Computer Science, unplugged?

The National Ctr for Women & Technology (NCWIT) has produced "Computer Science in a Box," a curriculum guide for teachers with students aged 9 to 14. CS in a Box  enables teachers to introduce concepts in computer science -- binary numbers, sorting networks, etc -- through activities that get students moving, interacting and thinking. And that don't involve using computers. 

One hoped-for outcome of this and other NCWIT measures is to increase the number of girl and women students who study science- and technology-related fields. 

The problem? The activities aren't effectively linked to their real-world contexts. And because there's no way for kids (or teachers) to connect the activities to anything, most kids (and teachers) are going to recall the activities, if they recall them at all, as pleasantly kinesthetic interludes between bouts of real learnin'. The science underpinning computers will be as mysterious as ever.

An example: The Binary Numbers teaching plan involves working with a standard set of five cards that demonstrate binary numbers (restricted to 1 and 0).  If a card is face-up, it's a 1, if it's face down, it's a zero. On the "1" side, each card has dots that demonstrate scaling by powers of 2 (1, 2, 4, 8, 16, although you'll note the order is reversed in the image below). 

 

In the whole-class activities, teachers and students explore making various numbers by arranging the cards to expose different values and interpreting these as binary representations. (Like for example, 15 is 0 1 1 1 1 [or 0 + 8 + 4 + 2 + 1] in our five-card or five bit system).

In the independent activities presented in a worksheet, appealingly, you're invited to use your five fingers as the integers in the scale to count--just using one hand--all the way to 31! Try it, it's way fun. (Even if your digital dexterity is a bit lame and you need to use your other hand to bend some of your fingers up or down in certain combinations.) Go ahead, try it, it only takes a minute. Here's a hint:

But, so? What's logarithmic scale to me or me to logarithmic scale that I should give a damn? THAT potentially fun bit of information, certainly the information needed to make all my finger-bending make sense, doesn't make an appearance in the NCWIT materials. And there's the problem: Imagine I'm a 9-year-old, I've put up with my teacher making me puzzle out the meaning of those cards, I've sat at my table or my desk bending my fingers and trying to count and occasionally getting corrected in public, and I understand that, yes, this bizarre system might actually be good for something. But what?

And with that, the experience fades. Later on someone at home asks, What did you do at school today, Little Lucinda?, and I reply, as usual, Nothing. When pressed, I admit that we did some counting, I might say we did some counting on our fingers, and if I'm assiduous in my efforts to forestall more questioning, I might even demonstrate. 

But understand? Forget it. 

What's missing, or among the several things that are missing, is the connection between "binary addressing" (1001 0101) and the way that I'm "naturally" or logically thrown into counting by powers of 2! (1, 10, 100, 1000, 10000, which is counting by powers of 10, is transformed into 1, 2, 4, 8, 16 and so on). And how do I get so thrown? As near as I can make out (and I'm obviously not a CS guy, or girl), once I limit myself to a given number of bits, say 8, my ability to represent numbers in binary is pretty limited: 

counting in binary to 9

0	0
1	1
2	10
3	11
4	100
5	101
6	110
7	111
8	1000
9	1001

In the table above, if we imagine using four fingers on one hand, we add new bits for the integers 1, 2, 4, and 8, and these also enable us to also represent 3, 5, 6, and 7. And then we're out of fingers.

But if I tie each of my integers to a "power of 2" number, and if I use all of the bits just as I did in my five-finger counting system, I'm suddenly representationally empowered: 

 

counting to 9 in a 5-bit binary system scaling by powers of 2

0	00000
1	00001
2	00010
3	00011
4	00100
5	00101
6	00110
7	00111
8	01000
9	01001

And see, I've got way more integers and combinations that I can use. 11111, for example, equals 31! 

NCWIT, however, just doesn't give me (whether I'm a teacher OR a student) the tools I need to understand why any of this means anything to anybody: 

One bit on its own can’t represent much, so they are usually grouped together in groups of eight, which can represent 

numbers from 0 to 255. A group of eight bits is called a byte.... Ultimately bits and bytes are all that a computer uses to store and transmit numbers, text, and all other information. 

Not enough. Not enough, by far, to get a teacher to invest classtime, energy and "teacher capital" in an activity that doesn't quite close its own circle.