Number

Number is a rich, many-sided domain whose simplest forms are compre- hended by very young children and whose far reaches are still being explored by mathematicians. Proficiency with numbers and numerical operations is an important foundation for further education in mathematics and in fields that use mathematics. Because much of this report attends to the learning and teaching of number, it is important to emphasize that our perspective is considerably broader than just computation. First, nu...

 Systems Science as a Subset of Other Sciences

Systems science is best seen as a science that consists of nested sub-sciences. It is presented most compactly using the notation of set theory. Let A represent a science of description. Let B represent a science of design. Let C represent a science of complexity. Let D represent a science of action (praxiology). Let E represent systems science. Then A ⊂ B ⊂ C ⊂ D ⊂ E illustrates the concept that we can learn something of systems science by first learning a science of description. ...

 Donald Knuth on Getting to the Source Material

Seibel: Do you feel like programmers and computer scientists are aware enough of the history of our field? It is, after all, a pretty short history. Knuth: There aren't too many that are scholars. Even when I started writing my books in 1963, I didn't think people knew what had happened In 1959. I was reading in American Scientist last week about people who had rediscovered an algorithm that Boyer and Moore had discovered in 1980. Ii happens all the time that people don't realize the glorio...