<html><head><style type="text/css"></style></head><body><div style="font-family:times new roman,new york,times,serif;font-size:12pt"> <div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"><div>Hi Asaf Among other things, our human brains are set up by nature to  -- take the world as it seems  -- want to learn the culture around us  -- believe (and then try to justify our beliefs)  -- especially believe our tribes, from family outwards  -- think of most things in terms of stories  -- disappear our beliefs into a "normal" which makes it difficult to think in other terms  -- desire explanations, but be satisfied with stories as answers These are some of the reasons that it was hard for our species to invent real science. Francis Bacon wrote a good critique of us in the early 1600s. <img src="file:///C:/Documents%20and%20Settings/Panasonic/Desktop/Sketch.jpg" alt=""> One of the difficulties of learning (teaching) science is that each and every one of the points above (and more) has to be gone against. We need something more like: -- the world is not as it seems -- our culture's views likely have nothing much to do with how the universe is set up -- think instead of believe -- especially be careful of our tribal pulls to believe like them -- most interesting things are not stories and can't be judged by story criteria -- have to fight the invisibility of "normal" -- we need to be super tough about what we provisionally accept as explanations for anything Most parents and teachers I've explained this to are shocked. It's so anti-social and rebellious! This is the last thing most of them want to help their children achieve. (And they are so successful.) I've mentioned this before, but every scientist has to fight every day to hang in on the second list as much as possible. This is because we are doing something more like adding some separate thinking-process-routines to our ways of thinking and knowing, rather than being able to really clean house and get all the bad thinking modules (some of which are good for other purposes) out of there. So it's a conflict. And (also mentioned before) there is such a large range and extent of good science results, that no scientist can repeat all the experiments, even though that is the only real way to deal with many of our human problems with this difficult pursuit. So most scientists think that a good ploy here is to start off doing real science involving real contact with nature dealing with interesting phenomena that are in the child's world, and doing the whole deal of speculating, measuring, modeling, comparing, predicting, reporting, etc. The "documents" that wind up through this process are superficially like documents produced by the processes of the first list, but have a completely different foundation and point of view. When scientists read results they expect that something really rigorous has actually been done (rather than just someone claiming that x y and z were done with results p q and r). However, scientists are human and some of them find reasons for cheating. The results of cheating look exactly like the real deal! This is why the process of science relies on scientists who can be more skeptical about the results of others than those who get entranced by their pet theories or decide to cheat for some reason. Feynmann: "Science means you don't have to trust the experts!" So ... What we *don't* want to do in the early stages of trying to teach children the point of view -- process, outlook, epistemology, etc. -- of science is to get expedient and try to teach from books (even if the book has really been vetted, and most aren't, this is not science). Or from computers (ditto). It's not someone else's results we are trying to get across first, it's how to get good results yourself! (A similar difference exists between learning to play music and taking a music appreciation class, but the outlook difference is much larger wrt real science and "science appreciation".) This is not at all easy to do. Part of cultural learning is to take what the culture does on faith and apply it to the problems of survival and happiness. The application of ideas that have been found to work can be done lots of the time without any interesting understanding. That they work is just fine with most people. (In engineering jet engines, suspension bridges, it's a good idea to use what is known to work!) When math and then science got refined to the point of great departures from what we are set up by nature to do, the society still exerts a huge pull to "remember and apply". But this is a very bad way to teach real math and real science. On the other hand we don't want to have to regress through every building block in order to do real thinking. One way that this is handled in both science and math is the idea of "Stable Neighborhood of Foundation" (SNOF), which is the idea of drawing boundary conditions around what you are going to treat as elementary and work outwards from there. This is done all the time in science, and more sneakily in math. So, for example, biologists have been in heaven since the 50s when they could really start to use chemistry as their SNOF. Chemistry is built on physics, but the chemists' SNOF is what QED determines chemical bonds to be, and just how QED actually works is not needed for their thinking (and this is good, because the physicists have been upset for years that they can model the behavior of QED to 11 decimal places -- it's one of the most accurate models in science -- but they just don't understand what the SNOF of QED is -- this is why the biologists are happier than the physicists). A good SNOF for children is addition, because it can be modeled very easily in the physical world, and doesn't at all require the more careful axiomatization and underlying framework in logic due to Peirce, Peano, Frege, Russell & Whitehead, etc. A nice architectural framework for simple addition is "incremental accumulation" (the operator could be called "increase by"), which again can be very successfully and deeply understood and used by first graders. Doing things repeatedly is also elementary for first graders. This allows us to use the computer in this case to only do what the children know to do, but lots faster and without getting bored. So a little script like this that very young children can write:                           