TypeError: ‘stepUp’ called on an object that does not implement interface HTMLInputElement

$.ajax is not expecting a DOMElement of type HTMLInputElement in the object you are passing to data. Try just giving it the value of the field instead:

var wordid = $('.wordId').val();
$.ajax({
    url: "assigner.php",
    type: "POST",
    data: { wordid: wordid, assign: assign}
}).done(function( e ) {
    /*alert( "word was saved" + e );*/
});