How do we get ideas? ... If we knew, learning would be a breeze. If we knew where we were going, we would be there. But we don't know.

Learning is a creative process. It is the art of going from one level of knowledge to another. Old ways of seeing are replaced by new ways. We don't know how this is done; there is no formula that accounts for it. All we know is that, somehow, when we learn we move from one knowing state to another -- we go from one way of dealing with a problem to another way. We can't know something before we know it.

This creates a predicament for the educator, because it requires helping someone move from state A to state B when there is no formula or known procedure for doing it. The trick in education, therefore, can be no better than to present mechanisms and procedures that seem promising as learning tools.

Playing my tennis tutorial games is an example. The games do no more than let the student find his or her own way, by providing structured simulations to let him/her perform trials or experiments in benign environments that resemble the real context of the skills. You do in pretend mode what you do in the real world. The player does the things in simulation that he might do at the court. He proceeds by trial and error, one shot at a time and takes cognitive steps in what is sometimes called chunking. It is a process of coming to know his tennis context, and thus himself as a tennis player. (By his ideas you shall know him.)

For a variety of reasons, however, simulations offer more than we can get in the real environment. For instance, simulation makes it easier to find "best results." For these reasons, too, it is expected that your chance of learning will improve. The simulations provide a way to learn about the interaction inductively, by observing the results one shot at a time. But there is no guarantee of success, no assurance that critical ideas will be triggered.

In tennis, the more conditions and demands you put on a shot, the more difficult it would be to bring it about. At a minimum, of course, to be successful, you have to be in good physical shape. Plus you have to know how to plant your feet and swing the racket. And you have to understand trajectories and the mechanics of hitting the ball. You especially have to know the racket's direction of motion, its speed, and its orientation angle when it meets the ball (the racket control variables, as I refer to them). Not to mention the need for a strategy to guide your choice of shots.

That's what my tennis tutorial games are all about. They're meant to help you see what to do under different game conditions and on the demands put by you on shots you might make. They are meant to help you understand the way the ball moves through space and how you should meet the ball with your racket to get desired results. That's not easy, because the direction and speed of both ball and racket are changing continuously. Timing thus becomes critical. Old ways of seeing the problems can get in the way, as well. To shape your stroke you have to know how you need to contact the ball. Using the games will help you learn about the interaction, one shot at a time, by observing the results.

Each game has its own simulation that lets you pretend you're hitting the ball at the court. And each deals with one or another of the basic tennis shots, such as drives, serves, drop shots, and volleys. Each program provides targets to shoot at, and you select racket conditions to try to hit the targets. Feedback is available to let you see in more detail how well you did.

WRONG!

Not to repeat myself, but should you happen to get the notion from reading the series books and playing the games that you wouldn't have to practice at the court any more, you'd be mistaken. So let me quickly disabuse you of the idea. By themselves the materials are only for study. You can learn from them, sure. But you don't swing a real racket or hit a real ball; you don't develop motor plans for hitting. In fact, the more subtle the contact, the more you have to practice. So practice at the court is just as important as ever. Maybe even more so, because with computer help you can practice smarter, using your valuable time more wisely. In short, the work is meant to foster sharp ideas. You can employ the programs to help find errors in your thinking and even find ways to optimize your shots. (Should you need more help, I'm also available to answer questions.) And if you're taking lessons, the smarter you hit the ball, the more you learn and the better you learn, because you'll have a deeper sense of what you're trying to do. The material makes that possible.

The games themselves are personalized, science-based simulations. I call the package, Select 'n Shoot, because they are formulated on a target-shooting game model, like dart throwing, handgun fixed-target shooting, bow and arrow target shooting, and the like. The games are meant to help you learn how to hit the ball -- not to actually practice swinging the racket, let me say again, but rather to show what you should be trying to do to make a good shot. In other words to help you see what has to be done to make your swing a success. This is what defines the stroke.

I should emphasize that the games are computer programs that use simulation for their implementation. The games are designed for application on an IBM-type computer (not Apple, for instance) and use the Microsoft Windows environment. I wrote the programs using Windows 98, so that's the best way to go, but you can use any operating system that's compatible with Windows 98. (To read the books you need a Word for Windows word processor).

