Updating a cell when a new form is submitted

Contrary to what many believe, it is actually possible.

When you edit your form, at the very bottom there's a checkbox where you can allow editing of submitted response:

If you use a newer version of the Google Forms, you can click on the Gear icon on the top right and see the following page:

Now, what you need to do is manually submit score for each student. After every submission, you will be offered a link to edit the submission. You need to manually copy and save each link to allow future editing.

If you want to automatically record the edit response link, you can do so via Google Apps Script.

This can be done with a script. Enter the following in Script Editor, found under Tools. Change the 'Name' to whatever is the name of the form field that should be used.

function formSheet(e) {
  var sheetName = e.namedValues['Name'][0];
  var sheet = SpreadsheetApp.getActiveSpreadsheet().insertSheet(sheetName);
  sheet.getRange(1, 1, 1, e.values.length).setValues([e.values]);
}

Then set a trigger using "Resources -> current project's triggers" in the menu. It should be "from spreadsheet", "on form submit".

This function also copies the submitted value to the first row of the new sheet.

Note: there cannot be two sheets with the same name, so if some name is submitted more than once, sheet creation will fail.

References: Event object, Sheet class methods.