Cindy - if he can't find any other alternative, please feel free to forward his contact info to me, or send my e-mail address to him (a Reply To will expose it), cc: me.
The rest of this is background for those who may be curious about the state of our educational system from someone on the inside - those with lives may return to them now. In the olden days, before CS was offered Pretty Much Everywhere, discrete math courses were often disguised by titles such as Finite Automata and State Machines and offered in Science or Engineering departments, while courses on Predicate Calculus, and Number Theory (e.g., Groups, Fields, and Rings) were typically required to be taken in Math departments. Some requirements have been gradually sliding down into earlier grades, to the point where Number Theory is now taught in small bites (pun fully intended) starting in middle schools as early as 5th grade (beginning the hierarchy with Whole numbers). Eventually, a number type or two, properties, identities, etc., are added, potentially up through Real numbers in high school, depending on whether Physics and/or Advanced Electronics is going to be taken. Some states are mandating CS fundamentals in every grade, from K through 12 (Virginia has come up with one of the best I've seen, as it includes sample lesson and unit plans in addition to the curriculum requirements). CS in K - 12 may sound ridiculous, but the sooner you can expose kids to the most basic concepts, it's much more likely they'll be able to continue the progression. I've taught binary math to kindergartners using pennies. They don't know that a penny is 1/100th of a dollar, because they can't understand what either of those concepts are, but they do know that pennies are shiny (I go to the bank to get rolls of new ones) and they see that others who are older use them to buy things. I just use pennies to represent ones, and absence of pennies as zeroes in binary, usually in egg cartons to immediately show the organization of bits, and making more obvious where the absences are. Kids learn how to read and say binary numbers (e.g., 10 isn't "ten", it's "one-zero", and they haven't learned decimal ten yet anyway, which is a good thing). It's much easier to teach binary math first, and higher-order number representations later, than the other way around. Then, we go through the four rules for binary addition - zero plus zero equals zero, zero plus one equals one, one plus zero equals one, and one plus one equals zero and carry a one to the left. It's easy for the kids to learn this by handling the pennies and moving them between egg carton depressions in accordance with those rules. In later grades, multiplication by two by moving each penny one space to the left is likewise a piece of cake, as well as division by two by moving each penny to the right. When kids learn a concept, they get to keep the pennies used in that day's lesson, and kids will do lots of things to become shiny penny hoarders. That includes stealing other kids' pennies, whereupon, when, not if caught, we make a detour into computing ethics, which is one of the sets of concepts required to be covered in every CS course! BTW, one of the reasons that we have to get girls exposed to STEM in a friendly way as early as possible is because peer pressure against them excelling in STEM starts around the fourth grade. I've actually overheard conversations among girls that young that go something like this: "Oh, you don't want to be too good at math and science because then you'll make the boys not like you because you're smarter. Then, they won't ask you out on dates, you won't get married, and you'll never have kids and grandkids." I am not making this up, and there are geographic/ethnic groups that reinforce this in spades - girls are supposed to get married after high school, have kids, and raise a family ... period. Based on what I've observed going on in K - 12 STEM in most states, I'm seriously wondering who will be keeping the lights on, let alone the rest of our infrastructure running, when I'm at the age where getting my favorite flavor of pudding will be the high point of my day. People with humanities degrees (almost no universities offer true liberal arts programs any more, where science and math are given equal emphasis to literature, history, etc.) are now preferable to become STEM teachers than people with STEM degrees. Part of it is because there are now ten people with humanities degrees for each job opening requiring them, but there are upwards of two STEM jobs for each person with such a degree, so people with humanities degrees are simply cheaper to hire. It's even worse in education, where recruiting people with STEM degrees is very difficult due to competition from commercial organizations, especially high-cost-of-living metro areas. Educational administrators almost all have humanities degrees now, as the old-timers who have STEM degrees and come up through the system are retiring as part of the continuing expansion of the number of Boomers leaving the workforce. It's become a perfect storm, and that's not a Good Thing. We now return the rest of you to your Life, already in progress ... All the Best, Jim KJ7JHE
