Unable to send multiple values to another page using php session variable

class shoppingCart
{
    
    var $product = array();
    
    /*
     * public function add( int $pid, $int $qt )
     *      @integer $pid - The product ID
     *      @integer $qt - Quantity of our product
     * 
     *  Adds a product to the cart
    **/
    
    public function add($pid, $qt)
    {
        // To check if the item is already in cart
        // FALSE means it is not in cart yet (default)
        $in_cart = false;
        
        // Checking if we have a quantity set (can't have 0 amount of an item)
        if($qt < 1)
        {
            throw new exception("You're not adding any amount of the item.");
        }
        
        // Checking if we have a cart
        if(isset($_SESSION['shopping_cart']))
        {
            // Retrieving the contents of our cart (so we can add an item to it)
            $items = $this->showSaved();
            
            // Iterating through our carts and rebuilding it
            // Doing it this way in case they buy the same item again
            // in which case we just add quantity to the product id
            foreach($items as $p_id => $quantity)
            {
                // Checking if the item already exists in the cart
                if($pid == $p_id)
                {
                    // It exists... add quantity
                    $quantity = $qt + $quantity;
                    
                    // Make sure we tell the rest of the script that it is in cart
                    $in_cart = true;
                }
                
                // Product ID (key) and it's quantity (value)
                $product[$p_id] = $quantity;
            }
        }
        
        // Checking if it wasn't in cart... in which case we add it to cart
        if($in_cart == false)
        {
            // It wasn't in cart. Add it to cart.
            // Product ID (key) and it's quantity (value)
            $product[$pid] = $qt;
        }
        
        // Setting the product array
        $this->product = $product;
        
        // Saving the cart
        $this->save();
    }
    
    /*
     * public function remove( int $pid [, $int $qt ])
     *      @integer $pid - The product ID
     *      @integer $qt - Quantity of product to be removed
     * 
     *  Removes an item from the cart or a certain quantity of that item
     *  (if $qt is not 0)
    **/
    
    public function remove($pid, $qt = 0)
    {
        // Checking if we have a cart
        if(isset($_SESSION['shopping_cart']))
        {
            // Checking if the item requested to be removed is actually in the cart
            if(isset($_SESSION['shopping_cart'][$pid]))
            {
                // It is set... checking if we have a quantity set
                // (to subtract in case we aren't removing entirely)
                if($qt !== 0)
                {
                    // We are not removing the entire item but a certain quantity of it
                    // Checking if we have this (or more) of the product (so we don't
                    // come by a negative amount of a product
                    if($qt >= $_SESSION['shopping_cart'][$pid])
                    {
                        // We don't have that much of the item to remove
                        throw new exception("Trying to remove {$qt} of a product when you only have {$_SESSION['shopping_cart'][$pid]} of it!");
                        
                        // Returning false
                        return false;
                    }
                    
                    // Subtracting the quantity of the product
                    $_SESSION['shopping_cart'][$pid] = $_SESSION['shopping_cart'][$pid] - $qt;
                    
                    // Success... return true
                    return true;
                }
                else
                {
                    // We are to completely remove the product from the cart
                    unset($_SESSION['shopping_cart'][$pid]);
                    
                    // Success... return true
                    return true;
                }
            }
            else
            {
                // The item is not even in the cart... can't remove nothing!!!
                throw new exception("Item doesn't exist in the cart. Nothing to remove.");
            }
        }
        else
        {
            // The shopping cart doesn't exist yet. (Empty cart)
            throw new exception("The cart is empty. Nothing to remove.");
        }
    }
    
    function showSaved()
    {
        // Returning the shopping cart as an array
        return (array) $_SESSION['shopping_cart'];
    }
    
    function save()
    {
        // Saving the cart to the session
        $_SESSION['shopping_cart'] = $this->product;
    }
    
    function clearCart()
    {
        // Resetting the shopping cart session to an empty array
        $_SESSION['shopping_cart'] = array();
    }
}

session_start();
$cart = new shoppingCart();
?>

<p>The Shopping Cart:</p>
<p>To <strong>add</strong> to cart, simply select the product you want to add and type in the quantity and click 'Add'.</p>
<p>To <strong>clear</strong> the cart, simply click 'Clear Cart'.</p>
<p>To <strong>remove</strong> from cart, simply select the product and type in the quantity to remove (or leave blank to remove the item entirely) and click 'Remove from Cart'.</p>
<form action="<?=$_SERVER['PHP_SELF']?>" method="POST">
<p>Product: <select name="prods">
<option value="1">Pair or Socks</option>
<option value="2">Pair of Underwear</option>
<option value="3">The House on the Hill</option>
<option value="4">Laundry detergent</option>
<option value="5">Juice Boxes</option>
<option value="6">PHP Dev's Book</option>
</select><br />
Quantity: <input type="text" name="qt" size="10" /><br />
<input type="submit" name="submit" value="Add" /> 
<input type="submit" name="clear" value="Clear Cart" /> 
<input type="submit" name="remove" value="Remove from Cart" /><p></form>
<pre>
<pre>

// Trying to accomplish... so we can catch our errors here and handle them
try
{
    // Adding to cart
    if(isset($_POST['submit']))
    {
        // Adding to cart
        $cart->add($_POST['prods'], $_POST['qt']);
        
        // Displaying to cart
        print_r($cart->showSaved());
    }

    // Completely clearing entire cart
    if(isset($_POST['clear']))
    {
        // Clearing the cart
        $cart->clearCart();
        
        // Displaying the cart
        print_r($cart->showSaved());
    }

    // ( Decreasing amount of / removing ) the item
    if(isset($_POST['remove']))
    {
        // Making sure that we have a legitimate quantity to remove (0 to remove entirely)
        $qt = (integer) (isset($_POST['qt']) && !empty($_POST['qt'])) ? $_POST['qt'] : 0;
        
        // Removing from the cart
        $cart->remove($_POST['prods'], $qt);
        
        // Displaying the cart array
        print_r($cart->showSaved());
    }
}
catch( exception $e )
{
    echo "<pre>";>
    echo $e->getMessage() . ' In ' . $e->getFile() . ':' . $e->getLine() . '<br /><br />';
    echo "Stack Trace<br />";
    echo $e->getTraceAsString();
    echo "</pre>";
}
?>