wp_enqueue_script does not recognize my js file?

my wp_enqueue_script does not seem to work, i can't understand why :

i have a child theme of twenty ten,
i wrote this in my functions.php file (in my theme) :

<?php
function my_scripts_method() {
    wp_enqueue_script(
        'patScript',
        get_stylesheet_directory_uri() . '/js/patScript.js',
        array('jquery')
    );
}
add_action('wp_enqueue_scripts', 'my_scripts_method');
?>

then in my header :

<script type="text/javascript" src="<?php get_stylesheet_directory_uri().'/js/patScript.js'; ?>"></script>

and the file is :

$(function () {
    alert("hello");
});

But alert does not work. The path is correct, when i echo get_stylesheet... it gives me the right path where my file is located. Would you have any idea?

Thanks a lot

EDIT : the console in Firefox tells me that :

$(function () {

"is not a function" : does it mean it does not recognize jquery? i added :

wp_enqueue_script("jquery");

above my previous enqueue script, but same thing...