on click of the button send the value of the first row to jquery and make a ajax call to second page and do the required calculations when ever by response of second page replace the button with result look for examples.
http://api.jquery.com/jQuery.ajax/
put your button in a span like this
<span id="result">
<button id="my-button">Get Score</button></span>
then in your response handling jquery put this
$("#result").html(you calculation result jquery variable);