Number Cross

PAL (Positive Answer Learning)


PAL (Positive Answer Learning) was created in 1989 specifically for Number Cross . The theory is based on Edward Arnold's T-SL (Timed-Sequence Learning) educational theory he created in 1984. Both theories broke from traditional educational thought related to computer software and how information was presented to the student using the computer. Timed-Sequence Learning challenged B.F. Skinner's linear learning approach.

B.F. Skinner's linear learning approach presented the student with small bits of knowledge. A student could not progress to a higher level until the lower level was successfully mastered. Mr. Arnold developed his theory while working on his Ed.D in Psychology at Vanderbilt/Tennessee State University. He attended a graduate student's experiment in Computer Assisted Learning. Young children were presented with spelling words using software designed around B.F. Skinner's linear learning approach. Mr. Arnold noticed that the children were all learning at different rates or speeds. He also noticed that "prior knowledge" affected the children's response. Most importantly, he noticed that although the children were learning at different rates or speeds, the software did not allow for those differences; a student could not advance, despite their prior knowledge of the material presented. Several students were trapped in a computer program where he or she had knowledge of answers but could not move forward and bypass the known material..

He also noticed that some of the children were unable to grasp the concepts and they were also stuck; they could not go backward to easier material. One-third of the students in the experiment were too advanced; one-third of the students were presented with material that was too difficult and one-third of the students were progressing.

Mr. Arnold told the professor that the experiment was flawed. The computer program, itself, was affecting the experiment. The computer program was flawed and any result would be questioned.

It took Mr. Arnold more than two months to create a computer program that allowed a student to move forward, backward or remain at one level. He named it Timed-Sequence Learning because the material was presented at a timed-sequence to allow the student to grasp the material at one of eight comprehension or learning speeds. Unlike B.F. Skinner's learning programs that used linear programming, Timed-Sequence Learning used non-linear programming. Originally there were seven speeds but Mr. Arnold added a eighth speed. This eighth speed allowed a student to press any key to move forward. This speed was for use with difficult material and also for handicapped students.

Mr. Arnold presented his theory and an example of its use in class. He was laughed at! No one, including the professor, understood what he was saying. Computers were new and their use in education was limited to games. The year was 1984. He received his first registered Federal copyright for Timed-Sequence Learning - TXu000163190 Timed-Sequence Learning to determine the learning speeds of words and paragraphs; T S L, words and paragraphs. Effective date 06-13-1984 . Over a period of years, the program would evolve. He would add real pictures, voice, and sound effects. His most unique use of the program was News Disk . News  Disk was the first newspaper on computer created in 1989. In 1992, several issues would be included in an exhibit of software at the National Demonstration Laboratory of the Smithsonian Institute. These programs would be removed from the exhibit because visitors laughed at them. No one believed that a computer would ever present the news. If it did, who would ever read it?

Computer Classics

Mr. Arnold began the Computer Classics series of software in 1984. His goal was to provide a comprehensive selection of software. He wanted to cover all areas of education. News Disk provided news. A series of titles covered literature - Dracula, The Headless Horseman, Aesop's Fables, and others. Religion was included with a series of Bible stories - The Story of Creation, The Fall from Grace, David and Goliath, The Christmas Story and My Bible Primer I. Each Timed-Sequence program was designed to run stand-alone or on a network system. Each program displayed the Computer Classics name and logo.

Number Cross

Number Cross was one of Mr. Arnold's most challenging programs. He wanted to create a program to teach basic mathematics but he was not sure of the format. Existing computer software for mathematics was designed for young children and presented the math problems as a game. One math problem was presented at a time. When the student completed the problem, a different problem was presented. However, there were a limited number of math problems and the problems were repeated. After several usages, the students recalled the math problem and the answer. Learning stopped as the student remembered the math problem and answer.

To solve the problem of math problems being repeated, he designed a randomizer engine that would generate random numbers to provide different problems. To challenge advanced students, he added four levels of difficult. Using Timed-Sequence, the program allowed a student to move from very easy to difficult problems. Originally, he mixed addition with subtraction to create a math problem that joined two concepts. However, initial experiments with young children demonstrated that this concept was too complex. He modified the program to generate problems of addition, subtraction, multiplication and division. He created four separate sections.

While the program worked, there was nothing unusual about it. It looked like several programs currently on the market. The only difference was that Mr. Arnold's math program had four levels and used random numbers for an almost unlimited variety of problems.


It was while Mr. Arnold was looking for a theme, something different, for his math program that he designed a series of grids to display sections of the problem. The grids allowed various numbers and math symbols ( +, -, *, and / ) to be displayed. As he experimented with the grids, he wrote program code to change grid square colors, present background images, and move numbers, he noticed that the grids had the ability to move numbers in any direction. The grids also allowed one problem to interact or intersect with another problem. They could intersect and interact horizontally and vertically. Mr. Arnold found his theme!

The grids allowed math problems to intersect and interact in horizontal or vertical patterns. One problem's answer created another problem or another answer. The grids became puzzles as one math problem expanded to additional math problems. Mr. Arnold created the name crossfooting. The name came from the concept of a footnote (used in literature as a basis) for the work and that the grid puzzles began with a single math problem that formed the entire puzzle. The math problems built upon one another and interacted. In addition, unlike other computer math programs, where one problem disappeared after it was solved,  the grids allowed the previous math problem to be seen. The student could see number relationships as one problem created another problem. The initial name was Number Crossfooting.

The name Crossfooting was created in 1989. The word crossover is frequently used in advertisement, today, but the name Crossfooting remains unknown. It is a method where numbers intersect and interact with other numbers in vertical and horizontal directions based on a single problem, that foots the puzzle and crosses with additional problems.


It was while Mr. Arnold was developing the grids that he realized they had the ability to change colors, move, and present digital background images. He experimented with these abilities but realized he was creating software that attracted only children. He modified the grids to also appeal to older (14 years and older) students. He used the term crossover.  The program crossed over from children to adults. Mr. Arnold's math program used two new and unique concepts - crossfooting (to allow math problems to intersect and interact with one another in a vertical and horizontal position) and crossover (to crossover from children's software to software that could be used by older students). Number Crossfooting  became Number Cross .

However, Number Cross was not finished. Mr. Arnold added a scoring module. This module kept scores of the number of problems completed. He added (but did not activate) a diagnostic module that recorded incorrect answers. He added (but did not activate) Team Play. Team Play allowed one or more students to challenge each other. He added the Master Puzzle. The Master Puzzle appeared after a secret random number of successfully completed puzzles. It presented a unique problem - it began with one number and three clues were given for the next number. After three unsuccessful attempts to solve the second number, the Master Puzzle would disappear and return later. If successfully completed, the student, or students, would receive a certificate (suitable for framing) declaring them a Master Player. No one ever successfully solved the math problem.

The program was dedicated to the memory of Clifton and Johnny Mae Heath. These two people believed math was one of the most important skills a person needed to be successful in life. The program ended with a small window. The window only appeared when the user exited the program.  The marketing phrase, "Math is the Common Sense of Life", also appeared.














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