CREATE TABLE teachers (id SERIAL, first_name VARCHAR(60), last_name VARCHAR(60));

CREATE TABLE training_modules (id SERIAL, course VARCHAR(60), teachers_id INTEGER[]);

teacher_name  id_count
bob teacher   4
sally lady    3
jimbo jones   5

SELECT tid, count(*) as id_count FROM training_modules tm, unnest(tm.teachers_id) as tid GROUP BY tid;

SELECT t.id, concat(t.first_name, ' ', t.last_name) AS teacher_name, tm.id_count FROM (SELECT unnest(training_modules.teachers_id) AS id_count, count(*) FROM training_modules GROUP BY id_count) AS tm INNER JOIN teachers t ON tm.id_count = t.id;

id |     t_name      | tc
----+-----------------+----
  5 | Jimbo Jones     |  5
  4 | Frank McGee     |  4
  6 | Sara Sarason    |  6
  2 | Joshua Jesps    |  2
  1 | Larry Bucatin   |  1
  3 | Natalie Fatali  |  3

SELECT t.id, concat_ws(' ', t.first_name, t.last_name) AS teacher_name, tm.id_count
FROM  (
   SELECT unnest(tm.teachers_id) AS id, count(*) AS id_count
   FROM   training_modules tm
   GROUP  BY 1
   ) AS tm
JOIN   teachers t USING (id);