In fact you don't even need a value for the "checked" attribute.
<input type="checkBox" checked/>
works just fine. If it isn't checked it will be sent as null so you can just check if the parameter is null. In my experience the value attribute for a checkBox--more often that not-- is superfluous. If other data is needed to be sent with the specific checkBox you bind a js function to the onClick of the checkBox and pass the HTML object to the function.