Each game has four parts. Two parts form a Practice section, a third part is the test or Challenge section, and the fourth part is the Feedback section. The Practice section lets you investigate your personal skills in hitting the ball. Challenge tests your hitting skills and rewards success in reaching targets. And the Feedback section lets you see in more detail how your shot worked out. Each program in the package lets you probe your personal tennis space, a space that’s ultimately defined by the constraints imposed on your game at the tennis court -- both in the way you perceive what's occurring and in the way you perform what is to be done. For return shots, you as the player would have to read the oncoming ball and apply your hitting strategy to create a return shot.

Finances always come into play when using programs like mine, so let's look at the details. We might think of each play of a game as a real-world tennis lesson and then compare it with the cost of that lesson (which can vary from large-group formats to private lessons and anything in between). There is always a range of prices to consider. For instance, private lessons with a teaching pro can easily go as high as $100.00 per hour, depending of course on the level of affluence of the area. But let's say for the purpose of discussion that the average is at half the price, or $50.00 per hour.

So a price of $50 for an hour with a game ranks it as financially equivalent to a single lesson. Okay. But when you've had your lesson, that's it, you're done, and the money is gone. Whereas you still have the game programs and can continue your study for another hour, and still another, and another. So the comparison improves considerably with time. This is a credible argument because you rarely learn a skill in one lesson; repeating trials is more the norm. And $50 an hour adds up very fast.

Now compare private lessons with group lessons. Say you have a group rate of $50.00 per hour and there are ten in the group. Your cost now drops to $5.00 per hour, which is a sizeable improvement. However, you can't expect to have the teaching pro's attention for the full hour, unless of course he/she lectures to the whole group for an hour. But in that case you aren't likely to get the attention you need for your particular problems (in which case the real lesson would be not to take another one). Much depends on how the teacher deals with this problem, so it's hard to determine the value of the lesson to you.

Suppose you have the program and you take a private lesson. If you've taken the time to study with the game, you could attend the lesson as a smarter student and understand more quickly and precisely what the pro is telling you and what you have to do to make your adjustments. You will likely have a better grasp of the ideas that are involved and won't have to spend as much pro time as you might otherwise, thus reducing the effective cost, since you can more quickly move on to other things.

Even if you aren't taking lessons, think of the many hours you waste at the court trying to figure our how to hit the ball and getting frustrated because you don't seem to be gaining on it. Plus the fact that mostly what you'd be doing is hitting the ball back to your hitting partner and even in that limited role not getting any feedback. With the games, though, you get a wide variety of shots and plenty of feedback. You can also write to me to discuss technical problems.

You can even use the games in grant proposals to illustrate the type of program you could develop. The USTA, for instance, is prepared to fund projects for disadvantaged kids, projects involving education, computers, and tennis designed to lift the kids out of the poverty mindset and bring them into the broader, healthier community. Other agencies and foundations offer comparable support.

And of course the computer program doesn't wear out, so you could sell it yourself or give it away as a birthday present. I don't recommend copying it, though, because that's not legal.

Tennis is a game of trajectories. You hit them into your opponent's court and your opponent hits them back to your court. Back and forth it goes. Each player tries to outmaneuver the other, hitting dazzling drives to the corners, subtle drop shots, passing shots, overheads ... whatever makes sense in line with your strategy and has a chance to score a point, possibly even win a game. (I don't know why it is, though, but some shots are more acceptable socially and even encouraged. Yet other shots are almost taboo. For instance it's quite acceptable to hit a slam winner, but somehow it's not acceptable to hit a drop shot winner. It's almost as if the drop shot surprise is too embarrassing to the receiver to accept socially. Is the Macho mystique at work here?) How well you do depends on how well you know trajectories and how familiar you are with the mechanics of the racket/ball interaction. When you hit the ball your intention is to drive it to some spot in your opponent's court. To be successful, you must know how it's to be done.

As a player, you serve or you create return shots. Either way you have to hit the ball, and for best results you have to hit it properly. For returns, you have to read your opponent's shot, intercept it, and find a way to return it. To have good results you need to know trajectories when you see them. And you have to be able to produce your own. It's this production knowledge that my Select 'n Shoot games are meant to impart.

