“Doubling up” on learning

In Randy Pausch’s “Last Lecture,” he defines a “head fake” as doing or learning one thing when your brain thinks you’re doing something else entirely. For instance, the brain “thinks” it’s learning to play baseball when it’s “really” learning teamwork. Part of what makes FIRST so effective is that the participants “really” learn the same things they would from any other sport, but what they “think” they learn, namely the technical skills required to build a robot, is far more valuable than moving a ball around. This post is about those sorts of multidisciplinary doublings (or triplings and so on), where different valuable skills are taught together. (I’m sure there’s a buzzword for it, so let me know in the comments.) As Douglas Hofstadter describes in Godel, Escher, Bach (review to follow), working on multiple levels and making connections between seemingly disparate topics is at the heart of intelligence. More practically, it saves time.

Consider this lesson plan which looks like mathematics but is “really” an introduction to computer science. The students are taught long division (or three-digit multiplication or something similar) in the normal way. The next day an educator with a comp sci background explains the idea of pseudo-code, a set of instructions without strict syntax that allow students the describe simple typographical operations. Afterwards the students write a “program” along the lines of “divide the first digit of the divisor into the first digit of the dividend and write the quotient above the line…”. Basically, the students should describe the process step by step and unambiguously, in their own language. The educator goes through a few of these with the class, pointing out flaws, improvements and subtleties of the algorithm along the way. He may introduce control structures such as conditionals and loops as necessary, to produce a “cleaner” version. Students then work long division problems, either with their own algorithm or the class’s. This lesson teaches students to think systematically about explicit instructions, while also approaching long division in a new way. Students are given copies of the class’s algorithm as a study aid for the test.

A key point about about computer science education: you don’t need a computer. For instance, before launching into a middle school geography course, the teacher can spend a day asking students to think about a generalized “country”. What does a country have? A name, a population, a location, a language, a capital city, a government system, the children might answer. Compile a list of information students will learn about every country over the year, then ask them questions about the data types. How might this information change, and what is constant? How does one fact affect or tie in to another? How does a country react with other countries? How are countries grouped? Before you know it, the teacher has laid the groundwork not only for the geography course, but also for object oriented programming.

Don’t stop there. If the students have the requisite programming experience, bring them into the computer lab and have them write programs to go through a list of country objects (which you provide). If they don’t, give them this information in a table and let them work through it by hand, writing down the process as well as the answer. The students should determine, for example, if there is a country named Foobaristan (no) or how many countries are in Europe (50). An advanced project is to calculate how many people speak Spanish. The students must figure out on their own to keep a running total of the populations only of Spanish-speaking countries going down the list. Afterwards, discuss why this is only an approximation, and share the real number of Spanish speakers (417 million).

Computer science is taught at a much higher grade level than is necessary. Projects like these help change that, while also giving students a head start within the current educational system (because anything is a head start). Methodical, logical reasoning is a skill taught in elementary school with varying success, but few realize that it is the foundation for a rewarding discipline and career (or at least I think so). In fact, it’s best to start on paper so the students don’t get bogged down in missing semicolons and integer arithmetic. Philosophically, this hints at the idea that computers don’t do anything magical or new. Perhaps more importantly, it’s cheaper.


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