students can play together, or one student can play with the computer as the opponent.

Computers as Tools

Computers serve as tools when they carry out definite functions, such as graphing, storing and retrieving information, and calculating. Elementary school children should be engaged in many projects that require collecting data, organizing the information, and making graphs to communicate their findings. It is useful to be able quickly to change a graphic representation so as to determine the display that most forcefully conveys the data. Graphing programs are therefore useful to learners. A program to learn and explore graphing is The Graph Club (Tom Snyder Productions). When using graphing programs, students need to be aware of the potential of the program and to experiment with different graphic representations.

Data base programs make it possible to collect large amounts of data, formulate questions, and organize and sort the information. Such programs can provide worthwhile learning activities for children; for example, the sorting activity discussed by Wiebe (1990) enables a learner to experience sorting and re-sorting as he or she mentally creates new categories with different attributes.

Spreadsheets are large tables in a row-and-column format in which cell values can be operated on and changed at any time. Spreadsheets can be used with elementary school children. Working with a simple spreadsheet template, students can deal with different variables in a single problem and note the relations among variables as the numbers are changed. Edwards and Bitter (1989) discuss using large numbers in a spreadsheet activity to extend pupils' understanding. For example, the activity for young learners could be: If 30 granola bars cost $20, how much would 60, 90, 120, ... , 450 cost?

Computers as Tutees

When a student programs the computer, the computer is the object of instruction, that is, serves as a tutee. To program, the child must know a computer language. BASIC (Beginner's All-purpose Symbolic Instruction Code) is one such language introduced to elementary school children. LOGO (Greek for "word") is another. LOGO was developed by Seymour Papert, a mathematician at the Massachusetts Institute of Technology. LOGO enables children to command a trianglelike figure, the turtle, to make lines and shapes on the monitor. A few simple commands, such as RIGHT 90 or FORWARD 30 give the learner great power to make geometric figures and designs. LOGO provides problem-solving experiences, and is interactive in that, over and over again, the learners directs, the computer responds, and the child reacts to the response. When using the LOGO program, the student is creative and engages in higher-level thinking to produce a design that meets certain criteria.