Digital (also known as DEC and Digital Equipment Company) did more than sell one of the first so-called minicomputers. It also published some of the first educational software to be used in regular subject classrooms and pioneered in supporting computing teachers. Our Collection includes several documents in the EduSystems series; “computers are for kids – EduSystems – expandable, economical”.
See, for example, HCLE Item 1015: Advanced Problems for Computer Mathematics. For $2, students and teachers received a 75 page resource manual that took at least two approaches to teaching programming and problem solving. (Today you can get it for free by clicking on the linked title above.)
As the general headings in this booklet suggest, approaches to mathematics can be dry, with abstract titles that are correct and descriptive but not particularly exciting.
- General Mathematics
- Intermediate and Advanced Algebra
- Probability and Statistics
- Mathematical Analysis and Physics
Under these headings you find sets of increasingly difficult problems that might be solved more easily using a computer program that either paper and pencil or calculator. Today, an educational software company would be likely to supply the student with either 1) a graphically fancy, game-like program that provides a solution to the student followed by a multiple choice quiz; or 2) a computer-generated video that lets the student make predetermined choices within the problem space without requiring that the student understand how to state the problems or generate the answer. In the mid-1960s when Advanced Problems for Computer Mathematics was published there were not computer graphics or videos. Only images created with typewriter characters could be made. There was no internet and no common medium on which to supply and store the programs. The most practical way to share the software was to print the program itself in the booklet and let the students type it into whatever computer they had access to. This process built a bridge between the academic discipline being studied (mathematics, in this case) and computer programming.
In Advanced Problems for Computer Mathematics problems were frequently presented in a way that suggested the steps required to solve them. Then, the student is instructed to; “Write a program…” (in BASIC.) A sample program is provided to demonstrate one possible solution. If the learner’s program actually worked (ran) after a couple of tries s/he could move on to a harder task. But the computer isn’t actually doing any teaching. It’s role is more like a laboratory or playing field. When the learner must troubleshoot and debug a teacher (or fellow student) will be a key tool for learning. Digital’s early approach to educational software illustrated the utility of the computer along with experience of computers’ limitations. It also demonstrated that answers might be approximations, not exact. There’s even a study of how rapidly and accurately (or inaccurately) π can be calculated. “At 10,000 terms, the approximation to π is off by 1 in the 4th decimal place.”
Advanced Problems for Computer Mathematics provides some abstract problems but several are word problems that suggest a variety of practical, real-world applications for computer programs.
- What’s the volume of a potato? A study in calculus.
- How far must someone travel to get from various places in Possible Gulch over Bell Mountain to Probable Junction? Bell Mountain has the shape of the normal distribution curve, providing a study in statistics.
- How does a crosswind affect a plane’s flight? An exercise in a simple simulation.
While the utility of the computer is demonstrated, alternatives to the latest technology are also supplied. For the potato problem, they include a solution Archimedes used over 2,000 years ago. Sometimes a bowl of water is all you need. As it says in the text; “Hey, that’s a good method…keep the beaker and get rid of the computer.” The computer is presented as a tool, but not the only tool. An interesting perspective considering the publication is from a computer company.
The document itself is worth studying. Even though the publication is about computers, it didn’t use desktop publishing software. There were no word processors at the time. Some pages are photocopies of computer printouts. Fonts change depending on the source. Symbols like π and graphics like the airplane were hand-drawn. The last page is copied from the list of Digital’s Sales and Service contacts around the world, an implicit reminder that at least one motivation for producing the series was to increase sales.
Computers, computing, and new ways and reasons to learn developed together. While such publications may have helped sales, they also represent a time when an industry knew it had to build itself, its user community, and its future workforce. Prior to this, there would’ve been a much smaller audience and the publications would be directed at professionals who cared more about content than layout. Soon after this, the audience was much larger and broader, and the expectations were for more polished presentations.
Preserving such documents for researchers and the curious is why we’re creating our virtual museum. Even one edition, like this one, can provide a cornerstone from which to build broader research projects and histories. Tell us where it leads you.