¿Cómo realizar un seguimiento de los cambios en los registros en SQL Server?

Una forma de hacerlo es usar ROW_NUMBER función con partición para detectar cuando el valor del Department cambios de columna.

Datos de muestra

DECLARE @T TABLE (ID int, Department nvarchar(100), dt date);
INSERT INTO @T (ID, Department, dt) VALUES
(1, 'English', 'Feb 3 2017'),
(1, 'English', 'Feb 4 2017'),
(1, 'Science', 'Mar 1 2017'),
(1, 'Science', 'Apr 2 2017'),
(1, 'Maths  ', 'Apr 7 2017'),
(2, 'Maths  ', 'Feb 1 2017'),
(2, 'Maths  ', 'Apr 7 2017'),
(3, 'Maths  ', 'Apr 3 2017'),
(4, 'Science', 'Feb 1 2017'),
(4, 'Maths  ', 'Apr 7 2017');

Consulta

WITH
CTE
AS
(
    SELECT
        ID
        ,Department
        ,dt
        ,ROW_NUMBER() OVER (PARTITION BY ID, Department ORDER BY dt DESC) AS rnPart
        ,ROW_NUMBER() OVER (PARTITION BY ID ORDER BY dt DESC) AS rnID
    FROM @T
)
SELECT
    ID
    ,Department
    ,dt
FROM CTE
WHERE
    rnPart = 1
    AND rnID <> 1
ORDER BY
    ID
    ,dt
;

Resultado

+----+------------+------------+
| ID | Department |     dt     |
+----+------------+------------+
|  1 | English    | 2017-02-04 |
|  1 | Science    | 2017-04-02 |
|  4 | Science    | 2017-02-01 |
+----+------------+------------+