Handling events only when model properties/columns are updated - Laravel Observer

I am dealing here with two events of a model, updating and updated as you can see in the below code. My concern is that I want to do some task in the updated event only if the teacherId has been changed, So I figured to check the value at the updating event and use a class property to know if it had been changed or not but that flag always returns false assuming its defined value.

namespace App\Observers;

class SubjectObserver {

private $shouldUpdateThreads = false;

/**
 * Listen to the ThreadList created event.
 * This events Fire when ThreadList is handled
 * @param \App\Observers\App\ThreadList $threadList
 */
public function created(\subject $subject) {

}

/**
 * Listen to the ThreadList saved event.
 * @param \App\Observers\App\ThreadList $threadList
 */
public function saved(\subject $subject) {

}

/**
 * Handling subject updated event 
 * Used to update the threads and related models
 * @param \subject $subject
 */
public function updated(\subject $subject) {
    info('After Update Event ' . $this->shouldUpdateThreads);
    if ($this->shouldUpdateThreads) {
        info_plus($subject);
    }
    info('After Update Check');
}

/**
 * Handling subject being updated event
 * Used to check if the teachers data has changed or not
 * @param \subject $subject
 */
public function updating(\subject $_subject) {

    $subject = \subject::find($_subject->id);

    $this->shouldUpdateThreads = ($subject->teacherId != $_subject->teacherId) ? true : false;

    info(($subject->teacherId != $_subject->teacherId));

    info("Thread update ? " . $this->shouldUpdateThreads);
}

public function deleted(\subject $subject) {
    info("Subject deleted");
}

}

Is this even the right apporach ? if not what am I doing wrong ?