Custom Options with Widget checkbox problem

I created a custom Flickr Widget for WordPress and successfully set up an options form for users to enter their Flickr information, but I cannot get the checkbox in the form to save whether or not it is checked. Any help would be greatly appreciated! Here are my widget(), form(), and update() functions:

function widget($args, $instance) {
    extract($args);

    $title = apply_filters('widget_title', $instance['title']);
    $displaynum = $instance['displaynum'];
    $flickrid = $instance['flickrname'];
    $num = 6;
    $feed = new SimplePie($instance['feed']);
    $feed->handle_content_type();
    $photostream = $instance['show_photostream'];

function update($new_instance, $old_instance) {
    $instance = $old_instance;

    $instance['title'] = strip_tags($new_instance['title'] );
    $instance['displaynum'] = strip_tags($new_instance['displaynum'] );
    $instance['feed'] = $new_instance['feed'];
    $instance['flickrname'] = $new_instance['flickrname'];
    $instance['show_photostream'] = (bool) $new_instance['show_photostream'];

    return $instance;
}

function form($instance) {
    $defaults = array (
        'title' => 'My Recent Flickr Uploads',
        'displaynum' => 6,
        'feed' => 'https://api.flickr.com/services/feeds/photos_public.gne?id=33927859@N06&lang=en-us&format=rss_200',
        'flickrname' => 'rastajellyfish',
        'show_photostream' => isset( $instance['show_photostream'] ) ? (bool) $instance['show_photostream'] : false
    );
    $instance = wp_parse_args( (array) $instance, $defaults); ?>

Any help would be greatly appreciated!!!