Repeat: car's location increase by 5 changes the car's location by 5 somethings over and over. This is completely understandable to them, because they have already acted it out with their bodies before getting their self drawn car to do the very same thing. I won't go through how accumulation is portrayed on the computer (but see if you can imagine ways to do this). A ten year old can very easily come up with the following script:                          Repeat                               car's speed increase by 5                               car's location increase by car's speed What happens, happens  ever more quickly! To help, you can have the car leave dots behind to show where it was at each time step of the repeat. This is not an equation in algebra. But it does say exactly where the car is going to be after each time through the repeat. It's *extremely important* to see that the meat of this covers the same ground (so to speak) as a second order differential equation of motion. DEs are "solved" symbolically to produce an expression for all locations for all time. Our "differential relationships" here are "acted out" to provide a sequence of the locations as *time evolves*. This is an old idea in math and science, but it is very tedious for humans to do. Babbage said "I wish to God these calculations were executed by steam!", and his first difference engine was just such a mechanical device to do incremental additive accumulations of DRs up to order 7. This is the math part of simple motion, which does produce a simulation (like the "physics" simulator) but the children make it themselves from a completely understandable SNOF. (And at this point is has nothing whatsoever to do with physics or science -- it's just math, and it's fun by itself). I've described elsewhere doing this several months before taking a look at what the world does when you drop something. This is to avoid leading the witness too much. We precisely would like to set up the conditions where the children can look at a physical record they have taken themselves and see that some of the math they did earlier seems to describe something similiar. Then to do the work to show that they are really similar. And so forth. You say below: >Instead of working with an equation that >represents a ball on a spring for example, we can work directly with >the ball on the spring. We don't want to work with regular DEs with children, but with powerful math that has been set up for how they can think about math. We don't want to work with a simulated "ball on the spring" (I think this is what you meant to say) because the canned simulation is just *someone's opinion* and is not a real ball on a spring. (In my strong opinion -- this is why I've been writing and writing about this -- this is a very bad way to go, and is exactly *not science* in its approach.) And balls on springs are easy enough to investigate (how about in 7th grade?). We find by pulling on the ball on the spring with a scale that the amount of strain on the scale seems "pretty nearly" to be proportional to the stretch of the spring . Here's one script that the children can come up with. We have to realize that the key is to measure the current length of the spring each time through the repeat and use it to generate the restoring "force".       Repeat           Spring's accel <- Spring's normalLength - Spring's length           Spring's accel multiply by 0.05           Spring's speed increase by Spring's accel + 4.0           Spring's length increase by Spring's speed Look at the bottom two lines first. They are the same differential relationship as the 2 stage one used for constant acceleration in the car and gravity examples above. We can use this because the acceleration can be treated as constant *within* each time step. The first two lines calculate the acceleration anew for each time step by calculating the stretch of the spring and then scaling it (part of the scaling here was done by adding the 4.0 on the next line). This is nicely simple and it is the incremental math way of connecting the "oomph" of the spring which is related to its length with accelerated motion of anything. This one is really fun, because if we make a record of the displacements as the model progresses, we get something that looks like a sine wave. This is not a trivial integration using the algebraic form of calculus but our "dynamic incremental math" using just additions generates this result directly, and acts it out as an animation in the bargain. <img src="file:///C:/Documents%20and%20Settings/Panasonic/Desktop/Sketch.jpg" alt="">(see attached picture) This is also a nice illustration of why differential models of any kind are so useful. The differential relationships of many non-linear gross behaviors can often be represented in the simplest of additive piecewise models. And, to say it again, we get real science when we do all three things: measure a real world something, come up with a model, make the model work and predict, and then compare the model against the physical record. Our opinion is that we need to find as many physical situations where the gross phenomena are:  -- in the world scale that the child lives in  -- where it is easy enough to investigate in sufficient detail what is happening  -- and where the math to model it is completely understandable to the child (sometimes the computer can really help). This is why science needs to be taught along lines that have the criteria I've put forth in this exposition. Best wishes, Alan </div><div style="font-family: times new roman,new york,times,serif; font-size: 12pt;"> <div style="font-family: arial,helvetica,sans-serif; font-size: 10pt;"><hr size="1">From: Asaf Paris Mandoki <asafpm@gmail.com> Subject: Re: [IAEP] Physics - Lesson plans ideas? [snip] Most of the Physics we know now has been done by: -observation -ideation of models (usually simplified) -using the models to make predictions -experimentation I think that the Physics activity can help mainly in doing the transition between the ideation of models and the making of predictions. Usually this is done with complicated tools such as differential equations. Instead of working with an equation that represents a ball on a spring for example, we can work directly with the ball on the spring. Greetings, Asaf </div></div></div></div> </body></html>