update failures

I’ve been trying to update our website:

and I keep getting error messages and the updates fail and are not installed. Any idea how to fix this?

This is the message I get when I try to update wordpress:
Downloading update from http://wordpress.org/wordpress-3.5.1-partial-0.zip…
Download failed.: Destination directory for file streaming does not exist or is not writable.
Installation Failed

This is what I get when I try to update wordfence security.
The update process is starting. This process may take a while on some hosts, so please be patient.
Enabling Maintenance mode…
Updating Plugin Wordfence Security (1/1)
Downloading update from http://downloads.wordpress.org/plugin/wordfence.3.5.2.zip…
An error occurred while updating Wordfence Security: Download failed. Destination directory for file streaming does not exist or is not writable..
Disabling Maintenance mode…
All updates have been completed.

Any ideas?
Trishka317