The games let you practice hitting the ball as you would have to do on the court, either for serves or against shots your opponent might hit. To be able to do this, each game simulates the play action, using science-based racket mechanics theory and equations of motion for the trajectories. With the games you will learn the dynamics. Not as a rocket scientist, using equations of motion. But as a player, hitting one ball at a time and seeing what happens. And that's not half bad.

Realism in a simulation is gained by using scientific principles to represent the context in which the game is played. A complete and fully realistic simulation would represent the court, the players, and the surrounding environment. But not all things are possible on a first-of-a-kind program -- or most any project, for that matter, and the games of Select 'n Shoot are just such programs. So, for instance, players are not represented in their full scope, being far too complex. The cost of producing the program, alone, would be prohibitive. So the games aren't perfect, though they are quite accurate.

Indeed, I suspect it's quite possible that, after considerable practice, your own choices of racket values for particular shots can be more accurate than the computer's. It's a matter of art being better than science in the particular event. Theories deal with classes of events and, as abstractions, leave out uncommon properties of specific events. But the special conditions can be taken into account for individual events. Reaching that point, though, is another matter.

To produce my simulations I began with the unencumbered ordinary world of the court, ignoring surrounding objects such as fencing, grandstands, spectators, trees, birds, and the like. Using official dimensions of the court and net I drew orthographic projections of the court from above and from the side. Then, with just the everyday court as my reference, I embedded the player, a natural but significant step. But the player brings along a visual perception capability and therefore sees the court in perspective. So I also added a perspective view to go with the orthographic projections.

It was only after stripping away all but the most essential ties between the court, ball, and perceiver that I was finally able to formulate and program the simulation. The result is the group of games of Select 'n Shoot. Each game in the package has its special attributes, because the shots they deal with are different. (You don't react to a lob the way you do to a drop shot. Or to an underspin drive. Or to a serve. The shots are different so the program features are different.) But the overall designs are common. There is, of course, a natural difference between programs for serves and those for returns. With the latter you have to provide shots presumed to be hit by an opponent. For serves, this obviously isn't required.

You will have noticed when playing that every time you increment the orientation angle of your racket back a bit to put more spin on the ball, while keeping the direction of motion of the racket the same, the ball bounces higher and doesn't go as far down court. And when you increment the angle in the other direction, you get a lower shot and the ball goes farther. Not only do you change the horizontal speed of the rebound (relative to the court), but you also change its direction. Each change may be okay in itself. But it’s not okay if you don’t want to change the horizontal speed of the ball or don't want to change the loft. To meet your specs, then, you have to do something about the unwanted effects. The games help you decide what to do.

The Feedback panel has a lot of stuff on it. The main items are of course the feedback displays. But there are also tutorials, such as you might find in an ordinary tennis book. So you can learn some of the technical aspects of the different types of shots. You can click on these pages whenever you choose.

For feedback you can see top and side views of the way your racket met the ball for the shot you just took. You can also get a perspective view of your shot leaving your racket and (hopefully) going over the net and landing in the other fellow's court precisely where you intended the ball to go and the way you wanted it to get there. You can also get top and side views of your racket orientation angles just after hitting the ball, as well as the immediate direction of the rebound. Plus there are top and profile views of your shot, and a slow motion projection of the ball leaving your racket. You can also get summary data on the shot. Where it landed, how fast it was going, etc.

My racket games are meant to foster ideas. Without them (the ideas, I mean) you'd be swinging blind, so to speak. You wouldn't know where you were going with the racket. The ideas give you the direction. They try to establish your purpose in the racket swing. You need the ideas to "see" what to do. The sharper your ideas, the better you can see and the better your chance of scoring points, in my games and ultimately at the court, and in that way you can improve your tennis. It's like shooting bullets, or golf balls, or footballs, or hockey pucks. The tennis ball is like the bullet and the racket is like the gun. In the games you learn by hitting shots one at a time in a simulated tennis environment.

When you swing at the ball you naturally have a target in mind (otherwise the ball would go out of the court or over the fence as often as over the net). So at least there's some direction to your shots; you have some idea how to hit the ball. But the direction may not be sharp enough to be competitive. It's not easy to thread the needle with your shots, like when trying to hit to within a few inches of a corner. That's where the computer comes in handy. It's still not easy, mind you, because it's not easy at the court. But at least the computer can help you direct the shots more precisely by helping you find better ways to hit the ball. That, in turn, expands your game and stretches your use of the court, letting you hit to spots you never thought possible to reach before.

