Edit XML file with PHP form

I have an XML file that I want to be able to edit using a form.

student.xml

<students>
  <student>
    <name>Jane Doe</name>
    <email>email@email.com</email>
    <school>School Name</school>
    <coach>Coach Name</coach>
  </student>
</students>

Basically my form is set up like this:

<form action= method="post">
  <label>School: </label>
  <input name="school" type="text" id="school" />
  <br />
  <input type="submit" name="button" id="button" value="Submit" />
</form>

PHP code in head of form:

<?php
  $xmlDoc = simplexml_load_file('student.xml')

  if(isset($_POST['submit'])){

   $s_school=$_POST['school']; //gets data from form

   $file = "student.xml";

   $doc = new DOMDocument('1.0');
   $doc->preserveWhiteSpace = true;
   $doc->load($file);
   $doc->formatOutput = true;

    $school=$xmlDoc->getElementsByTagName("school");
    $school_value=$xmlDoc->createTextNode($s_school);
    $school->appendChild($school_value);

    $post = $_POST;
    unset($post['submit']);

   $doc->save($file);
  }

?>

How can I use a form to edit my XML file? I don't want to add a new child I just want to edit the existing nodes.