error on update_metadata

I have a custom metadata table for taxonomy.

CREATE TABLE IF NOT EXISTS taxonomymeta (
meta_id bigint(20) unsigned NOT NULL AUTO_INCREMENT,
taxonomy_id bigint(20) unsigned NOT NULL DEFAULT ‘0’,
meta_key varchar(255) DEFAULT NULL,
meta_value longtext,
PRIMARY KEY (meta_id),
KEY taxonomy_id (taxonomy_id),
KEY meta_key (meta_key)
) ENGINE=MyISAM DEFAULT CHARSET=utf8 AUTO_INCREMENT=1 ;

My PHP code is as follows. But the data doesn’t get inserted into the table. Why?

<?php
add_action('category_add_form_fields', 'category_metabox_add', 10, 1);
add_action('category_edit_form_fields', 'category_metabox_edit', 10, 1);
add_action('created_category', 'update_category_metadata', 10, 1);
add_action('edited_category', 'update_category_metadata', 10, 1);

function category_metabox_add($tag) {
	$output = '
	<div class="form-field">
		<label for="price">价格</label>
		<input name="price" type="number">
	</div>
	';
	echo $output;
}

function category_metabox_edit($tag) {
	$output = '
	<tr class="form-field">
		<th scope="row" valign="top">
			<label for="price">Pricing</label>
		</th>
		<td>
			<input name="price" type="number" value="' . get_metadata("taxonomy", $tag->term_id, "price", true) . '">
		</td>
	</tr>
	';
	echo $output;
}

function update_category_metadata($term_id) {
	update_metadata("taxonomy", $term_id, "pricing", $_POST['pricing']);
}
?>