The simulations provide scientifically accurate and quantitative, precise trajectories for you to deliver. And it allows you to hit the ball in a scientifically accurate and precise way. It's a difference between quantitative precision and qualitative imprecision. You practice in simulation quantitatively, deciding how best to hit the ball, and this suggests how you might sharpen your skills qualitatively, the way you deal with the ball at the court. The precision of numbers in the simulation helps you learn to be more precise with your racket swing at the court. But you still have to practice at the court. Motor skills have to be refined. Racket subtlety isn't easy to come by.

As I said before, in each of the ten games there are three basic sections, two for hitting and one for seeing how you've done. They are Practice, Challenge, and Feedback. The Practice section, now, has two parts, which you can use independently of each other. In one division there are no specific targets; this is the simpler practice version and you more or less decide on your own where to place the ball. In the other division several targets are available to aim for, though only one at a time, the targets varying in size as well as location.

With each game you can take practice shots as long as you like. For return shots in practice there are a dozen oncoming trajectories and a variety of targets from which to choose and you can continue with whichever you want, it's your option. In the Challenge section, though, you are given a trajectory and you are given a target, like in a school exam, and you get only one try to be successful, to hit the target. You get points if your shot is on target.

You can switch between Practice and Challenge any time you want. Say you take a Challenge shot but miss your target. Well, you can switch to Practice to try to figure out what went wrong. And you can go directly back to Challenge if you think you've had enough practice and got the problem worked out.

To run a program you merely select your test conditions, decide how the racket should strike the ball, and then review the results. The computer does all the behind-the-scenes work. And you never have to pick up a ball.

The programs make it possible to simulate game conditions and test how best to hit specific shots. You yourself decide what shots to take and how to hit them. In Practice, you select your target and do what you can to get the ball there (by trying different combinations for your racket conditions, or what I call racket control variables). In Challenge, similarly, you decide how to hit the ball, but now the test target is given, the idea being to put you in a more realistic hitting situation. In fact, the gains from using simulation can be greater than what you might get by hitting the ball at the court, because at the court you don't get feedback or re-tries on your shots.

Whatever mode you're in, though, I suggest you don't try to remember what you did on prior shots. On each trial, just do what feels right and reasonable at the moment. If there's any memory work to be done, let it happen subconsciously. Let information accumulate internally and have their effect, building up ideas. It can take hundreds of trials and tests, and many kinds of things you might do.

The games might sound a bit like ordinary tennis books, at least for the Practice part. They are in fact like ordinary tennis books in that they provide normal instruction using text, graphics, and photos. In each of the programs I've included a few Notes and Help snippets, as well as diagrams of the racket/ball mechanics and pictures of the various shots. They also have suggestions for practice that you might run. But both the Practice and Challenge sections are more unlike ordinary books than like them, because they provide targets and are able to display dynamics -- ordinary books can't do that very well, if at all. And of course there's no feedback in ordinary books, because you're not "learning by doing."

The programs use motion deliberately to help you learn racket mechanics. In that way they are interactive, which means they let you try different ways to hit particular shots to find the best way. They draw on simulation to let you hit and make comparisons. They simulate the court action from your own perspective and provide mechanisms for you to spell out personal specs and to input values for your control variables, letting you control the results directly. And they let you practice your shots using numerical aids to help discriminate between different trajectories and racket conditions.

For its part, the Test, or Challenge, section offers targets in various forms, sizes, and locations to test your ability to hit them from different intercept points for different oncoming shots. That's not something you can find in ordinary books.

Each program in the package has the following elements:

• A (timed) title page
• A master panel: menus of diagnostics and tests
• A pre-conditions panel
• A library of oncoming shots (for returns only)
• A trajectory intercept panel (returns only)
• A feedback panel with multiple tutorial options
• Instruction notes, diagrams, and photos
• Glossary of terms
• A list of common problems
• Practice suggestions

There is the possibility of getting a bit confused when running a program. You're not dealing with simple games on a single page, so you have to keep track of what you're doing. Maybe it will help to point out that each game deals with its own shot, so that's the first thing to keep in mind. Then you decide between practice shots or challenge shots. And then you can try the Feedback section.

