childtheme_filtered_options.php

<?php

add_action ('admin_init', 'childtheme_opt_init');
/**
 * Add childtheme settings to the thematic theme
 * 
 * This will add childtheme options to the thematic theme settings
 * in the database, and add to the existing theme options page in Thematic
 **/
function childtheme_opt_init() {
	
	/* Add default values for the childtheme options to thematic default options array */
	add_filter( 'thematic_theme_default_opt','childtheme_add_default_ops', 10, 1 );
	
	/* Add childtheme field validation to thematic validation */
	add_filter( 'thematic_theme_opt_validation','childtheme_add_validation', 20, 2 );

	/* Add a settings section for our childtheme */
	add_settings_section( 
		'childtheme_section',				// Slug of this section
		__( 'Childtheme title', 'child-textdomain' ), 	// Title of this section (optional, can be empty string)
		'childtheme_section_html', 			// Callback function for this section description
		'thematic_theme_opt' 				// Add to the thematic setting sections
	);

	/* Add settings fields to the settings section */
	add_settings_field( 
		'childtheme_textarea', 				// Slug of the option
		__( 'Write some text', 'child-textdomain' ), 	// Title of the option
		'childtheme_pagetitle_top_html', 		// Callback for rendering the option
		'thematic_theme_opt', 				// Add to the thematic setting sections 
		'childtheme_section' 				// Add to the section defined above
	);

}


/**
 * Add default values for the child theme options 
 * to the thematic options array
 * 
 * @param   array  $defaults  The thematic default options
 * @return  array  $defaults  The new defaults 
 **/
function childtheme_add_default_ops( $defaults ) {
	$defaults['childtheme_textarea'] = 'Bacon!';
	return $defaults;
}


/**
 * Add validation of the child options to thematic
 * 
 * Thematic takes care of the thematic form data, we only need 
 * to worry about the childtheme settings we have created.
 *
 * @param   array  $output  The prepared array from thematic
 * @param   array  $input   The raw data from the form
 * @return  array  $output  The fully sanitized array
 **/
function childtheme_add_validation( $output, $input ) {
	if ( isset( $input['childtheme_textarea'] ) ) {
		$output['childtheme_textarea'] = wp_kses_post( $input['childtheme_textarea'] ) ;	
	}
	return $output;
}


/**
 * Do the title of settings section: childtheme_section
 * 
 * Would be an optional description
 **/
function childtheme_section_html() {
	// sound of one hand clapping
}


/**
 * Render the textarea for childtheme option: childtheme_textarea
 */
function childtheme_textarea_html() {
 	/* grab options from the database */
	$options = thematic_get_wp_opt( 'thematic_theme_opt', thematic_default_opt() );

	/* grab the default options */
	$defaults = thematic_default_opt();

	/* use default option if none exist in database */
	$options['childtheme_textarea'] = ( isset( $options['childtheme_textarea'] ) ? $options['childtheme_textarea'] : $defaults['childtheme_textarea'] );

	/* print the html */
?>
	<textarea rows="5" cols="94" id="childtheme_textarea" name="thematic_theme_opt[childtheme_textarea]"><?php echo $options['childtheme_textarea']; ?></textarea>
<?php
}

Looks like it's a bug where callback is specified as childtheme_pagetitle_top_html. I have changed it into childtheme_textarea_html and my custom textarea appeared!

Thank you for example!