If you merely love a casual game of chess, then you likely don't need to learn algebraic notation, the method of recording the sequential chess moves of your entire game. If you find intellectual pleasure in chess, however, then you must learn algebraic notation, because I guarantee that you'll love what the knowledge of algebraic notation can open you up to. And if you have children who enjoy chess, then you must teach them algebraic notation, as well; not only is it a great precocious math skill, but otherwise they, too, are closed off from studying and mastering the game. The study of chess is full of just the sort of things that delight little children--tricky pawn tricks, secret strategies, patterns that carry you straight to checkmate if you only recognize them as they're unfolding, etc.
Here's a little of what you can do:
algebraic notation in action
Will's a reluctant writer, so don't tell her that this is writing practice! Finding a specific point on a grid is a crucial math skill, and translating the board's play to paper builds her three-dimensional visualization skills, which will be powerfully useful throughout her life, everywhere from performing high-level physics to nagivating her way on the highway one day.
I date-stamp her game notations just as I date-stamp all our schoolwork, and I have her write them in one spiral-bound steno notebook. When she's a more mature player, she'll be able to play these games back and alter the outcomes using better decision-making. Also--what a cute memento of a childhood!
replaying a game using notation
Of course, right now Will usually chooses to replay a game, using her notation, immediately upon its conclusion--this is called a Post-Mortem, and it's actually an important strategy in chess study, as you have the unique opportunity to study the board and recognize better/alternate moves while your reasoning for making the original moves is still fresh in your mind. In chess club or at a competition, your teacher or coach will go through the Post-Mortem with you, and it's also an opportunity for them to see where your skills stand--needless to say, this opportunity is lost if you don't know algebraic notation.
Will simply thinks it's fun to play both sides. Sneakily, the Post-Mortem also requires her to read and translate the algebraic notation back to the board, again strengthening her math, logic, and three-dimensional visualization skills.
re-playing famous games
Here, Willow and Matt are re-playing Bobby Fischer's The Immortal Game, with Matt (and later me, because Matt doesn't have the practice at algebraic notation that Will and I do and got overwhelmed, poor dear) calling out the moves using algebraic notation, and each player moving where the notation says to. This sounds dry, I know, but if you like chess it's actually really fun--the game moves fast, since you're not sitting and thinking up the moves yourself, and it's a GOOD game, because it's one that great players have played, with exciting tricks and tricky traps and fabulously bold machinations. Usually the game that you're reading through will be annotated, as well, to point out both the genius moves and the boneheaded ones, and it's fun to see.
When we do these re-plays, I always position Willow on the winning side, to give her practice at developing a checkmate. It's especially fun because, when a great game is playing out in front of you, even a little child can often see and exclaim over these genius or boneheaded moves--there was much outraged shouting during this particular match over Donald Byrne's dead-end strategy of simply moving his king back and forth in the endgame. It's an excellent model, because you can see how the center is developed and how the pawns get sacrificed and how truly excellent it is to fork your opponent's pieces. Several times, after Fischer did something amazing, we rewound the pieces and played it out again to better see how he set it up.
And yes, that's how we spent last Friday night. Do not judge.
studying chess problems
Will's not normally a kid who loves worksheets, but nevertheless these are fun for her, probably because of their novelty. Worksheets set up chess problems, from simple "What are the possible moves for the knight here?" to the more challenging "Find the mate in two moves" types. Since these worksheets abstract chess from the board-and-pieces manipulatives, they distill into some serious intellectual work--consider the difference between solving 19+24 with Base 10 manipulatives, and solving the same problem on paper! Many studious chess players can go one step further, and work these problems, and even entire chess games, entirely in their heads, the same way that you and I mentally solve 19+24.
Will's also a member of our community's scholastic chess club for children, which is nice because she can play with children her own age and has access to coaching that we otherwise wouldn't be able to afford. She's also a scholastic member of the USCF, which means that she receives a children's chess magazine quarterly and can earn rankings when she competes--a leg up in case she decides to get serious about competitive chess later in life. Sydney's not yet interested in chess, so it's divide and conquer so far: Matt attends chess club meetings with Will, and I accompany her to competition. I'm looking forward, though, to Sydney's inevitable decision to try chess out for herself--just think about how much more fun we'll have when this game is truly an activity that the entire family enjoys together!
Until then, it's something special that Will has with just her parents, which, of course, is also pretty great.