A difference to keep in mind is that for returns you need an oncoming shot to hit. So you select one from the library -- you wouldn't do that for serves, obviously. Then you decide on a point of intercept from which to initiate your return. From this point there's another difference, because for your Practice shot you get a perspective view and a data summary of the opponent's shot. You don't get either for the Challenge shot. In both cases, though, you can click to the feedback panel once you've completed your return.

The central and most difficult part of learning how to hit the ball is the associated racket mechanics. Racket mechanics deals with the interaction between the racket and the ball. During the ball-racket contact there is a transfer of energy from the racket to the ball -- just as there is from the golf club to the golf ball, or the quarterback's arm to the football, and so on). What happens in the exchange depends on how the ball approaches the racket and how the racket meets it. Equations of motion describe how it works; they lay out the motion dynamics, or how the ball approaches the racket and rebounds back over the net. There are many possible rebounds and each case is different. In my programs you apply the simulations to play with the shots, one at a time, and build on the ideas as you go -- using the equations without using them, you might say. The studies are meant to bring you closer and closer inductively to what you should be doing at the court, to what is best for you, personally. They help you focus on that split-second contact with the ball. Many errors occur at this contact point.

The interaction between the racket and the ball is a complicated business, because it involves angles for both the ball approach and the motion of the racket to meet the ball. Plus it involves spin, both for the approach shot and your return -- i.e., the spin you want to put on it. It's a bit like politics, where you try to impose your own ideas on a bill proposed by another politician.

Your racket provides the only control you have over the motion of the ball, so you must hit the ball properly to get the results you want -- that's what makes the contact so critical. My programs force you to look at the nitty-gritty of the contact and make you aware of things you might not otherwise see. The goal is to detect hitting patterns for the different shots, something you can take to the courts, like slanting the racket face a bit more for this or that kind of shot, or hitting the ball a bit harder for a certain kind of drive. You can practice by selecting conditions of your racket for the moment of contact with the ball -- the values for Racket Orientation, Racket Direction of Motion, and Racket Speed, which define the control variables.

Racket speed is the speed of the racket when it hits the ball. Racket direction of motion is the direction of motion of the racket at the contact point. And racket orientation is the slant of the racket face relative to its motion direction at contact. At first you probably won't know what values to use -- it takes practice and guesswork. The basic idea is to learn to associate successful results with patterned racket configurations that generate the results. The patterns are what you transfer to the court.

Understanding how the ball behaves when it's hit not only improves your own shots, but also makes it easier to see what your opponent is doing, making your job easier. So it's doubly effective. For the same shot, your opponent has to contact the ball just as you would. It's like seeing your mirror image hitting the ball.

To see what's happening, of course, you have to understand what specific racket motions do, mirror image or not. You can look in the right places (even with sharp eyes) and still not SEE. You have to be able to READ what's happening, and for that you have to know the mechanics "language." You have to KNOW that one kind of racket motion leads to a crosscourt chip shot. That another signals a heavy topspin drive. That still another is a drop shot. And so on and so on. It's not an easy thing to do. It takes a lot of study and a lot of practice.

The general idea is this: When the ball hits the racket, it tends to rebound in the opposite direction from which it came, at about the same angle and speed, hopefully back toward your opponent, like bouncing a volleyball up off the floor. But -- and this is critical -- the angle, speed, and spin of the rebound depend on the "grip" and the "bounciness" of the strings of your racket, as well as on the speed you put on the racket and the orientation you give to the racket face. They are your conditions. It is these relationships you would be testing in the programs to personalize them; you specify them. It's the kind of detail you need to be more aware of. The more so as you sharpen your targets.

As part of the tennis context, many constraints affect the way the ball is to be hit. For example, the boundary lines and the shape and size of the net put limits on how hard and in which directions you can hit it from any given position. (Imagine hitting similar shots in a chemistry lab.) Gravity and air resistance, too, affect the shape of the trajectory and further limit how you can (or must) hit the ball to keep it from striking the net or flying out of bounds. There are also physiological limits, like the structure of your body, limbs, and joints; they both define and limit how you can hold the racket and swing at the ball. Properties of the racket and ball further determine what can happen. Your own speed, reach, disabilities, and strength are determinants, too, as are your perceptual and motor skills. And so are your opponent's characteristics. (Similar constraints apply to just about every other activity, in sports or otherwise.) This makes finding "best methods" very difficult.

In one display style the ball is shown in flat (orthographic) views of the court, from the top and from the side, in profile, the way home construction blueprints portray the (objective) structure of a house. In another style you see the ball in perspective, i.e., subjectively, as it would be seen and returned by you, assuming you’ve put yourself in the simulation to personalize the study. (The depiction becomes personalized when you select values that represent properties of the court, your racket, and your height.)

To conduct diagnostic trials with the programs, you first select conditions for the trials from given personalizing categories and then choose values for your racket properties (the racket control variables: speed, direction of motion, and orientation of your racket at the moment of contact with the ball).

For return shots in the Practice mode, the programs let you test various racket conditions for hitting the ball to targets of your own choosing. By testing many shots, and getting plenty of feedback on each one, you can build your sense of the tactics to apply and the correct way to hit the ball for different shots. You choose your technique according to the target and the type of shot you wish to hit -- like a lob or topspin drive). You need a lot of patience and a solid laboratory commitment, because you'll likely have to run hundreds of sample trials, particularly since tennis has a wide variety of shots, any one of which could, with considerable study and practice, become your favorite. In fact, you might prefer to specialize on a select sub-group of them, to suit your style of play.

In any case, you should begin to see the underlying dynamics concepts by building on the shot possibilities, one at a time (empirically rather than abstractly). In this way you can learn to orchestrate your swings more carefully and more productively -- after all, the swing you take depends on how you intend to contact the ball. And the way you contact it depends on what you're trying to do, on the kind of shot you're trying to make and where you want the ball to go. In this way, too, you can learn to hit the ball without having to be or become a rocket scientist.

I should say that my programs are very user-friendly, meaning that they're not difficult to use. (But this doesn't mean that the games themselves are necessarily easy to play. After all, they represent shots that can be made at the court in real games, and most of these shots are very difficult.) The programs were written with Microsoft’s Visual Basic, an object-oriented program development system, and operate in the Microsoft Windows environment. (In object-oriented systems, properties and methods are clustered around their objects, much as properties and actions associate with objects in the real world. This was not possible in earlier programming.) The simulations in these programs depict the motion of the tennis ball traversing the space of the court. Only the ball and the racket (in its orientation at the moment of contact with the ball) are displayed -- not the players, as I mentioned before.

As for the value of the games, let me say, first, they deal with the most critical and arguably a not commonly understood aspect of tennis, namely the interaction between racket and ball -- the only link between you and the ball.

Second, the experiments add to the value of normal tennis books because they supplement text and static visuals with motion, to develop in your mind a MODEL (a feeling or understanding) of the interaction.

Third, practice, and more practice, is essential for skills learning at the court. Whether you're alone or with a group, you learn by trial and error, drawing on knowledge of results.

Fourth, we learn skills by repeating trials over and over and by varying them. The programs each support these procedures. But you have to be careful not to use previous trials in repetition as a crutch. Try to make decisions on each shot independent of those of prior shots.

Fifth, and perhaps most important, the games sharpen your ideas and raise your level of knowledge of the game and the context in which it is played, giving you greater control over your on-court practice sessions and ultimately over your game.

There is no history of computer-assisted diagnostics for tennis, so we have no direct evidence of their true value. But there is good indirect evidence.

First, simulations derive their value from the amazing ability of the imagination to wrap itself around a symbol. We are great at make believe, even with meager settings, and we engage it with good effect.

Second, we've used simulation in one form or another for decades to understand complex environments and improve skills, and there is overwhelming evidence that they work, that understanding is in fact transferred to the skills arena. For example, aerospace professionals use simulation successfully to study man-machine systems.

Third, study is surely improved by realism of the simulation. Since the computer can provide increasingly accurate skills settings, it provides a solid basis for understanding. So it should help with tennis skills.

Finally, no skill can be performed successfully without an UNDERSTANDING -- an IDEA, PLAN of action, or mental MAP -- of what is to be done. The games provide a solid basis for developing correct racket/ball contact and for gaining more control in the real tennis setting.

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